Observer-Based Adaptive Control of Uncertain Nonlinear Systems Via Neural Networks

Abstract

In this paper, a novel observer-based control strategy is proposed for a class of uncertain continuous-time nonlinear systems based on the Hamilton–Jacobi–Bellman (HJB) equation. Due to the complexity of nonlinear systems, the approximately optimal control for affine uncertain continuous-time nonlinear systems is pursued. Considering that only the output variables can be measured in the control practice, the state observer is designed to reconstruct all system states by using the output variables. The observer-based policy iteration algorithm can solve the HJB equation within the adaptive dynamic programming framework for the unknown-state uncertain nonlinear systems, where a critic neural network is constructed to approximate the optimal cost function, and then, the approximate expression of the optimal control policy can be directly derived from solving the HJB equation. In addition, the stability of the whole closed-loop system is provided based on the Lyapunov analysis.