Latency Compensation in Multi Chaotic Systems Using the Extended OGY Control Method

Document Type : Research Article

Authors

Industrial Control Center of Excellence, Department of Systems and Control Engineering, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

The problem discussed in this paper is the effect of latency time on the OGY chaos control methodology in multi chaotic systems. The Smith predictor, rhythmic and memory strategies are embedded in the OGY chaos control method to encounter loop latency. A comparison study is provided and the advantages of the Smith predictor approach are clearly evident from the closed loop responses. The complex plants considered are coupled chaotic maps controlled by the extended OGY scheme. Simulation results are used to show the effectiveness of the applied Smith predictor scheme structure in multi chaotic systems.

Keywords


[1] J.C. Claussen, and H.G. Schuster, “Improved Control of Delayed Measured Systems,” Physical Review E, 70: 056225, 2004.
[2] J.C. Claussen, “Delayed Measurements in Pincare-Based Chaos Control,” Physical Review E, 70:046128, 2005.
[3] E. Scholl, and H.G. Schuster, Hand Book of Chaos, Wiley, 2008.
[4] E. Ott, C. Grebogi, and J.A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, pp. 1196–1199, 1990.
[5] K. Pyragas, “Continuous control of chaos by self- controlling feedback,” Physics Letters A, vol. 170, pp. 421-428, 1992.
[6] P. Hovel, “Effects of chaos control and latency in time-delay feedback methods,” PhD Thesis, 2004.
[7] S. Schikora, P. Hövel, H.J. Wünsche, E. Schöll, and F. Henneberger, “All-optical noninvasive control of unstable steady states in a semiconductor laser,” Physical Review Letters, 97:213902, 2006.
[8] D.J. Gauthier, D.W. Sukow, H.M. Concannon, and J.E.S. Socolar, “Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization,” Physical Review E, 50:2343, 1994.
[9] D.W. Sukow, M.E. Bleich, D.J. Gauthier, and J.E.S. Socolar, “Controlling chaos in a fast diode resonator using time-delay autosynchronization: experimental observations and theoretical analysis,” Chaos, 7:560, 1997.
[10] J.N. Blakely, “Experimental Control of a Fast Chaotic Time-Delay Opto-Electronic Device,” PhD Thesis, Duke University, 2003.
[11] W. Just, E. Reibold, H. Benner, K. Kacperski, P. Fronczak, and J. Holyst, “Limits of time delayed feedback control,” Physics Letters A, 254:158, 1999.
[12] W. Just, D. Reckwerth, E. Reibold, and H. Benner, “Influence of control loop latency on time delayed feedback control,” Physics Letters E, 59:2826, 1999.
[13] P. Hövel, and J.E.S. Socolar, “Stability domains for time-delay feedback control with latency,” Physics Letters E 68:036206, 2003.
[14] N. Corron, B. Hopper, and S. Pethel, “Limiter control of a chaotic RF transistor oscillator,” International Journal of Bifurcation and Chaos, vol. 13, no. 04, pp. 957-961, 2003.
[15] K. Myneni, T.A. Barr, N.J. Corron, and S.D. Pethel, “New method for the control of fast chaotic oscillations,” Physical Review Letters, 83: 2175, 1999.
[16] L. Illing, D.J. Gauthier, and J.N. Blakely, “Controlling fast chaos in optoelectronic delay dynamical systems,” Hand Book of Chaos Control, Second Edition, Wiley, 2008.
[17] E. Nobakhti, A. Khaki-Sedigh, and N. Vasegh,
“Control of Multi-Chaotic Systems using the Extended OGY Method,” International Journal of Bifurcation and Chaos, 25: 1550096, 2015.
[18] L. Jentoft, and Y. Li, “Stabilizing the Henon Map with the OGY Algorithm,” Report, Olin College of Engineering, 2008.
[19] K.M. Moudgalya, Digital Control, John Wiley & Sons Ltd., 2007.