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IMA Journal of Mathematical Control and Information 1989 6(1):97-117; doi:10.1093/imamci/6.1.97
© 1989 by Institute of Mathematics and its Applications
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A Feedback for an Infinite-Dimensional Linear-Quadratic Control Problem with a Fixed Terminal State

ZBIGNIEW EMIRSAJLOW

Institute of Control Engineering, Technical University of Szczecin Gen. Sikorskiego 37, 70-313 Szczecin, Poland

This paper deals with the linear–quadratic control problem (LQCP) with a fixed terminal state, for infinite-dimensional systems defined by evolution operators. It is shown that, under a suitable assumption involving the reachability set, the optimal control exists and is unique. To solve the problem effectively, its connection with the minimum-energy control for the perturbed system is exploited. Both open-loop and feedback descriptions of the optimal control are given. Important relationships between the controllability of the system and properties of the optimal control are described, and a feedback approximation to the optimal control is given.


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