Comparison between Chaos-Control Methods Efficiency for Discrete Systems

WSEAS Transactions on Systems and Control

Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 14, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 14, 2019

Comparison between Chaos-Control Methods Efficiency for Discrete Systems

AUTHORS: Lina A. Shalby

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ABSTRACT: Controlling unstable behaviour of many nonlinear dynamical systems is one of the recent interesting topics for researchers. Many methods are proposed to stabilize chaotic discrete time systems. In this paper, a comparison between different control methods is performed for distinguishing their efficiency. The used control methods are Ott-Grebogi-Yorke (OGY), Predictive Feedback Control (PFC), Time Delay Auto Synchronization (TDAS) and its extended (ETDAS), control methods based on self-organizing migrating algorithm (SOMA) and differential evolution (DE). They are briefly introduced and then applied to most popular discrete nonlinear systems 100 times. The controlled orbits of period-1 characteristics are evaluated, presenting the robust of each method according to autocorrelation, the number of required iterations, number of successfully controlled orbits, and max absolute value of the control input. TDAS and PFC methods are the most convenient to stabilize the chaotic attractor of the system.

KEYWORDS: Control Methods, Nonlinear Chaotic Discrete Systems, and Autocorrelation.

REFERENCES:

[1] J. Ackermann, Der Entwurf Linearer Regelungsysteme in Zustandsraum, Regulungstech. Prozess-Datanverarb 7, 1972, pp. 297—300.

[2] B. R. Andrievskii and A. L. FradkovZhu, Control of Chaos: Methods and Applications. I. Methods. Automation and remote control 64(5),2003, pp. 673–713.

[3] A. Boukabou and N. Mansouri, Predictive Control of Continuous Chaotic Systems. Int. J. Bifurcation Chaos 18(2), 2008, pp. 587–592.

[4] P. Celka, Experimantal verification of Pyragas’s Chaos Control method applied to Chua’s circuit. Int. J. Biforcation Chaos Appl. Sci. Eng. 4(6), 1994, pp. 29–36.

[5] M. De Sousa Vieira and AJ. Lichtenberg, Controlling chaos using nonlinear feedback with delay. Phys. Rev. E 54(2), 1996, pp. 1200–1207.

[6] D. Davendra and I. Zelinka, Self-organizing migrating algorithm, New Optimization Techniques in Engineering, 2016.

[7] A. A. Elsadany and A. M. Awad, Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes. Annals of Operations Research - Springer, 2019.

[8] E. J. Kostelich, et al. , Higher-dimensional targeting. Phys. Rev. E 47(1), 1993, pp. 305–310.

[9] Y. -C. Lai, M. Ding and C. Grebogi, Controlling hamiltonian chaos. Phys. Rev. E 47(1), 1993, pp. 86–92.

[10] G. A. Leonov, K. A. Zvyagintseva and O. A. Kuznetsova, Pyragas stabilization of discrete systems via delayed feedback with periodic control gain. IFAC-PapersOnLine 49(14), 2016, pp. 56–61.

[11] G. M. Mahmoud, et al. , Chaos control of integer and fractional orders of chaotic Burke-Shaw system using time delayed feedback control. Chaos, Solitons & Fractals 104, 2017, pp. 680-692.

[12] K. Mitsubori and K. Aihara, Delayed–feedback control of chaotic roll motion of a flooded ship in waves. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 458(2027), 2002, 2801-–2813.

[13] O. Morgul, On the Stability of Delayed Feedback Controllers. Phys. Lett. A 341(4), 2003, pp. 278–285.

[14] E. Ott, C. Grebogi, and J. A. Yorke, Controlling Chaos,Phys. Rev. Lett 64,1990, pp. 1196.

[15] B. T. Polyak, Stabilizing Chaos with Predictive Control. Automation and Remote Control 66(11), 2005, pp. 1791–1804.

[16] K. Pyragas, Continuous Control of Chaos by Self-Controlling Feedback.Phys. Lett. A 170 (6), 1992, pp. 421-–428.

[17] K. Pyragas, Control of Chaos via Extended Delay Feedback. Phys. Lett. A 206(5-6), 1995, pp. 323-–330.

[18] K. Pyragas, Delayed feedback control of chaos. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 364(1846), 2006, pp. 2309– 2334.

[19] E. Scholl and H. G. Schuster, ¨ Handbook of chaos control, John Wiley & Sons, 2008.

[20] R. Senkerik, Z. Oplatkova, I. Zelinka, and D. Davendra. Evolutionary chaos controller synthesis for stabilizing chaotic Henon maps. Complex Systems 20(3), 2012, pp. 205–214.

[21] L. A. Shalby,Predictive Feedback Control Method for Stabilization of Continuous Time Systems. Advances in Systems Science and Applications 17(4), 2017, pp. 1–13.

[22] T. Ushio, Limitation of Delayed Feedback Control in Nonlinear Discrete-Time Systems. IEEE Trans. Circ. Syst. 43(9), 1996, pp. 815–816.

[23] T. Ushio and S. Yamamoto, Prediction-based Control of Chaos. Phys. Lett. A 264(1), 1999, pp. 30–35.

[24] S. Vaidyanathan, Adaptive control of a chemical chaotic reactor. Int. J. PharmTech Res. 8(3), 2015, pp. 377–382.

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 14, 2019, Art. #36, pp. 284-290

Copyright Β© 2019 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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