Backstepping based neural [formula omitted] optimal tracking control for nonlinear state constrained systems with input delay and disturbances

Abstract

This paper focuses on the problem of H∞ optimal tracking control for a class of nonlinear state constrained systems with input delay and disturbances. With the aid of Pade approximation, an auxiliary variable is devised to eliminate the effects of input delay. Combining barrier Lyapunov functions (BLFs) with backstepping design technique, a feedforward adaptive controller is designed to transform the tracking control problem of nonlinear state constrained system into an equivalent H∞ control problem of input-affine error system without state constraints, wherein neural networks (NNs) are employed to approximate unknown system dynamics. Then based on single-network adaptive dynamic programming (ADP), an H∞ optimal feedback controller is developed by utilizing a single critic network to learn the Nash equilibrium related to Hamilton–Jacobi–Isaacs (HJI) equation. Therefore, the whole tracking controller can be constructed by integrating the feedforward adaptive controller with the optimal feedback controller. Moreover, it is proven by Lyapunov’s theory that all signals within the closed-loop system are uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin without violating any state constraints. Two simulation examples are also presented to validate the effectiveness of the proposed approach.