Title: Lyapunov exponent-based PID control for noisy chaotic systems

Authors: Baghdadi Hamidouche; Kamel Guesmi; Najib Essounbouli

Addresses: Department of Electrical Engineering, University of Djelfa, Djelfa, Algeria ' CReSTIC, University of Reims, Reims, France ' CReSTIC, University of Reims, Reims, France

Abstract: This paper addresses the stabilisation issue of noisy chaotic systems. It proposes a new hybrid control approach that combines the proportional-integral-derivative (PID) method with the delayed feedback technique. The idea is to turn the structural stabilisation problem into an optimisation one. The goal is to determine the PID gains that give the lowest value of the largest-Lyapunov exponent. The difference between the system's current state and its delayed value, by one period, is used as the PID argument. As a result, the systems chaotic orbits are structurally stabilised to the greatest extent possible, the stable zone is extended, and the stabilisation time is reduced. Numerical simulations are carried out to show the effectiveness of the proposed approach on two well-known benchmarks of chaotic systems.

Keywords: chaotic systems; delayed feedback control; optimisation; proportional-integral-derivative; PID; largest-Lyapunov exponent.

DOI: 10.1504/IJAAC.2024.139435

International Journal of Automation and Control, 2024 Vol.18 No.4, pp.408 - 424

Received: 01 Jul 2023
Accepted: 30 Jul 2023
Published online: 02 Jul 2024 *

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