Stability analysis of intelligent English translation system based on model predictive control algorithm

Stability analysis of intelligent English translation system based on model predictive control algorithm | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Stability analysis of intelligent English translation system based on model predictive control algorithm Fan YANG This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2769081/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 07 Jun, 2023 Read the published version in Soft Computing → Version 1 posted 4 You are reading this latest preprint version Abstract English translation systems often require manual input to convert speech into text document mode, which leads to poor translation results. In order to improve the intelligence of the intelligent English translation system, based on the machine learning algorithm, this paper constructs an intelligent English translation system based on the model predictive control algorithm, and combines the self-triggering MPC with the robust control to propose a corresponding control solution. That is, a robust self-triggering MPC method is proposed for linear systems with constraints. Moreover, this paper studies the stability and robustness of MPC in continuous time systems and describes the interfaces to be used in the system and the performance requirements of the system. In addition, this paper analyzes and describes the feasibility of the system development plan. Finally, this paper designs experiments to analyze the model performance from the system translation accuracy rate, system login security and system stability. The research results show that the model constructed in this paper has certain practical effects. Model prediction control algorithm English translation artificial intelligence machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The machine translation system uses machine learning methods to provide online translation services in multiple languages. The system was born in the 1940s and 50s of the last centuries and has been continuously developed with the emergence of computer technology. It plays a very important role in promoting the development of the modern information industry, and at the same time has a strong practical significance in promoting the development of the information society [ 1 ]. A machine translation system of good quality can make a more reasonable and scientific description of the two languages (the original language and the target language). The original language and the target language described here should be independent of each other, and there is no mutual influence relationship. Such translation systems are usually divided into three periods. In the first period, the original sentence substructure is represented by the code structure identifier, and in the second period, one language structure identifier is transformed into another target language structure identifier, and In the third period, the sentences to be output that constitute the target language of the translation. In the first period, the system not only needs to analyze the part of speech and usage in the original language, but also needs to analyze the sentence grammar in the original language, so that the language structure in the original sentence can be displayed with coded signs[ 2 ] Then, the system forms the grammar and structure contained in the target sentence in accordance with the relevant requirements of the target language grammar, and finally obtains the target sentence formed by the target language words. Therefore, grammar theory plays a very important role in the translation process of machine translation systems [ 3 ]. Enhancing communication and cooperation and learning more advanced science and technology in the world are inseparable from language exchanges. In today's highly developed information technology, science and technology need continuous development and innovation to bring great convenience and diversification to Chinese people in learning foreign languages [ 4 ]. In the process of learning foreign languages, electronic dictionaries bring great practicability, functionality, and convenience to people in learning English. The advantages of current electronic dictionaries are mainly manifested in more comprehensive functions, network updates, and intelligence. In order to improve the accuracy of electronic dictionary translation and improve the various shortcomings of manual translation, it is necessary to develop a new English translation system. There is a big difference between machine dictionaries and ordinary dictionaries. In the latter, entries are usually annotated in a language that naturally evolves with culture. Machine dictionaries cannot simply use this annotation method, and it is not very easy. Therefore, the information of the former requires a specific interpretation of each entry through related symbols, which is the so-called dictionary encoding [ 5 ]. 2. Related Work In the 21st century, the application of Chinese speech recognition technology has entered a stage of rapid development, and many companies and units have joined the ranks of dedicated research on speech [ 6 ]. Speech recognition technology has gradually matured after more than 50 years of development. This technology has gradually moved from theoretical knowledge research to the application market step by step, and its related applications and systems have slowly entered people's field of vision [ 7 ]. Foreign countries have also applied speech recognition technology in education. They use speech recognition technology to improve the pronunciation accuracy when learning a language [ 8 ]. In the past, most of the ways people learn a language can only be learned by imitation, and they cannot accurately compare whether there is a problem with their pronunciation. However, speech recognition technology can improve this phenomenon. "TalktoMe" is a language learning system developed by a company in the United States. After the user speaks to the system, the system will also display the waveform comparison chart of the user's pronunciation and the standard pronunciation [ 9 ]. The user can use the difference between the waveforms to find out which syllables of his syllables are inaccurate and correct them. my country also has certain applications of speech recognition technology. For example, HKUST Xunfei Company is a company that conducts related research on speech. They mainly study voice wake-up technology, voice recognition technology and interactive technology. At present, they are not only researching these technologies, but also using these technologies to carry out corresponding product development [ 10 ]. At the same time, a series of smart products have also been introduced, such as smart speakers, which have applied some voice-related technologies [ 11 ]. The speaker uses the voice recognition technology interface provided by iFLYTEK to process the language, so that the speaker can "understand" the user's language and make corresponding answers and responses to the user's requirements. These smart terminals mainly use speech recognition technology. Domestic immigration work has gradually become intelligent office. For example, Sichuan is the first province to have a simultaneous translation system for foreign-related police affairs. The system has an online translation APP mode [ 12 ]. The online translation APP is a smart software installed by the police in their mobile phones. Through this software, the police can apply for simultaneous interpretation services to the background at any time. The Android voice real-time translation system for immigration inspection studied in the literature [ 13 ] is also a software with voice translation function to facilitate immigration processing. The system tentatively conducted experiments on how to apply a "speech recognition" technology that has developed rapidly in recent years. Many units have developed speech recognition