Discrete-Time Uncertain LQ Optimal Control with Indefinite Control Weight Costs

Abstract

This paper deals with a discrete-time uncertain linear quadratic (LQ) optimal control, where the control weight costs are indefinite . Based on Bellman’s principle of optimality, the recurrence equation of the uncertain LQ optimal control is proposed. Then, by using the recurrence equation, a necessary condition of the optimal state feedback control for the LQ problem is obtained. Moreover, a sufficient condition of well-posedness for the LQ problem is presented. Furthermore, an algorithm to compute the optimal control and optimal value is provided. Finally, a numerical example to illustrate that the LQ problem is still well-posedness with indefinite control weight costs.