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Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

Ju Wu, Tong Wang, Min Ma

TL;DR

This work tackles finite-time adaptive fuzzy tracking for a class of nonlinear pure-feedback systems subject to full-state constraints. By transforming the plant to a strict-feedback form using the Mean-Value Theorem and employing a finite-time-stable error transformation alongside an integral barrier Lyapunov framework, the authors guarantee that the output tracking error converges to a predefined neighborhood within a fixed finite horizon $T_0$ while states remain within prescribed bounds. Fuzzy logic systems online approximate unknown dynamics, and a Nussbaum-type function handles unknown control direction, all within a backstepping design that yields semi-global ultimate boundedness of all signals. The feasibility of parameter choices is checked a priori through a semi-infinite optimization, and two simulation examples corroborate finite-time convergence, constraint satisfaction, and robust adaptation under disturbances.

Abstract

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy.

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

TL;DR

This work tackles finite-time adaptive fuzzy tracking for a class of nonlinear pure-feedback systems subject to full-state constraints. By transforming the plant to a strict-feedback form using the Mean-Value Theorem and employing a finite-time-stable error transformation alongside an integral barrier Lyapunov framework, the authors guarantee that the output tracking error converges to a predefined neighborhood within a fixed finite horizon while states remain within prescribed bounds. Fuzzy logic systems online approximate unknown dynamics, and a Nussbaum-type function handles unknown control direction, all within a backstepping design that yields semi-global ultimate boundedness of all signals. The feasibility of parameter choices is checked a priori through a semi-infinite optimization, and two simulation examples corroborate finite-time convergence, constraint satisfaction, and robust adaptation under disturbances.

Abstract

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy.
Paper Structure (6 sections, 3 theorems, 70 equations, 11 figures)

This paper contains 6 sections, 3 theorems, 70 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Problem Statement and Preliminaries
  3. Controller Design
  4. Feasibility Check
  5. Simulation Illustration
  6. Conclusion

Key Result

Lemma 1

For a continuous function $\psi (x):\mathbb{R}^n \to \mathbb{R}$ which is defined on a compact ${{\Omega }_{x}}\in \mathbb{R}^n$, there exists a fuzzy logic system ${{W}^{T}}S(x)$ which can be used to approximate $\psi (x)$ with the technique including singleton, center average defuzzification and p where $W={{[{{\omega }_{1}},{{\omega }_{2}},\ldots ,{{\omega }_{N}}]}^{T}}$ is the ideal weight vec

Figures (11)

  • Figure 1: Curves of $z_1$ and interval of $\mu(t)$ and $-\mu(t)$.
  • Figure 2: Curve of transformed output tracking error $e$.
  • Figure 3: Curves of states $x_1,x_2$ and intervals $k_{c1},k_{c2}$.
  • Figure 4: Curves of adaptation parameters ${\hat{\theta}}_1,{\hat{\theta}}_2$
  • Figure 5: Curves of virtual control $\alpha_1$ and system input $u(t)$
  • ...and 6 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Lemma 2
  • Remark 1
  • Lemma 3