technology and provided an open platform to allow major enterprises and units to conduct research on the application of this technology. The system built in the literature [ 14 ] is an application for speech recognition in Chinese and English developed by the interface of speech recognition technology provided by iFLYTEK’s speech cloud open platform. The rapid development of science and technology has also catalyzed a series of new development technologies [ 15 ]. For example, some of the more widely used technologies currently include a series of shaping development technologies such as java, C#, and Python. Using these technologies, programmers can perform rapid development on page development, which has resulted in many relatively complete and easy-to-operate page development technologies. For example, Jquery, Extjs, and Easy-UI are some front-end development technologies that are popular and have a well-formed structure system. If these technologies are used for non-commercial use, they are free, and their source code is also open to the outside world, which not only makes it easy for developers to use but also easy to learn [ 16 ]. At the same time, a series of molding tools such as MySql, Sqlserver, Oracle, etc. can also be used to process the data. The use of these tools improves the efficiency of developers to manage data and facilitates developers to manipulate data. These aspects are the most basic technical support required for system development. In addition, in order to allow developers to quickly develop the system, the operation technology is gradually convenient and fast. For example, Hiberate and other technologies are based on object-oriented, and batch data operations can maximize resource utilization [ 17 ]. At present, the "speech recognition" technology is gradually developing and expanding, and the accuracy of the recognition of voices with a large vocabulary that is not a specific person can reach 98%. The accuracy of recognizing the voice of a specific person can be higher than that of not a specific person [ 18 ]. According to the current situation, speech recognition technology can be applied to ordinary products, and people's satisfaction with the application of speech recognition technology has reached more than 85%. This phenomenon shows that there are more products using this technology, and the market demand will gradually increase. Now, there are already many products that use voice recognition technology in the market [ 19 ]. 3. The Inherent Robustness Of Continuous-time Systems The meaning of robustness is that when the controlled system has uncertainties, such as interference, it can still maintain some of its performance. Moreover, stability and internal robustness refer to ignoring the uncertainty of the system. For the existing continuous-time system, we ignore the uncertainty of the system, and take the linear system as an example: $$\dot {x}=f\left( x \right)+g\left( x \right)u$$ 1 The cost function is: $$V\left( {x,u\left( \cdot \right)} \right)=\int\limits_{0}^{T} {l\left( {x\left( s \right),u\left( s \right)} \right)ds+F\left( {x\left( T \right)} \right)}$$ 2 When the \(x\left( s \right)={x^u}\left( {s;x,t} \right)\) terminal is bound, there is: $$\begin{gathered} x\left( T \right) \in {X_f}, \hfill \\ l\left( {x,u} \right)=\frac{1}{2}\left| u \right|_{R}^{2}+q\left( x \right) \hfill \\ \end{gathered}$$ 3 \(q\left( x \right)\) is a positive definite matrix. Solving the optimal controller is to solve: $$\hbox{min} \left\{ {l\left( {x,u} \right)+} \right\}$$ 4 According to the quadratic optimal control theory, the Hamiltonian function is constructed: $$H=\frac{1}{2}{u^T}Ru+q\left( x \right)+{\left[ {\nabla V_{T}^{o}\left( x \right)} \right]^T}\left( {f\left( x \right)+g\left( x \right)u} \right)$$ 5 The governing equation is: $$\frac{{\partial H}}{{\partial U}}=RU+g{\left( x \right)^T}\nabla V_{T}^{o}\left( x \right)=0$$ 6 $${\kappa _T}\left( x \right)= - {R^{ - 1}}g\left( x \right)\nabla V_{T}^{o}\left( x \right)$$ 7 If conditions C1-C4 are all met, then there are: $$\dot {V}_{T}^{o}\left( x \right)+\bar {q}\left( x \right)+\frac{1}{2}\left| {{\kappa _T}\left( x \right)} \right|_{R}^{2}=0$$ 8 When \(\bar {q}\left( x \right)=q\left( x \right)+\frac{{\partial {V^o}\left( {x,0} \right)}}{{\partial t}}\) , \({\kappa _T}\left( x \right)\) is the optimal solution of the optimal control problem in the infinite time domain. If the three elements are satisfied: terminal cost \(F\left( x \right)=0\) (no terminal cost function); terminal constraint condition \({X_f}=\left\{ 0 \right\}\) (terminal equation constraint); a local controller \({\kappa _f}\left( x \right)=0\) (the system remains unchanged when there is no control function). Obviously, conditions C1-C3 have been established. Through \({\kappa _f}\left( 0 \right)=0\) , \(f\left( {0,0} \right)=0\) , \(l\left( {0,0} \right)=0\) , we can get: $$f\left( {0,{\kappa _f}\left( 0 \right)=0,\dot {F}\left( {0,{\kappa _f}\left( 0 \right)+l\left( {0,{\kappa _f}\left( 0 \right)} \right)} \right)} \right)=0$$ 9 At this time, condition 4 is satisfied. Therefore, the closed-loop system is asymptotically stable in the attraction domain. The system is asymptotically stable in the attraction domain. The terminal constraint set is \(X={R^n}\) (no terminal constraint), and the terminal cost function is defined as: $$F:=\frac{1}{2}{x^T}{P_f}x$$ 10 The controller is \({\kappa _f}\left( x \right)={K_f}x\) (if the system has constraints, it is defined as \({\kappa _f}\left( x \right)=0\) ). Taking a linear system as an example, we assume: $$\begin{gathered} \dot {x}=Ax+Bu, \hfill \\ l\left( {x,u} \right)=\frac{1}{2}\left( {\left| x \right|_{Q}^{2}+\left| u \right|_{R}^{2}} \right),\left( {Q>0.R>0} \right) \hfill \\ \end{gathered}$$ 11 The system has no constraints, that is, \(X={R^n},U={R^m}\) , satisfies the conditions C1-C3. If \({P_f}>0\) and it satisfies the Lyapunov equation: $$A_{f}^{t}P{A_f}+{Q_f}=0$$ 12 We assume: $$\begin{gathered} {A_f}:=A+B{K_f} \hfill \\ {Q_f}=Q+K_{f}^{T}R{K_f} \hfill \\ \end{gathered}$$ 13 At this time, the condition C4: \(\left[ {\dot {F}+l} \right]\left( {x,{\kappa _f}\left( x \right)} \right) \leqslant 0\) is satisfied. Therefore, the closed-loop system is asymptotically stable in the domain of attraction \({R^n}\) . The terminal cost function \(F\left( x \right)=0\) is a costless function. The terminal constraint condition is \({X_f}\) . The role of the model predictive controller is to make the system transition from the \({X_f}\) state to the \({X_N}\) state, and the handling of such problems is similar to the constrained terminal equation. The difference is that \({X_N} \in {X_f}\) is used instead of \({X_f}=\left\{ 0 \right\}\) . Terminal cost function under terminal constraints Model predictive control including terminal cost \(F\left( x \right)\) and terminal constraint \({X_N} \in {X_f}\) is widely studied in the current research field. For linear systems, there is a cost function: $$F\left( x \right){\text{=}}V_{{uc}}^{o}\left( x \right)=\frac{1}{2}{x^T}{F_f}x=V_{\infty }^{o}\left( x \right)$$ 14 Under ideal circumstances, it can be approximately regarded as an optimal control problem in the infinite time domain, so that the advantages of infinite time domain control can be fully utilized. We assume: $$l\left( {x,u} \right)=\frac{1}{2}\left( {\left| x \right|_{Q}^{2}+\left| u \right|_{R}^{2}} \right),\left( {Q>0.R>0} \right)$$ 15 $$\begin{gathered} {A_f}:=A+B{K_f} \hfill \\ {Q_f}=Q+K_{f}^{T}R{K_f} \hfill \\ \end{gathered}$$ 16 The Lyapunov equation is satisfied: $$A_{f}^{T}P{A_f}+{Q_f}=0$$ 17 Therefore, the conditions C1-C4 are satisfied. The closed loop system is asymptotically stable. For nonlinear systems and closed-loop systems, the same method can be used for linearization. Theoretical basis of discrete time systems The difference equation form of the controlled system can be described as follows: $$x\left( {k+1} \right)=f\left( {x\left( k \right),u\left( k \right)} \right)$$ 18 $$y\left( k \right)=g\left( {x\left( k \right)} \right)$$ 19 4. System Construction Designing the system architecture is an indispensable part of the system development process. In this system, the client is multi-terminal, which needs to support the mobile terminal and the PC terminal. The mobile terminal is developed under the Android environment. The Android operating system can run not only on mobile phones, but also on tablets or other smart devices. The PC terminal is developed based on the B/S architecture, and the program is easy to maintain and update, and there is no need to consider system compatibility. The server side deploys the database and application server separately to improve the stability and robustness of the system. The speech recognition interface is an indispensable interface for software developers to use the engine to use the speech technology. The engine includes speech recognition and speech dictation. The interface is used to receive the voice input by the experiencer, and then recognize the voice, and finally transmit the recognition result to the system. The English machine translation feature based on semantic information preprocesses the syntax to form an English phrase tree. The specific steps of the technical route are: selecting word attributes, syntactic and semantic features; training the features to form decoded sentences; testing the decoded sentences and outputting the test results; aligning words and syntax; marking the part-of-speech features according to the alignment features, and the output becomes the node attributes of the English phrase tree. The technical route schedule is shown in Fig. 1 . The upper computer module is used as the carrier to remotely transmit the management information of the control system. Moreover, the information transmission uses a three-tier system model, namely the basic layer, the middle layer, and the application layer. The specific system structure information transmission model is shown in Fig. 3 . The segmented voice segments are reconnected again. After that, we will complete the playback function of the connected voice segment according to the received audio. If the speech library still needs speech, it indicates that the speech synthesis technology can find the language that it matches, which means that speech synthesis is running normally. If the language is not needed in the speech library, then it has no way to find the corresponding language. Therefore, speech synthesis cannot work normally, and at this time, the user needs to download the corresponding speech library. The running process of this module is shown in Fig. 4 . Moreover, these English word semantic interpretation information needs to occupy a large number of lines, which requires a larger interface to accommodate it. However, the mobile phone interface we usually use is limited, so we must use the scroll bar of word explanation in the system interface design process. When the user is not connected to the Internet, the English translation system itself under the information condition will regard the offline query as its own matching query. At this time, the offline query will perform word query through the software dictionary that has been installed in the English translation system under the information condition. The operation steps of offline query are shown in Fig. 5 . It can be seen from Fig. 3 that the specific process of offline query is: the user first enters the main interface of the English translation system under the information condition, and then opens the input box on the main interface, and enters the content that the user needs to query in the input box, such as words, phrases, and sentences. The network makes the required inquiry request and sends it, and the user can also select a different mobile network to send the inquiry request. The online query operation steps are shown in Fig. 6 . 5. Model Performance Analysis In the entire process of developing a software system, testers should test the system from the beginning of the software requirements analysis to the end of the software development. There are several reasons why the software needs to be tested for such a long time. First, the development engineer may cause the software system to be inconsistent with the requirements in the process of developing the system, that is, the phenomenon of more development functions and less development functions, so testers need to conduct detailed inspections and corrections. Second, the development engineer is not necessarily familiar with the business process of the entire system and may only understand part of the business process of the functional module he is responsible for. Therefore, there may be BUG in the development process. At this time, we need to find out the BUG by testing the software. After an excellent test case is executed, BUGs that have not been discovered before can be found. The following points need to be paid attention to when testing the system: 1. When writing test cases, it should be done from the following aspects: test points, input content, expected output results and actual output results. Before the test, there should be an expected output result. If the actual test result is inconsistent with the expected test result, it is likely that there is a BUG in the software system and should be modified. 2. When testing, the boundary value should be tested, such as the boundary value of the date interval, the boundary value of the amount, and the boundary value of the quantity. The boundary value that does not conform to common sense should be tested. 3. When testing, it is necessary not only to test the conventional input, but also to test the unconventional input, such as: fill in the space in the required items, fill in the symbol in the name, etc., so that the unconventional input needs to be verified. 4. In the process of testing, various methods can be used to test to ensure that as many bugs in the system as possible are found. 5. In the process of software testing, it is necessary to allow testers to test the software system as much as possible to avoid developers from testing their own code. 6. In the final test of the system, it is necessary to simulate the production environment as much as possible and test the system in the production environment to avoid software system problems caused by inconsistent operating environments. First of all, this paper conducts a system login test through 45 groups of login names, and each group has 100 accounts. The results are shown in Table 1 and Fig. 7 . Table 1 Statistical table of login function test results NO Login accuracy rate (%) NO Login accuracy rate (%) NO Login accuracy rate (%) 1 100 16 100 31 100 2 100 17 100 32 100 3 100 18 100 33 100 4 100 19 100 34 100 5 100 20 100 35 100 6 100 21 100 36 100 7 100 22 100 37 100 8 100 23 100 38 100 9 100 24 100 39 100 10 100 25 100 40 100 11 100 26 100 41 100 12 100 27 100 42 100 13 100 28 100 43 100 14 100 29 100 44 100 15 100 30 100 45 100 Next, this paper analyzes the translation effect of the translation system through 45 sets of data, and each set has 1,000 sentences that need to be translated. The statistical translation results are shown in Table 2 and Fig. 8 . Table 2 Statistical table of translation accuracy NO accuracy NO accuracy NO accuracy NO accuracy NO accuracy NO accuracy 1 97.3 16 97.7 31 98.2 9 98.7 24 98.1 39 98.6 2 97.1 17 98.0 32 97.8 10 97.4 25 98.7 40 98.5 3 98.3 18 98.0 33 97.5 11 96.8 26 98.8 41 96.6 4 98.6 19 97.6 34 98.4 12 97.5 27 98.8 42 98.7 5 98.5 20 96.5 35 97.1 13 97.7 28 98.8 43 97.6 6 98.8 21 97.9 36 97.7 14 97.3 29 99.0 44 96.9 7 97.0 22 98.2 37 99.0 15 98.3 30 98.9 45 98.4 8 98.6 23 96.9 38 97.8 -- -- -- -- -- -- 6. Conclusion In the two-way translation process between Chinese and English, a Chinese-English machine translation system can be quickly designed by using a combination of phrase translations based on the grammatical requirements of the two languages. The translation system has many advantages, such as strong practicability, flexible translation, and wide coverage. This paper analyzes the functional and non-functional requirements of the system, describes the detailed requirements of each functional module, and also describes the interfaces to be used in the system and the performance requirements of the system. Moreover, this paper analyzes and describes whether the development plan of the system is feasible. In addition, the system also plays a positive role in translation between Chinese and other languages. Declarations Compliance with Ethical Standards Conflict of interest The authors declare that they have no conflict of interests Ethical approval This article does not contain any studies with human participants performed by any of the authors. Data Availability Data will be made available on request. References G. V. Garje, and G. K. Kharate, “Survey of machine translation systems in India,” International Journal on Natural Language Computing, vol. 2, no. 4, pp. 47-65, 2013. Y. Graham, T. Baldwin, A. 