Linear-Quadratic Optimal Control Problems for Discrete Descriptor Systems

Abstract

The control in the feedback form and the optimal cost are obtained for four linear-quadratic control problems by discrete descriptor systems in a Hilbert space. Special solutions of the implicit operator Riccati equations used here act in all state space and in general case they are not non-negative definite unlike the operators in the subspace and the non-negative definite solutions, acting in all state space, as it was in other authors papers. The examples show that the considered operator Riccati equations have no non-negative definite solutions though the corresponding optimal control problems have the unique solutions.