Global Chaos Control of Non-Autonomous Systems

Hsiao, Yung Chia; Tung, Pi Cheng

doi:10.1006/jsvi.2001.4091

Cited by 2 publications

(1 citation statement)

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“…In 1992 another approach, based on delayed feedback control, was presented for stabilizing unstable periodic orbits of continuous time chaotic systems, called Pyragas method [4]. In recent years, many nonlinear techniques for chaos control were used, such as feedback linearization [5][6][7], sliding mode control [8][9][10], Lyapunov based control [11][12][13] and fuzzy system based control [14][15][16]. In all of the mentioned methods the chaotic system has a deterministic differential equation; there is no random parameter or random excitation on the system governing equation.…”

Section: Introductionmentioning

confidence: 99%

Control of stochastic chaos using sliding mode method

Salarieh

Alasty

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ 6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper.

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