Optimality recovery of feedback control system based on discrete-time state dependent riccati equation

In this paper, optimality recovery of a control method based on the discrete-time state-dependent Riccati equation (DSDRE) is discussed. The relationship between the DSDRE method and the Hamilton-Jacobi-Bellman equation (HJBE) concerned with optimal control for discrete-time nonlinear systems is addressed briefly. Based on the relationship, the stability of the DSDRE method is investigated with the Lyapunov theorem. As a result, the asymptotical stability holds for the DSDRE strategy is proven for some special case, and the optimality does not hold under infinite-horizon criteria in general. Hence an iterative numerical method is proposed to improve and recover the optimality along a state trajectory obtained by the DSDRE strategy. The method is verified through numerical simulations.