Adaptive type-2 fuzzy second order sliding mode control for nonlinear uncertain chaotic system

TL;DR

This paper introduces an adaptive type-2 fuzzy higher order sliding mode controller that stabilizes uncertain chaotic systems, reducing chattering and ensuring stability through Lyapunov-based adaptation laws.

Contribution

It presents a novel combination of adaptive type-2 fuzzy systems with higher order sliding mode control for chaotic systems, improving robustness and reducing chattering.

Findings

Effective stabilization of uncertain chaotic systems demonstrated

Chattering significantly reduced using Super Twisting algorithm

Lyapunov stability of the closed-loop system verified

Abstract

In this paper, a robust adaptive type-2 fuzzy higher order sliding mode controller is designed to stabilize the unstable periodic orbits of uncertain perturbed chaotic system with internal parameter uncertainties and external disturbances. In Higher Order Sliding Mode Control (HOSMC),the chattering phenomena of the control effort is reduced, by using Super Twisting algorithm. Adaptive interval type-2 fuzzy systems are proposed to approximate the unknown part of uncertain chaotic system and to generate the Super Twisting signals. Based on Lyapunov criterion, adaptation laws are derived and the closed loop system stability is guaranteed. An illustrative example is given to demonstrate the effectiveness of the proposed controller.