An Approximate Optimal Control Approach for Robust Stabilization of a Class of Discrete-Time Nonlinear Systems With Uncertainties

Abstract

In this correspondence paper, the robust stabilization of a class of discrete-time nonlinear systems with uncertainties is investigated by using an approximate optimal control approach. The robust control problem is transformed into an optimal control problem under some proper restrictions on the bound of the uncertainties. For the purpose of dealing with the transformed optimal control, the discrete-time generalized Hamilton–Jacobi–Bellman equation is introduced and then solved using the successive approximation method with neural network implementation. In addition, a numerical simulation is included to illustrate the effectiveness of the robust control strategy.