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Cite Share Download PDF Status: Published Journal Publication published 07 Jun, 2023 Read the published version in Soft Computing → Version 1 posted Reviewers agreed at journal 11 Apr, 2023 Reviewers invited by journal 08 Apr, 2023 Editor assigned by journal 08 Apr, 2023 First submitted to journal 02 Apr, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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YANG","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIie3RsWrDMBCA4RMCdVGTVRlK8wgCgwkkkAfJYi/O4nbOYKigkGzx2scoBDIrHLiLi1cPHTSVDhk8dSqhUiCjHLp10A/CYN+HkAwQCv3XVnbdKGLsg8KQUjRXSW0X11SeyWjDMvk3Ihs+Fn3T8u0dv3TxAXyITMBqmu6Qg4RitvCS+jGb6OoTODhSL9M93moDVfagfETncdQxhDkpK0HWaMkgkUShnzTHWOoTAqeUCXLCdPfMpeglbR6Zw9oS5ojC9JVeIaP2GMNha4ndZgLVMnpBe8lJz1kGTR51+hvdjZEWiuldWSKarph5yVgDc3/hyQ3Qn8vrxDPuuldAu57voVAoFAL4Ba7cXKjHOJU4AAAAAElFTkSuQmCC","orcid":"","institution":"Fuzhou University of International Studies and Trade","correspondingAuthor":true,"prefix":"","firstName":"Fan","middleName":"","lastName":"YANG","suffix":""}],"badges":[],"createdAt":"2023-04-03 01:19:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2769081/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2769081/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00500-023-08653-4","type":"published","date":"2023-06-07T21:07:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":35545214,"identity":"a6894db0-fd78-4431-8409-4eb1d92937d7","added_by":"auto","created_at":"2023-04-10 17:50:23","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":80356,"visible":true,"origin":"","legend":"\u003cp\u003eSystem application architecture diagram\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/922745d74c42b37a62b28875.png"},{"id":35544494,"identity":"eef55f84-6f0c-47a0-8a99-0e0dd9ab0350","added_by":"auto","created_at":"2023-04-10 17:42:23","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":123489,"visible":true,"origin":"","legend":"\u003cp\u003eTechnical route of translation system\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/e6fa6a2b46f2a308a5e2bce4.png"},{"id":35544496,"identity":"503ca1d5-13af-43cf-bafc-658f24b1969b","added_by":"auto","created_at":"2023-04-10 17:42:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":136260,"visible":true,"origin":"","legend":"\u003cp\u003eThree-tier system structure information transmission model\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/2d762dd00ce10783c35a045b.png"},{"id":35544501,"identity":"3a857146-f182-4050-99da-31df9682fedd","added_by":"auto","created_at":"2023-04-10 17:42:23","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":82730,"visible":true,"origin":"","legend":"\u003cp\u003ePronunciation module workflow\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/8d1551f890fc6891a5c8e66c.png"},{"id":35545216,"identity":"c705d8cd-1cd9-44cf-b333-a2dea3045f37","added_by":"auto","created_at":"2023-04-10 17:50:23","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":64373,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of offline query steps\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/b47b26cfa61badbdccecb215.png"},{"id":35544499,"identity":"ab1e46d7-350b-440b-b418-8250947daabf","added_by":"auto","created_at":"2023-04-10 17:42:23","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":80487,"visible":true,"origin":"","legend":"\u003cp\u003eOnline query operation steps\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/0028edd9c42e09f2d99dc5ca.png"},{"id":35545998,"identity":"d1396150-847c-4c9f-ac5d-f3b2f9b3ab5a","added_by":"auto","created_at":"2023-04-10 17:58:23","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":16195,"visible":true,"origin":"","legend":"\u003cp\u003eStatistical diagram of login function test results\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/fbe7526eb7e6b3a3804ab746.png"},{"id":35544495,"identity":"e6fff3f1-be7b-4107-b315-22648b730fcb","added_by":"auto","created_at":"2023-04-10 17:42:23","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":37536,"visible":true,"origin":"","legend":"\u003cp\u003eStatistical diagram of translation accuracy\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/6a60acd34a28a86b08332206.png"},{"id":44731954,"identity":"51aac009-dd91-4ab7-95d6-04e89150df43","added_by":"auto","created_at":"2023-10-16 21:48:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":841265,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2769081/v1/9ec4b43a-0c46-414c-96e9-b9aca22dc64a.pdf"}],"financialInterests":"","formattedTitle":"Stability analysis of intelligent English translation system based on model predictive control algorithm","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe machine translation system uses machine learning methods to provide online translation services in multiple languages. The system was born in the 1940s and 50s of the last centuries and has been continuously developed with the emergence of computer technology. It plays a very important role in promoting the development of the modern information industry, and at the same time has a strong practical significance in promoting the development of the information society [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A machine translation system of good quality can make a more reasonable and scientific description of the two languages (the original language and the target language). The original language and the target language described here should be independent of each other, and there is no mutual influence relationship. Such translation systems are usually divided into three periods. In the first period, the original sentence substructure is represented by the code structure identifier, and in the second period, one language structure identifier is transformed into another target language structure identifier, and In the third period, the sentences to be output that constitute the target language of the translation. In the first period, the system not only needs to analyze the part of speech and usage in the original language, but also needs to analyze the sentence grammar in the original language, so that the language structure in the original sentence can be displayed with coded signs[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] Then, the system forms the grammar and structure contained in the target sentence in accordance with the relevant requirements of the target language grammar, and finally obtains the target sentence formed by the target language words. Therefore, grammar theory plays a very important role in the translation process of machine translation systems [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eEnhancing communication and cooperation and learning more advanced science and technology in the world are inseparable from language exchanges. In today's highly developed information technology, science and technology need continuous development and innovation to bring great convenience