Adaptive chaos control: A novel continuous-time approach for enhanced stability

Abstract

Stabilizing chaotic systems with robustness, speed, and smoothness remains a significant challenge due to issues like chattering and slow convergence associated with traditional control methods. This paper proposes a novel continuous-time adaptive robust control (CTARC) scheme to overcome these limitations and enhance the stabilization of uncertain chaotic systems. CTARC employs smooth control functions; specifically hyperbolic secant and inverse hyperbolic sine functions to eliminate chattering and achieve faster, more precise convergence to equilibrium. Unlike conventional controllers that simplify system dynamics by removing nonlinearities, this approach preserves them, thereby improving robustness against time-varying disturbances and model uncertainties. A Lyapunov-based stability analysis rigorously establishes the asymptotic stability of the proposed control strategy. Numerical simulations on the Shimizu–Morioka​ chaotic system and a memristor-based hyperchaotic system validate CTARC’s superiority in convergence speed, energy efficiency, and stability compared to existing adaptive methods. By reducing transient effects like overshoots and oscillations, the proposed scheme ensures smoother transitions and minimizes energy consumption, addressing critical limitations of traditional methods. These results highlight CTARC’s potential as a robust and energy-efficient solution for chaos stabilization and provide a foundation for future developments in complex system control.