Barrier Lyapunov function-based adaptive fuzzy control for general dynamic modeling of affine and non-affine systems

In this paper, first, general dynamic modeling is proposed for multi-input/output nonlinear systems in the form of affine and non-affine systems. Then, an observer barrier function-based adaptive fuzzy scheme is suggested to estimate unknown functions. Briefly, the main contributions of the proposed scheme are: (1) the proposed modeling can be employed in various classes of nonlinear systems, e.g., Single Input–Single Output (SISO), Single Input–Multi Output (SIMO), Multi Input–Single Output (MISO), and Multi Input–Multi Output (MIMO) systems with square or non-square control gain matrix, (2) by combining an observer error signal and the barrier Lyapunov function, the proposed Observer-based Barrier Lyapunov Function (OBLF) method can be employed to solve the problems of output constraint by preventing the output from violating the constraint, and (3) a non-singular robust adaptive fuzzy approach is presented for various classes of nonlinear systems so that the uncertainties are attenuated by a robust bounded 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}-like control term. The proposed scheme guarantees the stability of the closed-loop system based on the Strictly Positive Real (SPR) condition and OBLF theory, but it does not need the SPR conditions to be well known. Finally, to show the usefulness of the proposed technique, the simulation examples are employed for various classes of nonlinear affine and non-affine systems with square or non-square control gains.