Nonlinear optimal control for supply chain networks under time-delays

Nonlinear optimal control for supply chain networks under time-delays | 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 Nonlinear optimal control for supply chain networks under time-delays Gerasimos Rigatos, Pierluigi Siani, Mohammed Al-Numay, Masoud Abbaszadeh, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4145311/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 The article proposes a nonlinear optimal control method for treating the control and stabilization problem of supply chain networks and inventories under time-delays. The state-space model of the supply chain network is considered to have as state variables the customer's demand and the inventories of the manufacturer, of the retailers and of the distributors. The control inputs of the model are the manufacturer's production and the retailer's ordering quantities. The model is subject to time-delays. It is proven that the dynamic model of the supply chain is differentially flat. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the supply chain a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The method achieves fast and accurate tracking of the targeted setpoints by the state variables of the supply chain system under moderate variations of the control inputs. Financial Mathematics Systems Engineering Industrial Engineering supply chains inventory industrial production differential flatness properties nonlinear Hinfinity control Taylor series expansion Jacobian matrices Riccati equation global stability Full Text Additional Declarations The authors declare no competing interests. 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. 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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-4145311","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":282391224,"identity":"5a50ec22-001a-4bd0-a1ad-b8cdbdc66a6f","order_by":0,"name":"Gerasimos 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The state-space model of the supply chain network is considered to have as state variables the customer's demand and the inventories of the manufacturer, of the retailers and of the distributors. The control inputs of the model are the manufacturer's production and the retailer's ordering quantities. The model is subject to time-delays. It is proven that the dynamic model of the supply chain is differentially flat. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the supply chain a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. 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