Adaptive robust fault-tolerant control for nonlinear systems with prescribed performance

Based on prescribed performance, backstepping, and H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} techniques, adaptive robust fault-tolerant control for strict-feedback nonlinear systems with prescribed performance is investigated in the paper. A prescribed performance function, which is characterized by the maximum overshoot, convergence rate, and steady-state error, is utilized for the output error transformation. Based on the error transformation model, an adaptive robust fault-tolerant controller is designed, which guarantees that the output tracking error is bounded by the prescribed performance function and the effect of external disturbances and approximation errors is attenuated by H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} tracking performance. The compensation control strategy is adopted in the fault-tolerant control system, where the fault functions are approximated by neural networks. It is shown by Lyapunov stability theory that the state trajectories of the closed-loop system are bounded, the prescribed dynamic performance for the output tracking error is achieved, and the H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} tracking performance is guaranteed whether the faults occur or not. Finally, comparative simulation results show the effectiveness of the proposed approach.