and diversification to Chinese people in learning foreign languages [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. In the process of learning foreign languages, electronic dictionaries bring great practicability, functionality, and convenience to people in learning English. The advantages of current electronic dictionaries are mainly manifested in more comprehensive functions, network updates, and intelligence. In order to improve the accuracy of electronic dictionary translation and improve the various shortcomings of manual translation, it is necessary to develop a new English translation system. There is a big difference between machine dictionaries and ordinary dictionaries. In the latter, entries are usually annotated in a language that naturally evolves with culture. Machine dictionaries cannot simply use this annotation method, and it is not very easy. Therefore, the information of the former requires a specific interpretation of each entry through related symbols, which is the so-called dictionary encoding [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Related Work","content":"\u003cp\u003eIn the 21st century, the application of Chinese speech recognition technology has entered a stage of rapid development, and many companies and units have joined the ranks of dedicated research on speech [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Speech recognition technology has gradually matured after more than 50 years of development. This technology has gradually moved from theoretical knowledge research to the application market step by step, and its related applications and systems have slowly entered people's field of vision [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Foreign countries have also applied speech recognition technology in education. They use speech recognition technology to improve the pronunciation accuracy when learning a language [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In the past, most of the ways people learn a language can only be learned by imitation, and they cannot accurately compare whether there is a problem with their pronunciation. However, speech recognition technology can improve this phenomenon. \"TalktoMe\" is a language learning system developed by a company in the United States. After the user speaks to the system, the system will also display the waveform comparison chart of the user's pronunciation and the standard pronunciation [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The user can use the difference between the waveforms to find out which syllables of his syllables are inaccurate and correct them. my country also has certain applications of speech recognition technology. For example, HKUST Xunfei Company is a company that conducts related research on speech. They mainly study voice wake-up technology, voice recognition technology and interactive technology. At present, they are not only researching these technologies, but also using these technologies to carry out corresponding product development [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. At the same time, a series of smart products have also been introduced, such as smart speakers, which have applied some voice-related technologies [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The speaker uses the voice recognition technology interface provided by iFLYTEK to process the language, so that the speaker can \"understand\" the user's language and make corresponding answers and responses to the user's requirements. These smart terminals mainly use speech recognition technology. Domestic immigration work has gradually become intelligent office. For example, Sichuan is the first province to have a simultaneous translation system for foreign-related police affairs. The system has an online translation APP mode [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The online translation APP is a smart software installed by the police in their mobile phones. Through this software, the police can apply for simultaneous interpretation services to the background at any time. The Android voice real-time translation system for immigration inspection studied in the literature [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] is also a software with voice translation function to facilitate immigration processing. The system tentatively conducted experiments on how to apply a \"speech recognition\" technology that has developed rapidly in recent years. Many units have developed speech recognition technology and provided an open platform to allow major enterprises and units to conduct research on the application of this technology. The system built in the literature [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] is an application for speech recognition in Chinese and English developed by the interface of speech recognition technology provided by iFLYTEK\u0026rsquo;s speech cloud open platform.\u003c/p\u003e \u003cp\u003eThe rapid development of science and technology has also catalyzed a series of new development technologies [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. For example, some of the more widely used technologies currently include a series of shaping development technologies such as java, C#, and Python. Using these technologies, programmers can perform rapid development on page development, which has resulted in many relatively complete and easy-to-operate page development technologies. For example, Jquery, Extjs, and Easy-UI are some front-end development technologies that are popular and have a well-formed structure system. If these technologies are used for non-commercial use, they are free, and their source code is also open to the outside world, which not only makes it easy for developers to use but also easy to learn [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. At the same time, a series of molding tools such as MySql, Sqlserver, Oracle, etc. can also be used to process the data. The use of these tools improves the efficiency of developers to manage data and facilitates developers to manipulate data. These aspects are the most basic technical support required for system development. In addition, in order to allow developers to quickly develop the system, the operation technology is gradually convenient and fast. For example, Hiberate and other technologies are based on object-oriented, and batch data operations can maximize resource utilization [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAt present, the \"speech recognition\" technology is gradually developing and expanding, and the accuracy of the recognition of voices with a large vocabulary that is not a specific person can reach 98%. The accuracy of recognizing the voice of a specific person can be higher than that of not a specific person [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. According to the current situation, speech recognition technology can be applied to ordinary products, and people's satisfaction with the application of speech recognition technology has reached more than 85%. This phenomenon shows that there are more products using this technology, and the market demand will gradually increase. Now, there are already many products that use voice recognition technology in the market [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e"},{"header":"3. The Inherent Robustness Of Continuous-time Systems","content":"\u003cp\u003eThe meaning of robustness is that when the controlled system has uncertainties, such as interference, it can still maintain some of its performance. Moreover, stability and internal robustness refer to ignoring the uncertainty of the system.