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Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers. (English) Zbl 1153.93431
Summary: This paper illustrates the control of chaos using a fuzzy estimating system based on batch training and recursive least square methods for a continuous time dynamic system. The fuzzy estimator system is trained on both Ott-Geobogi-Yorke (OGY) control algorithm and Pyragas’s delayed feedback control algorithm. The system, considered as a case study, is a Bonhoeffer-van der Pol (BVP) oscillator. It is found that the implemented fuzzy control system constructed on OGY algorithm results in smaller control transient response than that of the OGY control algorithm itself. The transient response of Pyragas fuzzy control does not show a significant improvement in compare to the Pyragas control itself. In general the proposed control techniques show very effective low cost energy behavior in chaos control in compare to conventional non-linear control methods. Also the robustness of controlled system against random disturbances increases when the fuzzy estimation of OGY or Pyragas controller is used as a chaos controller.

93C42Fuzzy control systems
37D45Strange attractors, chaotic dynamics
37N35Dynamical systems in control
Full Text: DOI
[1] Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos. Phys rev lett 64, 1196-1199 (1990) · Zbl 0964.37501
[2] Ott, E.: Chaos in dynamical systems. (2002) · Zbl 1006.37001
[3] Chen, G.: Controlling chaos and bifurcation in engineering systems. (2000) · Zbl 0929.00012
[4] Shinbort, T.; Ott, E.; Grebogi, C.; Yorke, J.: Using chaos to direct trajectories to targets. Phys rev lett 65, 3215-3218 (1990)
[5] Mehta, N. J.; Henderson, R. M.: Controlling chaos to generate aperiodic orbits. Phys rev A 44, 4861-4865 (1991)
[6] Arecchi, F. T.; Boccaletti, S.; Ciofini, M.; Meucci, R.: The control of chaos: theoretical schemes and experimental realizations. Int J bifurcat chaos 8, No. 8, 1643-1655 (1998) · Zbl 0941.93529
[7] Hwang, C. C.; Fung, R. F.; Hsieh, J. Y.; Li, W. J.: Nonlinear feedback control of the Lorenz equation. Int J eng sci 37, 1893-1900 (1999) · Zbl 1210.93033
[8] Yu, X.: Variable structure control approach for controlling chaos. Chaos, solitons & fractals 8, No. 9, 1577-1586 (1997)
[9] Konishi, K.; Hirai, M.; Kokame, H.: Sliding mode control for a class of chaotic systems. Phys lett A 245, 511-517 (1998)
[10] Tsai, H. H.; Fuh, C. C.; Chang, C. N.: A robust controller for chaotic systems under external excitation. Chaos, solitons & fractals 14, 627-632 (2002) · Zbl 1005.93019
[11] Fuh, C. C.; Tsai, H. H.: Control of discrete-time chaotic systems via feedback linearization. Chaos, solitons & fractals 13, 285-294 (2002) · Zbl 0978.93519
[12] Liaw, Y. M.; Tung, P. C.: Controlling chaos via state feedback cancellation under a noisy environment. Phys lett A 211, 350-356 (1996)
[13] Calvo, O.; Cartwright, J. H. E.: Fuzzy control of chaos. Int J bifurcat chaos 8, 1743-1747 (1998) · Zbl 0941.93526
[14] Guan, X.; Chen, C.: Adaptive fuzzy control for chaotic systems with H$\infty $tracking performance. Fuzzy sets syst 139, 81-93 (2003) · Zbl 1053.93022
[15] Ramesh, M.; Narayanan, S.: Chaos control of bonhoeffer-van der Pol oscillator using neural networks. Chaos, solitons and fractals 12, 2395-2405 (2001) · Zbl 1004.37067
[16] Chen G, Dong X. Identification and control of chaotic systems: an artificial neural network approach. Proceedings of the IEEE International Symposium on Cric Syst, Seattle, WA, April 29-May 3, 1995. p. 1177-82
[17] Wang, L. X.: A course in fuzzy systems and control. (1997) · Zbl 0910.93002
[18] Fradkov L. Control of chaos: Methods and applications. Tutorial presentation at 21th IASTED Conference (MIC2002), 2002
[19] Moon, F. C.: Chaotic and fractal dynamics. (1992)