Adaptive Fuzzy Sliding Mode Control for a Class of Uncertain Nonaffine Nonlinear Strict-Feedback Systems

Characteristic Model-Based Adaptive Control for a Class of MIMO Uncertain Nonaffine Nonlinear Systems Governed by Differential Equations

“…where λ i > 0,μ i > 0, and 0 < m i < 1 represent design constants. e adaptive controller (22) includes estimated parameters θ i,k , and the performance of asymptotic tracking with zero error or near zero can be obtained by adjusting the design parameters λ i > 0, μ i > 0, and 0 < m i < 1.…”

“…Let φ i,k � θ i,k − θ i,k be the parameter estimation error. e error equation of the closed-loop system can be expressed by substituting (22) into (4) as follows:…”

“…Consider an MIMO nonaffine nonlinear system (1) satisfying Assumptions 1 and 2. If the adaptive tracking controller is designed as (22) with update law (23), the sampling period T s < T min , and controller parameters n), then the following properties are guaranteed:…”

“…Over the past decades, nonaffine nonlinear system control has received considerable attention, and many important results have been presented on the design of such controllers [5-12, 14, 15]. Owing to the universal approximation theorem, some adaptive control schemes based on fuzzy logic systems [16][17][18][19][20][21][22] and neural networks [8,10,[23][24][25] have been developed for uncertain nonaffine nonlinear systems. Nevertheless, these approaches typically incur heavy computational costs.…”

“…We note that SISO systems are only considered in [39,40] and linear systems are only considered in [40]. (2) An adaptive controller based on this first-order characteristic model for position tracking control (see formula (22)) is designed by adaptively estimating the time-varying coefficients of the characteristic model (see formula (23)). In the existing literature, no results have been reported on the adaptive control design based on the first-order characteristic model for our considered class of nonaffine multivariable systems.…”