Indefinite LQ optimal control for discrete-time uncertain systems

This paper is concerned with a linear quadratic (LQ) optimal control for discrete-time uncertain systems, with indefinite state and control weighting matrices in the cost function. Firstly, a recurrence equation of general optimal control problem for discrete-time uncertain systems is obtained by applying Bellman’s principle of optimality. Then, the optimal state feedback control is obtained based on the recurrence equation. Moreover, a sufficient condition of well-posedness for the LQ problem is proposed and a general expression for the optimal control set is given. Furthermore, a numerical example is presented by using the obtained results. Finally, as an application of the indefinite LQ optimal control, an optimal production inventory problem of uncertain environment is solved.