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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

Type
Article accepté pour publication ou publié
Date
1992
Journal name
Applied Mathematics and Optimization
Volume
26
Number
2
Publisher
Springer
Pages
139-169
Publication identifier
Metadata
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Author(s)
Cannarsa, Piermarco
Frankowska, Halina
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 / Keywords
Optimal control; Distributed parameter systems; Dynamic programming; Optimality conditions; Strongly continuous semigroups; Nonsmooth analysis