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

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.