Research on convergence influence based on generalized Young's convolution inequality for PD- and P-type ILC systems with integral intervention

Research on convergence influence based on generalized Young's convolution inequality for PD- and P-type ILC systems with integral intervention | 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 Article Research on convergence influence based on generalized Young's convolution inequality for PD- and P-type ILC systems with integral intervention Yan Liu, DingYun Hou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7620655/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the process of ILC convergence analysis, there is a phenomenon that the actual tracking error is far exceed the engineering tolerance in the initial number of iterations, even when the lambda- or sup-norm metric convergence analysis meets the requirements. In this paper, the convergence analysis method based on the Lebesgue-p norm is adopted. This method not only avoids the above situations, but also improves the analysis and verification of the influence of the integral compensation link on the tracking performance. Subsequently, the convergence characteristics of the first- and second-order PID-type iterative learning control (ILC) schemes for linear time-invariant (LTI) systems with no direct-through terms and the first- and second-order PI-type ILCs for LTI systems with direct-through terms are analyzed by using the generalized Young inequality of the convolution integral, and the tracking errors are evaluated using the Lebesgue-p norm. At the same time the impact of integrated embedding on convergence is once again demonstrated in the corresponding traditional PD- and P-type ILC rules, and the convergences are guaranteed for the second-order ILCs, while the monotonicity of convergence are guaranteed for the first-order ILCs. Finally, the efficacy and validity are confirmed by numerical simulations. Physical sciences/Engineering Physical sciences/Mathematics and computing Iteration learning control Integration Lebesgue-p norm Convergence Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7620655","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":524187182,"identity":"54b170a3-ef7c-491f-96e5-02b0be51d9cb","order_by":0,"name":"Yan 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