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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3030 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3030 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3030 archive 351 disk0/00/00/29/83 2016-01-15 01:57:59 2021-08-27 17:13:00 2016-01-15 01:57:59 monograph show 2 Frankowska H. AL0659 Optimal Trajectories Associated to a Solution of Contingent Hamilton-Jacobi Equation pub iis_met prog_sds In this paper we study the existence of optimal trajectories associated with a generalized solution to Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable. But, in a way analogous to the use of distributions in PDE, we replace the usual derivatives with "contingent epiderivatives" and the Hamilton-Jacobi equation by two "contingent Hamilton-Jacobi inequalities". We show that the value function of an optimal control problem verifies these "contingent inequalities". Our approach allows the following three results: (1) The upper semicontinuous solutions to contingent inequalities are monotone along the trajectories of the dynamical system. (2) With every continuous solution V of the contingent inequalities, we can associate an optimal trajectory along which V is constant. (3) For such solutions, we can construct optimal trajectories through the corresponding optimal feedback. They are also "viscosity solutions" of a Hamilton-Jacobi equation. Finally we prove a relationship between super-differentials of solutions introduced in Crandall-Evans-Lions and the Pontryagin principle and discuss the link of viscosity solutions with Clarke's approach to the Hamilton-Jacobi equation. 1987-06 published WP-87-069 WP-87-069 10 1884 public working_paper IIASA, Laxenburg, Austria 29 FALSE info:eu-repo/semantics/book