Value function and optimality conditions for semilinear control problems
Cannarsa, Piermarco; Frankowska, Halina (1992), Value function and optimality conditions for semilinear control problems, Applied Mathematics and Optimization, 26, 2, p. 139-169. http://dx;doi.org/10.1007/BF01189028
TypeArticle accepté pour publication ou publié
Journal nameApplied Mathematics and Optimization
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Abstract (EN)This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx′(t)=Ax(t) + f(t, x(t), u(t)), u(t) ε U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.
Subjects / KeywordsOptimal control; Distributed parameter systems; Dynamic programming; Optimality conditions; Strongly continuous semigroups; Nonsmooth analysis
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