Abstract
In this paper, we propose an adaptive steady state control scheme for parameter estimation of chaotic systems, which is based on the LaSalle invariant principle. By adaptive stabilizing the chaotic motion to a steady state, one can obtain the unknown parameters, assuming that independent variables and the structure of underlying dynamical evolution equations for the chaotic system are available. Two nonlinear chaotic systems, the well-known Chua’s circuit and L\(\ddot{u}\) system, are chosen as our examples. The simulation results demonstrate the effectiveness of the proposed scheme.
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References
Chen, G., Dong, X.: From Chaos to Order. World Scientific, Singapore (1998)
Parlitz, U.: Estimating Model Parameters from Time Series by Autosynchronization. Phys. Rev. Lett. 76, 1232–1235 (1996)
Maybhate, A., Amritkar, R.E.: Use of Synchronization and Adaptive Control in Parameter Estimation from a Time Deries. Phys. Rev. E 59, 284–293 (1999)
Chang, W.D.: Parameter Identification of Chen and L Systems: a Differential Evolution Approach. Chaos, Solitons & Fractals 32, 1469–1476 (2007)
Pisarenko, V.F., Sornette, D.: Statistical Methods of Parameter Estimation for Deterministically Chaotic Time Series. Phys. Rev. E 69, 36122 (2004)
Li, L.X., Yang, Y., Peng, H.P., Wang, X.D.: Parameters Identification of Chaotic Systems via Chaotic Ant Swam. Chaos, Solitons & Fractals 28, 1204–1211 (2006)
Annan, J.D., Hargreaves, J.C.: Efficient Parameter Estimation for a Highly Chaotic System. Tellus, 56A, p. 520 (2004)
Chen, S.H., Hu, J., Wang, C.H., Lv, J.H.: Adaptive synchronization of uncertain rossler hyperchaotic system based on parameter identification. Phys. Lett. A 321, 50–55 (2004)
Lv, J.H., Zhang, S.H.: Controlling Chen’s chaotic attractor using backstepping design based on parameters identification. Phys. Lett. A 286, 148–152 (2001)
Lie, J., Chen, S., Xie, J.: Parameter Identification and Control of Uncertain Unified Chaotic system via Adaptive Extending Equilibrium Manifold. Chaos, Solitons & Fractals 19, 533–540 (2004)
Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of an Ergodic Chaotic Cipher. Phys. Lett. A 311, 172–179 (2003)
LaSalle, J.P.: The Extent of Asymptotic Stability. Proc. Natl. Acad. Sci. USA 46(3), 363–365 (1960)
Hartley, T.T.: In: Proceedings of the American Control Conference, Pittsburgh, PA, p.419 (1989)
Lv, J., Chen, G.: A New Chaotic Attractor Coined. Int. J. Bifurcat. Chaos 12(3), 659–661 (2002)
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Shi, C., Che, Y., Han, C., Wang, J., Deng, B., Wei, X. (2011). Parameter Estimation in a Class of Chaotic System via Adaptive Steady State Control. In: Ma, M. (eds) Communication Systems and Information Technology. Lecture Notes in Electrical Engineering, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21762-3_92
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DOI: https://doi.org/10.1007/978-3-642-21762-3_92
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21761-6
Online ISBN: 978-3-642-21762-3
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