Delayed Sliding Mode Control of Chaotic Systems
Received 07 September 2023; accepted 21 December 2023; published 29 February 2024
2024, Vol. 20, no. 2, pp. 277-293
Author(s): Hamidouche B., Guesmi K., Essounbouli N.
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.
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