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Existence of a Minimizing Sequence of Trajectory-Control Pairs with Bounded Controls for Linear Control Problems

Alexander J. Zaslavski

Abstract


In this paper we study two large classes of finite-dimensional linear control systems which are identified with the corresponding complete metric spaces of integrands satisfying a growth condition. For most elements of the first space of integrands (in the sense of Baire category) we establish the existence of a minimizing sequence of trajectory-control pairs with bounded controls. We also establish that for most elements of the second space (in the sense of Baire category) the infimum on the full admissible class of trajectory-control pairs is equal to the infimum on a subclass of trajectory-control pairs whose controls are bounded by a certain constant.

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