On Quadratic Optimal Control of Nonlinear Discrete-Time Systems

This paper presents two nonlinear, discrete-time optimal control system designs. The first one is the quasi-optimal control for nonlinear discrete-time dynamic systems, based essentially on iterative algorithms. The second one is the discrete-time state-dependent Riccatti equation (DSDRE) method, which aims to solve a nonlinear optimal control problem through a Riccati equation that depends on the state. Our main contribution in this paper is to carry out a stability study of nonlinear systems associated with DSDRE controllers and to compare the performances of the two optimal controls via numerical simulation study. Unlike the analytical approach, DSDRE approach is able to neutralize exceeding at the transient phase, and shows easier ability for implementation.