\u003c/p\u003e \u003cp\u003eFor the existing continuous-time system, we ignore the uncertainty of the system, and take the linear system as an example:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\dot {x}=f\\left( x \\right)+g\\left( x \\right)u$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe cost function is:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$V\\left( {x,u\\left( \\cdot \\right)} \\right)=\\int\\limits_{0}^{T} {l\\left( {x\\left( s \\right),u\\left( s \\right)} \\right)ds+F\\left( {x\\left( T \\right)} \\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhen the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x\\left( s \\right)={x^u}\\left( {s;x,t} \\right)\\)\u003c/span\u003e\u003c/span\u003e terminal is bound, there is:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} x\\left( T \\right) \\in {X_f}, \\hfill \\\\ l\\left( {x,u} \\right)=\\frac{1}{2}\\left| u \\right|_{R}^{2}+q\\left( x \\right) \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(q\\left( x \\right)\\)\u003c/span\u003e \u003c/span\u003e is a positive definite matrix. Solving the optimal controller is to solve:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\hbox{min} \\left\\{ {l\\left( {x,u} \\right)+\u0026lt;\\nabla V_{T}^{o}\\left( x \\right),f\\left( x \\right)+g\\left( x \\right)u\u0026gt;} \\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAccording to the quadratic optimal control theory, the Hamiltonian function is constructed:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$H=\\frac{1}{2}{u^T}Ru+q\\left( x \\right)+{\\left[ {\\nabla V_{T}^{o}\\left( x \\right)} \\right]^T}\\left( {f\\left( x \\right)+g\\left( x \\right)u} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe governing equation is:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\frac{{\\partial H}}{{\\partial U}}=RU+g{\\left( x \\right)^T}\\nabla V_{T}^{o}\\left( x \\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${\\kappa _T}\\left( x \\right)= - {R^{ - 1}}g\\left( x \\right)\\nabla V_{T}^{o}\\left( x \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIf conditions C1-C4 are all met, then there are:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\dot {V}_{T}^{o}\\left( x \\right)+\\bar {q}\\left( x \\right)+\\frac{1}{2}\\left| {{\\kappa _T}\\left( x \\right)} \\right|_{R}^{2}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhen \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\bar {q}\\left( x \\right)=q\\left( x \\right)+\\frac{{\\partial {V^o}\\left( {x,0} \\right)}}{{\\partial t}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa _T}\\left( x \\right)\\)\u003c/span\u003e\u003c/span\u003e is the optimal solution of the optimal control problem in the infinite time domain.\u003c/p\u003e \u003cp\u003eIf the three elements are satisfied: terminal cost \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left( x \\right)=0\\)\u003c/span\u003e\u003c/span\u003e (no terminal cost function); terminal constraint condition \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_f}=\\left\\{ 0 \\right\\}\\)\u003c/span\u003e\u003c/span\u003e (terminal equation constraint); a local controller \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa _f}\\left( x \\right)=0\\)\u003c/span\u003e\u003c/span\u003e (the system remains unchanged when there is no control function). Obviously, conditions C1-C3 have been established. Through \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa _f}\\left( 0 \\right)=0\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f\\left( {0,0} \\right)=0\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(l\\left( {0,0} \\right)=0\\)\u003c/span\u003e\u003c/span\u003e, we can get:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$f\\left( {0,{\\kappa _f}\\left( 0 \\right)=0,\\dot {F}\\left( {0,{\\kappa _f}\\left( 0 \\right)+l\\left( {0,{\\kappa _f}\\left( 0 \\right)} \\right)} \\right)} \\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAt this time, condition 4 is satisfied. Therefore, the closed-loop system is asymptotically stable in the attraction domain. The system is asymptotically stable in the attraction domain.\u003c/p\u003e \u003cp\u003eThe terminal constraint set is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X={R^n}\\)\u003c/span\u003e\u003c/span\u003e (no terminal constraint), and the terminal cost function is defined as:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$F:=\\frac{1}{2}{x^T}{P_f}x$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe controller is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa _f}\\left( x \\right)={K_f}x\\)\u003c/span\u003e\u003c/span\u003e (if the system has constraints, it is defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\kappa _f}\\left( x \\right)=0\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTaking a linear system as an example, we assume:\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} \\dot {x}=Ax+Bu, \\hfill \\\\ l\\left( {x,u} \\right)=\\frac{1}{2}\\left( {\\left| x \\right|_{Q}^{2}+\\left| u \\right|_{R}^{2}} \\right),\\left( {Q\u0026gt;0.R\u0026gt;0} \\right) \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe system has no constraints, that is, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X={R^n},U={R^m}\\)\u003c/span\u003e\u003c/span\u003e, satisfies the conditions C1-C3. If \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P_f}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e and it satisfies the Lyapunov equation:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$A_{f}^{t}P{A_f}+{Q_f}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWe assume:\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} {A_f}:=A+B{K_f} \\hfill \\\\ {Q_f}=Q+K_{f}^{T}R{K_f} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAt this time, the condition C4: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[ {\\dot {F}+l} \\right]\\left( {x,{\\kappa _f}\\left( x \\right)} \\right) \\leqslant 0\\)\u003c/span\u003e\u003c/span\u003e is satisfied. Therefore, the closed-loop system is asymptotically stable in the domain of attraction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R^n}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe terminal cost function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left( x \\right)=0\\)\u003c/span\u003e\u003c/span\u003e is a costless function. The terminal constraint condition is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_f}\\)\u003c/span\u003e\u003c/span\u003e. The role of the model predictive controller is to make the system transition from the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_f}\\)\u003c/span\u003e\u003c/span\u003e state to the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_N}\\)\u003c/span\u003e\u003c/span\u003e state, and the handling of such problems is similar to the constrained terminal equation. The difference is that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_N} \\in {X_f}\\)\u003c/span\u003e\u003c/span\u003e is used instead of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_f}=\\left\\{ 0 \\right\\}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTerminal cost function under terminal constraints\u003c/p\u003e \u003cp\u003eModel predictive control including terminal cost \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(F\\left( x \\right)\\)\u003c/span\u003e\u003c/span\u003e and terminal constraint \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({X_N} \\in {X_f}\\)\u003c/span\u003e\u003c/span\u003e is widely studied in the current research field. For linear systems, there is a cost function:\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$F\\left( x \\right){\\text{=}}V_{{uc}}^{o}\\left( x \\right)=\\frac{1}{2}{x^T}{F_f}x=V_{\\infty }^{o}\\left( x \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eUnder ideal circumstances, it can be approximately regarded as an optimal control problem in the infinite time domain, so that the advantages of infinite time domain control can be fully utilized.