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

Aubin, J.-P. & Frankowska, H. (1989). Dynamic Regulation of Controlled Systems, Inertia Principle and Heavy Viable Solutions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-89-086

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Abstract

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.

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