Approximate Optimal Control of Nonlinear Systems with Mismatched Perturbations Based on Asymptotically Stable Critic Neural Network

Abstract

In this paper, the approximate optimal control problem for nonlinear systems with mismatched perturbations is addressed through asymptotically stable critic neural network (NN). By employing the estimated perturbation via nonlinear perturbation observer, the online updated value function is constructed to reflect the real-time perturbations, regulation and control simultaneously. In order to solve the Hamilton-Jacobi-Bellman equation, an asymptotically stable critic NN is established based on the novel nested update laws. Thus, the approximate optimal control is obtained to guarantee the closed-loop system to be uniformly ultimately bounded based on the Lyapunov's direct method. Simulation results illustrate the effectiveness of the developed control scheme.