Numerical Solution for a Controlled Nonconvex Sweeping Process

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dc.contributor.author Nour, Chadi
dc.contributor.author Zeidan, Vera
dc.date.accessioned 2021-11-23T14:23:30Z
dc.date.available 2021-11-23T14:23:30Z
dc.date.copyright 2021 en_US
dc.date.issued 2021-11-23
dc.identifier.issn 2475-1456 en_US
dc.identifier.uri http://hdl.handle.net/10725/13125
dc.description.abstract A numerical method and the theory leading to its success are developed in this letter to solve nonstandard optimal control problems involving sweeping processes, in which the sweeping set C is non-convex and coincides with the zero-sublevel set of a smooth function having a Lipschitz gradient, and the fixed initial state is allowed to be any point of C. This numerical method was introduced by Pinho et al. (2020) for a special form of our problem in which the function whose zero-sublevel set defines C is restricted to be twice differentiable and convex, and the initial state is confined in the interior of their convex set C. The remarkable feature of this method is manifested in approximating the sweeping process by a sequence of standard control systems invoking an innovative exponential penalty term in lieu of the normal cone, whose presence in the sweeping process renders most standard methods inapplicable. For a general setting, we prove that the optimal solution of the approximating standard optimal control problem converges uniformly to an optimal solution of the original problem (see Remark 3). This numerical method is shown to be efficient through an example in which C is not convex and the initial state is on its boundary. en_US
dc.language.iso en en_US
dc.title Numerical Solution for a Controlled Nonconvex Sweeping Process en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.idnumber 200502681 en_US
dc.author.department Computer Science And Mathematics en_US
dc.relation.journal IEEE Control Systems Letters en_US
dc.journal.volume 6 en_US
dc.article.pages 1190-1195 en_US
dc.keywords Standards en_US
dc.keywords Process control en_US
dc.keywords Optimal control en_US
dc.keywords Integrated circuit modeling en_US
dc.keywords Coercive force en_US
dc.keywords Upper bound en_US
dc.keywords Optimization en_US
dc.identifier.doi https://doi.org/10.1109/LCSYS.2021.3089977 en_US
dc.identifier.ctation Nour, C., & Zeidan, V. (2021). Numerical solution for a controlled nonconvex sweeping process. IEEE Control Systems Letters, 6, 1190-1195. en_US
dc.author.email chadi.nour@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url https://ieeexplore.ieee.org/abstract/document/9458952 en_US
dc.orcid.id https://orcid.org/0000-0003-4378-7459 en_US
dc.author.affiliation Lebanese American University en_US

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