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Infinite horizon optimal control problems in the light of convex analysis in Hilbert spaces. (English) Zbl 1311.49084
Summary: In this paper, a class of linear-quadratic infinite horizon optimal control problems is considered. Problems of this type are not only of practical interest. They also appear as an approximation of nonlinear problems. The key idea is to introduce weighted Sobolev spaces as state space and weighted Lebesgue spaces as control spaces into the problem setting. We investigate the question of existence of an optimal solution in these spaces and establish a Pontryagin-type maximum principle as a necessary optimality condition including transversality conditions.

MSC:
49N10 Linear-quadratic optimal control problems
49K15 Optimality conditions for problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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