Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure‐Feedback Non‐Affine Nonlinear Systems in the Presence of Input Constraints

Abstract

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

Approximation‐Based Robust Adaptive Backstepping Prescribed Performance Control for a Huger Class of Nonlinear Systems

“…This paper proposed a novel adaptive neural PPC scheme for large classes of nonlinear nonstrict-feedback systems with prescribed performance under the effect of input saturation. Compared with previously published methods [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], the restrictive assumption that the upper and lower bounds of control gain functions must be positive constants or coefficients is relieved under the proposed method. The innovative error transformation proposed in this paper also overcomes the nondifferentiable obstacle and complex deductions corresponding to traditional PPC schemes.…”

“…Unlike other methods [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], we aim here to achieve this objective in the presence of the following assumptions and lemmas. [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], we assume only the signs of the control gain functions to be known. This effectively relaxes the a priori boundedness assumption.…”

“…The input saturation constraint also appears in many actual systems, such as industrial robots and numerical control machines [36][37][38]. If it is ignored during control system design, it can cause inaccuracy, instability, or even deteriorate the performance of the entire closed-loop system.…”

“…(1) Unlike other strategies [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], this is the first instance in which an adaptive control problem of a large class of nonstrict-feedback systems with continuous, possibly unbounded control gain functions fall under both prescribed performance and input saturation constraints.…”