A priori estimates for operational differential inclusions and necessary conditions for optimality
Frankowska, Halina (1990), A priori estimates for operational differential inclusions and necessary conditions for optimality, in Bensoussan, Alain; Lions, Jacques-Louis, Analysis and Optimization of Systes Proceedings of the 9th International Conference Antibes, June 12–15, 1990, Springer : Berlin, p. 519-528. http://dx.doi.org/10.1007/BFb0120074
TypeCommunication / Conférence
Conference title9th International Conference on Analysis and Optimization of Systes
Book titleAnalysis and Optimization of Systes Proceedings of the 9th International Conference Antibes, June 12–15, 1990
Book authorBensoussan, Alain; Lions, Jacques-Louis
Series titleLecture Notes in Control and Information Sciences
Number of pages994
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Abstract (EN)Derivation of necessary conditions for optimality in optimal control theory relies on variational calculus of control systems. We provide here such calculus for the semilinear differential inclusion 1 x′∈Ax+F(t,x),x(0)=x0 (1) where A is the infinitesimal generator of a C o-semigroup on a separable Banach space X and F: [0,T]×X∼ X is a set-valued map. Such inclusion encompass a number of control systems, including those with state dependent controls. We prove a relaxation theorem and investigate infinitesimal generators of reachable sets and variational inclusions. Results are applied to derive necessary conditions for optimality for some semilinear optimal control problems.
Subjects / Keywordscontrol problems; optimality; differential inclusions
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