Optimal control of a chaotic map: Fixed point stabilization and attractor confinement

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 2, 1997, Pages 437-446

  Piccardi, C ^a   Ghezzi, L L ^a,b  

^a POLITECNICO DI MILANO   (Italy)

^b CREMS Centre for Research on Health Economics Social and Health Care Management Carlo Cattaneo University LIUC   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031064173     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497000315     Document Type: Article

References (32)

1. Bertsekas, D. P. [1982] "Distributed dynamic programming," IEEE Trans. Automat. Contr. 27, 610-616.
2. Bertsekas, D. P. [1995] Dynamic Programming and Optimal Control (Athena Scientific, Belmont, Mass.).
3. Bertsekas, D. P. & Rhodes, I. B. [1971] "On the minimax reachability of target sets and target tubes," Automatica 7, 233-247.
4. Bertsekas, D. P. & Tsitsiklis, J. N. [1989] Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ).
5. Bryson, A. E. & Ho, Y.-C. [1975] Applied Optimal Control (Hemisphere, Washington, DC).
6. Callier, F. M. & Desoer, C. A. [1991] Linear System Theory (Springer-Verlag, NY).
7. Chen, G. [1994] "Optimal control of chaotic systems," Int. J. Bifurcation and Chaos 4, 461-463.
8. Chen, G. [1997] "Control and synchronization of chaotic systems (a bibliography)," ECE Dept., Univ. of Houston, TX - available from ftp: "uhoop.egr.uh.edu/ pub/TeX/chaos.tex" (login name "anonymous" password: your email address).
9. Chen, G. & Dong, X. [1992] "On feedback control of chaotic nonlinear dynamic systems," Int. J. Bifurcation and Chaos 2, 407-411.
10. Chen, G. & Dong, X. [1993a] "From chaos to order - Perspectives and methodologies in controlling chaotic nonlinear dynamical systems," Int. J. Bifurcation and Chaos 3, 1363-1409.
11. Chen, G. & Dong, X. [1993b] "On feedback control of chaotic continuous-time systems," IEEE Trans. Circ. Syst. I 40, 591-601.
12. Fowler, T. B. [1989] "Application of stochastic control techniques to chaotic nonlinear systems," IEEE Trans. Automat. Contr. 34, 201-205.
13. Galias, Z. [1995] "New method for stabilization of unstable periodic orbits in chaotic systems," Int. J. Bifurcation and Chaos 5, 281-295.
14. Ghezzi, L. L. & Piccardi, C. [1997] "PID control of a chaotic system: An application to an epidemiological model," Automatica 33, in press.
15. Goh, B. S. [1980] Management and Analysis of Biological Populations (Elsevier, Amsterdam).
16. Hammad, A., Jonckheere, E., Cheng, C.-Y., Bhajekar, S. & Chien, C.-C. [1996] "Stabilization of chaotic dynamics: A modern control approach," Int. J. Control 64, 663-677.
17. Hartley, T. T. & Mossayebi, F. [1992] "A classical approach to controlling the Lorenz equations," Int. J. Bifurcation and Chaos 2, 881-887.
18. May, R. M. & Oster, G. F. [1976] "Bifurcation and dynamic complexity in simple ecological models," Am. Nat. 110, 573-599.
19. Moran, P. A. P. [1950] "Some remarks on animal dynamics," Biometrics 6, 251-258.
20. Nijmeijer, H. & Berghuis, H. [1995] "On Lyapunov control of the Duffing equation," IEEE Trans. Circ. Syst. I 42, 473-477.
21. Ogorzalek M. J. [1993] "Taming chaos: Part II - Control," IEEE Trans. Circ. Syst. I 40, 700-706.
22. Olsen, L. F., Truty, G. L. & Schaffer, W. M. [1988] "Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark," Theor. Pop. Biol. 33, 344-370.
23. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
24. Paskota, M., Mees, A. I. & Teo, K. L. [1995] "Directing orbits of chaotic dynamical systems," Int. J. Bifurcation and Chaos 5, 573-583.
25. Ricker, W. E. [1954] "Stock and recruitment," J. Fish. Res. Board Can. 11, 559-623.
26. Romeiras, E. J., Grebogi, C., Ott, E. & Dayawansa, W. P. [1992] "Controlling choatic dynamical systems," Physica D58, 165-192.
27. Roux, J. C., Simoyi, R. H. & Swinney, H. L. [1983] "Observation of a strange attractor," Physica 8D, 257-266.
28. Shinbrot, T., Ott, E. & Grebogi, C. [1990] "Using chaos to direct trajectories to targets," Phys. Rev. Lett. 65, 3215-3218.
29. Starobinets, I. M. & Pikovsky, A. S. [1993] "Multistep method for controlling chaos," Phys. Lett. A181, 149-152.
30. Vincent, T. L. & Yu, J. [1991] "Control of a chaotic system," Dynamics and Control 1, 35-52.
31. Xu, D. & Bishop, S. R. [1994] "Steering dynamical trajectories to target a desired state," Chaos, Solitons & Fractals 4, 1931-1942.
32. Yau, C.-H., Bajaj, A. K. & Nwokah, O. D. I. [1993] "Robust control of a chaotic vibratory system," Int. J. Bifurcation and Chaos 3, 1075-1081.