Robust adaptive chatter-free finite-time control method for chaos control and (anti-)synchronization of uncertain (hyper)chaotic systems

This paper presents a novel robust adaptive chatter-free finite-time control (RACFFTC) strategy for chaos control and (anti-) synchronization of a class of uncertain (hyper) chaotic systems. First, non-singular terminal slidingmode surfaces are introduced. Second, a RACFFTC controller with appropriate adaptive laws is designed to provide robustness, high control precision, and fast and finite-time convergence without requiring prior knowledge of the upper bounds of the uncertainties and external disturbances. Because the proposed RACFFTC controller consists of a discontinuous function under integral, the chattering effect is eliminated. The global finite-time stability of the closed-loop system is rigorously proven. Numerical simulations are presented to demonstrate the robustness, effectiveness and feasibility of the proposed strategy.