\u003c/p\u003e \u003cp\u003eWe assume:\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$$l\\left( {x,u} \\right)=\\frac{1}{2}\\left( {\\left| x \\right|_{Q}^{2}+\\left| u \\right|_{R}^{2}} \\right),\\left( {Q\u0026gt;0.R\u0026gt;0} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} {A_f}:=A+B{K_f} \\hfill \\\\ {Q_f}=Q+K_{f}^{T}R{K_f} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe Lyapunov equation is satisfied:\u003cdiv id=\"Equ17\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ17\" name=\"EquationSource\"\u003e\n$$A_{f}^{T}P{A_f}+{Q_f}=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e17\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTherefore, the conditions C1-C4 are satisfied. The closed loop system is asymptotically stable. For nonlinear systems and closed-loop systems, the same method can be used for linearization.\u003c/p\u003e \u003cp\u003eTheoretical basis of discrete time systems\u003c/p\u003e \u003cp\u003eThe difference equation form of the controlled system can be described as follows:\u003cdiv id=\"Equ18\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ18\" name=\"EquationSource\"\u003e\n$$x\\left( {k+1} \\right)=f\\left( {x\\left( k \\right),u\\left( k \\right)} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e18\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ19\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ19\" name=\"EquationSource\"\u003e\n$$y\\left( k \\right)=g\\left( {x\\left( k \\right)} \\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e19\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"4. System Construction","content":"\u003cp\u003eDesigning the system architecture is an indispensable part of the system development process. In this system, the client is multi-terminal, which needs to support the mobile terminal and the PC terminal. The mobile terminal is developed under the Android environment. The Android operating system can run not only on mobile phones, but also on tablets or other smart devices. The PC terminal is developed based on the B/S architecture, and the program is easy to maintain and update, and there is no need to consider system compatibility. The server side deploys the database and application server separately to improve the stability and robustness of the system.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe speech recognition interface is an indispensable interface for software developers to use the engine to use the speech technology. The engine includes speech recognition and speech dictation. The interface is used to receive the voice input by the experiencer, and then recognize the voice, and finally transmit the recognition result to the system.\u003c/p\u003e \u003cp\u003eThe English machine translation feature based on semantic information preprocesses the syntax to form an English phrase tree. The specific steps of the technical route are: selecting word attributes, syntactic and semantic features; training the features to form decoded sentences; testing the decoded sentences and outputting the test results; aligning words and syntax; marking the part-of-speech features according to the alignment features, and the output becomes the node attributes of the English phrase tree. The technical route schedule is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe upper computer module is used as the carrier to remotely transmit the management information of the control system. Moreover, the information transmission uses a three-tier system model, namely the basic layer, the middle layer, and the application layer. The specific system structure information transmission model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe segmented voice segments are reconnected again. After that, we will complete the playback function of the connected voice segment according to the received audio. If the speech library still needs speech, it indicates that the speech synthesis technology can find the language that it matches, which means that speech synthesis is running normally. If the language is not needed in the speech library, then it has no way to find the corresponding language. Therefore, speech synthesis cannot work normally, and at this time, the user needs to download the corresponding speech library. The running process of this module is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMoreover, these English word semantic interpretation information needs to occupy a large number of lines, which requires a larger interface to accommodate it. However, the mobile phone interface we usually use is limited, so we must use the scroll bar of word explanation in the system interface design process. When the user is not connected to the Internet, the English translation system itself under the information condition will regard the offline query as its own matching query. At this time, the offline query will perform word query through the software dictionary that has been installed in the English translation system under the information condition. The operation steps of offline query are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e that the specific process of offline query is: the user first enters the main interface of the English translation system under the information condition, and then opens the input box on the main interface, and enters the content that the user needs to query in the input box, such as words, phrases, and sentences. The network makes the required inquiry request and sends it, and the user can also select a different mobile network to send the inquiry request. The online query operation steps are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Model Performance Analysis","content":"\u003cp\u003eIn the entire process of developing a software system, testers should test the system from the beginning of the software requirements analysis to the end of the software development. There are several reasons why the software needs to be tested for such a long time. First, the development engineer may cause the software system to be inconsistent with the requirements in the process of developing the system, that is, the phenomenon of more development functions and less development functions, so testers need to conduct detailed inspections and corrections. Second, the development engineer is not necessarily familiar with the business process of the entire system and may only understand part of the business process of the functional module he is responsible for. Therefore, there may be BUG in the development process. At this time, we need to find out the BUG by testing the software.\u003c/p\u003e \u003cp\u003eAfter an excellent test case is executed, BUGs that have not been discovered before can be found. The following points need to be paid attention to when testing the system: 1. When writing test cases, it should be done from the following aspects: test points, input content, expected output results and actual output results. Before the test, there should be an expected output result. If the actual test result is inconsistent with the expected test result, it is likely that there is a BUG in the software system and should be modified. 2. When testing, the boundary value should be tested, such as the boundary value of the date interval, the boundary value of the amount, and the boundary value of the quantity. The boundary value that does not conform to common sense should be tested. 3. When testing, it is necessary not only to test the conventional input, but also to test the unconventional input, such as: fill in the space in the required items, fill in the symbol in the name, etc., so that the unconventional input needs to be verified. 4. In the process of testing, various methods can be used to test to ensure that as many bugs in the system as possible are found. 5. In the process of software testing, it is necessary to allow testers to test the software system as much as possible to avoid developers from testing their own code. 6. In the final test of the system, it is necessary to simulate the production environment as much as possible and test the system in the production environment to avoid software system problems caused by inconsistent operating environments.