Robust Adaptive Controller Design for a Class of Uncertain Nonlinear Systems Using Online T–S Fuzzy-Neural Modeling Approach

TLDR

Although studies on adaptive T‑S fuzzy‑neural controllers exist for some nonaffine nonlinear systems, little is known about more complicated uncertain nonlinear systems, and traditional T‑S fuzzy control struggles to model them due to uncertain nonlinear functions. The study proposes an online T‑S fuzzy‑neural modeling and control method for uncertain nonlinear systems with certain outputs. The authors approximate a virtual linearized system with a T‑S fuzzy‑neural model, identify it online, design a robust adaptive tracking controller, and prove closed‑loop stability using strictly positive real Lyapunov theory. The scheme guarantees asymptotic tracking of desired trajectories, and simulations demonstrate its effectiveness and applicability.

Abstract

This paper proposes a novel method of online modeling and control via the Takagi-Sugeno (T-S) fuzzy-neural model for a class of uncertain nonlinear systems with some kinds of outputs. Although studies about adaptive T-S fuzzy-neural controllers have been made on some nonaffine nonlinear systems, little is known about the more complicated uncertain nonlinear systems. Because the nonlinear functions of the systems are uncertain, traditional T-S fuzzy control methods can model and control them only with great difficulty, if at all. Instead of modeling these uncertain functions directly, we propose that a T-S fuzzy-neural model approximates a so-called virtual linearized system (VLS) of the system, which includes modeling errors and external disturbances. We also propose an online identification algorithm for the VLS and put significant emphasis on robust tracking controller design using an adaptive scheme for the uncertain systems. Moreover, the stability of the closed-loop systems is proven by using strictly positive real Lyapunov theory. The proposed overall scheme guarantees that the outputs of the closed-loop systems asymptotically track the desired output trajectories. To illustrate the effectiveness and applicability of the proposed method, simulation results are given in this paper.