Smooth and Heavy Solutions to Control Problems

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/2711 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/2711 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/2711 archive 351 disk0/00/00/26/56 2016-01-15 01:56:00 2021-08-27 17:12:22 2016-01-15 01:56:00 monograph show 2 Aubin J.-P. 7347 Smooth and Heavy Solutions to Control Problems pub iis_met prog_sds We introduce the concept of viability domain of a set-valued map, which we study and use for providing the existence of smooth solutions to differential inclusions. We then define and study the concept of heavy viable trajectories of a controlled system with feedbacks. Viable trajectories are trajectories satisfying at each instant given constraints on the state. The controls regulating viable trajectories evolve according a set-valued feedback map. Heavy viable trajectories are the ones which are associated to the controls in the feedback map whose velocity has at each instant the minimal norm. We construct the differential equation governing the evolution of the controls associated to heavy viable trajectories and we state their existence. 1985-07 published WP-85-044 WP-85-044 1134 public working_paper IIASA, Laxenburg, Austria 16 FALSE info:eu-repo/semantics/book