Adaptive control of uncertain lorenz system using decoupled backstepping

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 14, Issue 4, 2004, Pages 1439-1445

  Ge, S S ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Controlling chaos; Decoupled backstepping; Lorenz system

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; FEEDBACK CONTROL; LINEARIZATION; MATHEMATICAL OPERATORS; NONLINEAR CONTROL SYSTEMS; PARAMETER ESTIMATION; UNCERTAIN SYSTEMS;

CONTROLLING CHAOS; DECOUPLED BACKSTEPPING; LORENZ SYSTEM; SINGULARITY-FREE ADAPTIVE CONTROL;

ADAPTIVE CONTROL SYSTEMS;

EID: 13844255222     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404010035     Document Type: Article

References (19)

1. Chen, G. & Dong, X. [1998] From Chaos To Order (World Scientific, Singapore).
2. Fradkov, A. L. & Pogromsky, A. Yu. [1998] Introduction to Control of Oscillations and Chaos (World Scientific, Singapore).
3. Gallegos, J. A. [1994] "Nonlinear regulation of a Lorenz system by feedback linearization techniques," Dyn. Contr. 4, 277-298.
4. Ge, S. S., Wang, C. & Lee, T. H. [2000] "Adaptive back-stepping control of a class of chaotic systems," Int. J. Bifurcation and Chaos 10, 1149-1156.
5. Ge, S. S., Hang, C. C., Lee, T. H. & Zhang, T. [2001] Stable Adaptive Neural Network Control (Kluwer, Boston, MA).
6. Ge, S. S. & Wang, J. [2002] "Robust adaptive control for a class of perturbed strict feedback nonlinear systems," IEEE Trans. Neural Networks 13, 1409-1419.
7. Isidori, A. [1989] Nonlinear Control System, 2nd edition (Springer-Verlag, Berlin).
8. Kanellakopoulos, I., Kokotović, P. & Morse, A. [1991] "Systematic design of adaptive controllers for feedback linearizable systems," IEEE Trans. Automat. Contr. 36, 1241-1253.
9. Khalil, H. [1996] Nonlinear Systems, 2nd edition (Prentice-Hall, NJ).
10. Krstić, M., Kanellakopoulos, I. & Kokotović, P. [1995] Nonlinear and Adaptive Control Design (John Wiley, NY).
11. LaSalle, J. P. [1968] "Stability theory for ordinary differential equations," J. Diff. Eqs. 4, 57-65.
12. Lenz, H. & Obradovic, D. [1997] "Robust control of the chaotic Lorenz system," Int. J. Bifurcation and Chaos 7, 2847-2854.
13. Liao, T. L. [1998] "Observer-based approach for controlling chaotic systems," Phys. Rev. E57, 1604-1610.
14. Lorenz, E. N. [1963] "Deterministic non-periodic flow," J. Atmos. Sci. 20, 130-141.
15. Wang, C. & Ge, S. S. [2001] "Adaptive backstepping control of uncertain Lorenz system," Int. J. Bifurcation and Chaos 11, 1115-1119.
16. Ye, X. & Jiang, J. [1998] "Adaptive nonlinear design without a priori knowledge of control directions," IEEE Trans. Automat. Contr. 43, 1617-1621.
17. Yoshizawa, T. [1966] Stability Theory by Lyapunov's Second Method (The Mathematical Society of Japan).
18. Yu, X. H. [1996] "Controlling Lorenz chaos," Int. J. Syst. Sci. 27, 355-359.
19. Zeng, Y. & Singh, S. N. [1997] "Adaptive control of chaos in Lorenz system," Dyn. Contr. 7, 143-154.