\u003c/p\u003e \u003cp\u003eFirst of all, this paper conducts a system login test through 45 groups of login names, and each group has 100 accounts. The results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical table of login function test results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLogin accuracy rate (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLogin accuracy rate (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eLogin accuracy rate (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, this paper analyzes the translation effect of the translation system through 45 sets of data, and each set has 1,000 sentences that need to be translated. The statistical translation results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStatistical table of translation accuracy\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eaccuracy\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e97.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e97.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e98.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e98.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e98.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e98.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e97.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e98.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e97.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e98.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e98.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e98.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e96.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e98.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e96.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e97.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e98.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e97.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e98.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e98.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e98.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e96.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e97.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e98.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e 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align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e97.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eIn the two-way translation process between Chinese and English, a Chinese-English machine translation system can be quickly designed by using a combination of phrase translations based on the grammatical requirements of the two languages. The translation system has many advantages, such as strong practicability, flexible translation, and wide coverage. This paper analyzes the functional and non-functional requirements of the system, describes the detailed requirements of each functional module, and also describes the interfaces to be used in the system and the performance requirements of the system. Moreover, this paper analyzes and describes whether the development plan of the system is feasible. In addition, the system also plays a positive role in translation between Chinese and other languages.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompliance with Ethical Standards\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no conflict of interests\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis article does not contain any studies with human participants performed by any of the authors.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eG. V. Garje, and G. K. Kharate, \u0026ldquo;Survey of machine translation systems in India,\u0026rdquo; International Journal on Natural Language Computing, vol. 2, no. 4, pp. 47-65, 2013. \u003c/li\u003e\n\u003cli\u003eY. Graham, T. Baldwin, A. Moffat, et al., \u0026ldquo;Can machine translation systems be evaluated by the crowd alone,\u0026rdquo; Natural Language Engineering, vol. 23, no. 1, pp. 3-30, 2017. \u003c/li\u003e\n\u003cli\u003eO. Caglayan, M. Garc\u0026iacute;a-Mart\u0026iacute;nez, A. Bardet, et al., \u0026ldquo;Nmtpy: A flexible toolkit for advanced neural machine translation systems,\u0026rdquo; The Prague Bulletin of Mathematical Linguistics, vol. 109, no. 1, p. 15, 2017. \u003c/li\u003e\n\u003cli\u003eH. Small, K. W. Boyack, and R. Klavans, \u0026ldquo;Identifying emerging topics in science and technology,\u0026rdquo; Research policy, vol. 43, no. 8, pp. 1450-1467, 2014. \u003c/li\u003e\n\u003cli\u003eQ. Jiang, W. Gao, S. 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Walker, et al., \u0026ldquo;Assessing children\u0026rsquo;s home language environments using automatic speech recognition technology,\u0026rdquo; Communication Disorders Quarterly, vol. 32, no. 2, pp. 83-92, 2011. \u003c/li\u003e\n\u003cli\u003eH. H. J. Chen, \u0026ldquo;Developing and evaluating an oral skills training website supported by automatic speech recognition technology,\u0026rdquo; ReCALL, vol. 23, no. 1, pp. 59-78, 2011. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Model prediction, control algorithm, English translation, artificial intelligence, machine learning","lastPublishedDoi":"10.21203/rs.3.rs-2769081/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2769081/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEnglish translation systems often require manual input to convert speech into text document mode, which leads to poor translation results. In order to improve the intelligence of the intelligent English translation system, based on the machine learning algorithm, this paper constructs an intelligent English translation system based on the model predictive control algorithm, and combines the self-triggering MPC with the robust control to propose a corresponding control solution. That is, a robust self-triggering MPC method is proposed for linear systems with constraints. Moreover, this paper studies the stability and robustness of MPC in continuous time systems and describes the interfaces to be used in the system and the performance requirements of the system. In addition, this paper analyzes and describes the feasibility of the system development plan. Finally, this paper designs experiments to analyze the model performance from the system translation accuracy rate, system login security and system stability. The research results show that the model constructed in this paper has certain practical effects.\u003c/p\u003e","manuscriptTitle":"Stability analysis of intelligent English translation system based on model predictive control algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-04-10 17:42:18","doi":"10.21203/rs.3.rs-2769081/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2023-04-11T04:36:04+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-04-08T10:59:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-04-08T10:54:25+00:00","index":"","fulltext":""},{"type":"submitted","content":"Soft Computing","date":"2023-04-02T21:19:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"soft-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"soco","sideBox":"Learn more about [Soft Computing](https://www.springer.com/journal/500)","snPcode":"500","submissionUrl":"https://submission.nature.com/new-submission/500/3","title":"Soft Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8885b779-80cb-4cf7-b68d-ec00469f9d15","owner":[],"postedDate":"April 10th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T21:32:08+00:00","versionOfRecord":{"articleIdentity":"rs-2769081","link":"https://doi.org/10.1007/s00500-023-08653-4","journal":{"identity":"soft-computing","isVorOnly":false,"title":"Soft Computing"},"publishedOn":"2023-06-07 21:07:55","publishedOnDateReadable":"June 7th, 2023"},"versionCreatedAt":"2023-04-10 17:42:18","video":"","vorDoi":"10.1007/s00500-023-08653-4","vorDoiUrl":"https://doi.org/10.1007/s00500-023-08653-4","workflowStages":[]},"version":"v1","identity":"rs-2769081","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2769081","identity":"rs-2769081","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}