Dynamic Regulation of Controlled Systems, Inertia Principle and Heavy Viable Solutions

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3299 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3299 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3299 archive 351 disk0/00/00/32/58 2016-01-15 01:59:33 2021-08-27 17:13:32 2016-01-15 01:59:33 monograph show 2 Aubin J.-P. 7347 Frankowska H. AL0659 Dynamic Regulation of Controlled Systems, Inertia Principle and Heavy Viable Solutions pub iis_met prog_sds Existence of viable (controlled invariant) solutions of a control problem regulated by absolutely continuous open loop controls is proved by using the concept of viability kernels of closed subsets (largest closed controlled invariant subsets). This is needed to provide dynamical feedbacks, i.e., differential equations governing the evolution of viable controls. Among such differential equations, the differential equation providing heavy solutions (in the sense of heavy trends), i.e., governing the evolution of controls with minimal velocity is singled out. Among possible applications, these results are used to define global contingent subsets of the contingent cones which allow to prove the convergence of a modified version of the structure algorithm to a closed viability domain of any closed subset. 1989-11 published WP-89-086 WP-89-086 10 1134 1884 public working_paper IIASA, Laxenburg, Austria 33 FALSE info:eu-repo/semantics/book