Adaptive tracking control of chaotic systems with applications to synchronization

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 54, Issue 9, 2007, Pages 2019-2029

  Loría, Antonio ^a   Zavala Río, Arturo ^b  

^a UNIV PARIS SUD   (France)

^b INSTITUTO POTOSINO DE INVESTIGACIÓN CIENTÍFICA Y TECNOLÓGICA   (Mexico)

Author keywords

Adaptation; Chaos control; Controlled synchronization; Parameter uncertainty

Indexed keywords

ADAPTIVE ALGORITHMS; ADAPTIVE CONTROL SYSTEMS; CONTROL THEORY; DYNAMICAL SYSTEMS; OSCILLATORS (ELECTRONIC); PARAMETER ESTIMATION; SYNCHRONIZATION;

ADAPTIVE TRACKING CONTROL; DUFFING EQUATION; PARAMETER UNCERTAINTY;

CHAOTIC SYSTEMS;

EID: 34648840451     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2007.904682     Document Type: Article

References (24)

1. L. M. Pecora and T. L. Carroll, "Synchronizing chaotic circuits," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 38, pp. 453-456, 1991.
2. G. Kolumban, M. P. Kennedy, and L. O. Chua, "The role of synchronization in digital communications using chaos - Part II: Chaotic modulation of chaotic synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 11, pp. 1129-1140, 1998.
3. K. M. Kuomo, A. V. Oppenheim, and S. H. Strogatz, "Synchronization of Lorenz-based chaotic circuits with applications to communications," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 10, pp. 626-633, 1993.
4. Z. Jiang, "Advanced feedback control of chaotic systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 2, pp. 244-249, 2002.
5. A. L. Fradkov and A. Y. Pogromsky, "Speed gradient control of chaotic continuous-time systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, no. 11, pp. 907-914, 1996.
6. A. Harb, A. Zaher, A. Al-Quaisia, and M. Zohdi, "Estimation-based control of chaotic Duffing oscillators," Int. J. Vibration Contr. 2004.
7. A. Loría, E. Panteley, and H. Nijmeijer, "Control ofthe chaotic Duffing equation with uncertainty in all parameters," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 12, pp. 1252-1256, 1998.
8. D. Frey, "On adaptive chaotic encoding," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 45, no. 11, pp. 1200-1205, 1998.
9. U. Parlitz, L. Junge, and L. Kocarev, "Synchronization-based parameter estimation from time series," Phys. Rev. E, vol. 54, no. 6, pp. 6253-6259, 1996.
10. U. Parlitz, "Estimating model parameters from time series by autosynchronization," Phys. Rev. Lett., vol. 76, pp. 1232-1235, 1996.
11. D. Yu and A. Wu, "Comments on "estimating model parameters from time series by autosynchronization"," Phys. Rev. Lett., vol. 94, 2005, 219401.
12. S. Chen and J. Lü, "Parameters identification and synchronization of chaotic systems based upon adaptive control," Phys. Lett. A, vol. 299, pp. 353-358, 2002.
13. A. Loría and E. Panteley, "Stability, told by its developers," in Advanced Topics Contr. Syst. Theory, A. Loría, F. Lamnabhi-Lagarrigue, and E. Panteley, Eds. London: Springer Verlag, 2006, Lecture Notes in Control and Information Sciences, to be published.
14. H. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002.
15. W. Hahn, Theory and Application of Liapunov's Direct Method. Englewood Cliffs, NJ: Prentice-Hall, 1963.
16. K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice-Hall, 1989.
17. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness. Englewood Cliffs, NJ: Prentice-Hall, 1989.
18. A. Loría, E. Panteley, D. Popović, and A. Teel, "δ-persistency of excitation: A necessary and sufficient condition for uniform attractivity," in Proc. 41st IEEE Conf. Decision Contr., Las Vegas, NV, 2002, pp. 3506-3511, REG0623.
19. A. Loría, E. Panteley, D. Popović, and A. Teel, "A nested Matrosov theorem and persistency of excitation for uniform convergence in stable non-autonomous systems," IEEE Trans. Autom. Contr., vol. 50, no. 2, pp. 183-198, 2005.
20. R. Marino and P. Tomei, "Global adaptive output feedback control of nonlinear systems - Part I: Linear parameterization," IEEE Trans. Autom. Contr., vol. 38, pp. 17-32, 1993.
21. E. Panteley, A. Loría, and A. Teel, "Relaxed persistency of excitation for uniform asymptotic stability," IEEE Trans. Autom. Contr., vol. 46, no. 12, pp. 1874-1886, 2001.
22. A. P. Morgan and K. S. Narendra, "On the stability of nonautonomous differential equations x = A + B(t)]χ with skew-symmetric matrix B(t)," SIAM J. Contr. Opt., vol. 15, no. 1, pp. 163-176, 1977.
23. R. Ortega and M. Spong, "Adaptive motion control of rigid robots: A tutorial," Automatica, vol. 25-6, pp. 877-888, 1989.
24. R. Ortega, A. Loría, P. J. Nicklasson, and H. Sira-Ramírez, Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications. London, U.K.: Springer Verlag, 1998, Communications and Control Engineering.