Anti-chaos control of perturbed second-order systems: A disturbance observer-based H∞-control approach

Roger Miranda-Colorado and Rubén Garrido

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: Different real-life systems such as chemical, economic, and mechatronic systems may be required to exhibit a chaotic behavior for different applications. In these cases, such a behavior must be ensured despite the inherent disturbances that may appear when dealing with real-time applications. Hence, this paper develops a methodology ensuring that a second-order system behaves as a chaotic system. Besides, the novel scheme maintains the chaotic behavior despite matched and unmatched disturbances. The proposed chaotization method consists of a controller divided into two parts, a disturbance observer and a H∞ controller. The disturbance observer compensates for the effect of matched disturbances and the H∞ formalism achieves the chaotization of the second-order system while the matched and unmatched disturbances’s effect is attenuated. A complete mathematical development theoretically validates the proposed scheme. Furthermore, the performance of the proposed controller is validated through an extensive numerical study and is compared against a previously proposed anti-chaos control technique and a fixed-time sliding mode controller that compensates for matched and unmatched disturbances. The maximum Lyapunov exponent is used to demonstrate the existence of chaos in the closed-loop system. Then, the numerical results show the superior performance of the novel chaotization approach.

Keywords: Chaotization; Anti-chaos control; H∞ control; Second-order system; Disturbance observer (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925011932

DOI: 10.1016/j.chaos.2025.117180

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