Delayed Sliding Mode Control of Chaotic Systems

This paper presents a comprehensive investigation of delayed sliding-mode control and synchronization of chaotic systems. The findings of this paper offer valuable insights into chaos control and synchronization and provide promising prospects for practical applications in various domains where the control of complex dynamical systems is a critical question. In this paper, we propose three approaches of control to regulate chaotic behavior and induce synchronization between the system’s state and its delayed value, by one period, of the unstable periodic orbits (UPOs). The stabilization ability of each controller is demonstrated analytically based on Lyapunov theory. Furthermore, we provide a bridge between classical stability and structural one through the use of the synchronization error, as an argument of the controller, instead of the classical tracking error.
Through three sets of simulations, we demonstrate the effectiveness of the proposed approaches in driving the chaotic system toward stable, simple, and predictable periodic behavior. The results confirm the rapid achievement of stabilization, even with changes in the sliding surface and control activation time point showing, hence, the approaches’ adaptability and reliability. Furthermore, the controlled system exhibits remarkable insensitivity to changes in initial conditions, thus showing the robustness of the proposed control strategies.