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Value function and optimality conditions for semilinear control problems (1992)

Cannarsa, Piermarco ; Frankowska, Halina

Springer

Applied mathematics & optimization 26 (1992), S. 139-169

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ISSN: 1432-0606

Keywords: Optimal control ; Distributed parameter systems ; Dynamic programming ; Optimality conditions ; Strongly continuous semigroups ; Nonsmooth analysis ; 49A22 ; 49B22 ; 49A52 ; 47D05

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01189028

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