Adaptive Fuzzy Backstepping Control for A Class of Nonlinear Systems With Sampled and Delayed Measurements

Abstract

This paper investigates the adaptive fuzzy backstepping control and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis for a class of nonlinear systems with sampled and delayed measurements. In the control scheme, a fuzzy-estimator (FE) model is used to estimate the states of the controlled plant, while the fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system. The controller is obtained based on the FE model by combining the backstepping technique with the classic adaptive fuzzy control method. In the stability analysis, all the signals in the closed-loop system are guaranteed to be semiglobally uniformly ultimately bounded (SUUB) and the outputs of the system are proven to converge to a small neighborhood of origin. Furthermore, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is investigated and the outputs of the closed-loop system are bounded in the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. Two examples are given to illustrate the effectiveness of the proposed control scheme.