Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode

Abstract

This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.