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Feedback control for discrete descriptor systems

Kurina G.A.

Systems Science

2002

Vol. 28, nr 2

29-40

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 nonnegative definite, unlike the operators in the subspace and the nonnegative definite solutions. The examples show that the operator Riccati equations considered have no nonnegative definite solutions though the corresponding optimal control problems have the unique solutions.

Feedback control for time-varying descriptor systems.

Kurina GA.

Systems Science

2000

Vol. 26, nr 3

47-59

The control in the feedback form and the optimal cost are obtained for different linear-quadratic optimal control problems by time-varying descriptor systems in Hilbert space. For that purpose the operator which is the solution of the operator Riccati equation is used. This operator acts in all state space, unlike the operator in the subspace in the case of a singular operator before the derivative, which determines an optimal control with the help of part of the state variable. In contrast to previous works of other authors the regularity of the pencil of operators from the state equation is not required. At the end of the paper the feedback control for linear-quadratic optimal control problems with the degenerate Legendre condition is considered.