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This paper studies a linear-quadratic control problem for discrete-time switched systems with subsystems perturbed by uncertainty. Analytical expressions are derived for both the optimal objective function and the optimal switching strategy. A two-step pruning scheme is developed to efficiently solve such problem. The performance of this method is shown by two examples.

Uncertainty theory is a branch of axiomatic mathematics that deals with human uncertainty. Based on uncertainty theory, this paper discusses linear quadratic (LQ) optimal control with process state inequality constraints for discrete-time uncertain systems, where the weighting matrices in the cost function are assumed to be indefinite. By means of the maximum principle with mixed inequality constraints, we present a necessary condition for the existence of optimal state feedback control that involves a constrained difference equation. Moreover, the existence of a solution to the constrained difference equation is equivalent to the solvability of the indefinite LQ problem. Furthermore, the well-posedness of the indefinite LQ problem is proved. Finally, an example is provided to demonstrate the effectiveness of our theoretical results.

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