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IMA Journal of Mathematical Control and Information 1991 8(2):179-208; doi:10.1093/imamci/8.2.179
© 1991 by Institute of Mathematics and its Applications
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A Unified Approach to Optimal Feedback in the Infinite-Dimensional Linear–Quadratic Control Problem with an Inequality Constraint on the Trajectory or Terminal State

ZBIGNIEW EMIRSAJLOW

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

This paper develops a unified approach to optimal feedback control in the infinite-dimensional linear-quadratic control problem with an inequality constraint on the trajectory or terminal state. A general abstract Hilbert-space framework for the problem is provided, and then the results are specified to concrete optimal problems for a linear infinite-dimensional system which allows unboundedness in the input and output operators. In all cases, the same technique is used in order to obtain the optimal control in feedback form; in some cases, the differential Riccati equation is derived for the optimal cost operator.


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