Adaptive control of discrete-time chaotic systems: a fuzzy control approach. (English) Zbl 1061.93501

Summary: This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T-S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm.


93C10 Nonlinear systems in control theory
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
93C42 Fuzzy control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] Chen, G.; Dong, X., From chaos to order: perspectives and methodologies in controlling chaotic nonlinear dynamic systems, Int. J. bifurcat. chaos, 3, 6, 1363-1409, (1993) · Zbl 0886.58076
[2] Fradkov, A.L.; Pogromsky, A.Yu., Introduction to control of oscillations and chaos, (1999), World Scientific Singapore · Zbl 0945.93003
[3] Chen G, Fradkov AL. Chaos Control and Synchronization Bibliographies (1987-2001). Available from WWW: http://www.ee.cityu.edu.hk/ gchen/chaos-papers.html
[4] Ogorzalek, M.J., Taming chaos: part II–control, IEEE trans. circ. syst. I, 40, 10, 700-706, (1993) · Zbl 0850.93354
[5] Richter, H.; Reinschke, K.J., Local control of chaotic systems–a Lyapunov approach, Int. J. bifurcat. chaos, 8, 7, 1565-1573, (1998) · Zbl 0941.93523
[6] Sinha, S.C.; Henrichs, J.T.; Ravindra, B., A general approach in the design of active controllers for nonlinear systems exhibiting chaos, Int. J. bifurcat. chaos, 10, 1, 165-178, (2000) · Zbl 1090.37528
[7] Pyragas, K., Continuous control of chaos by self-controlling feedback, Phys. lett. A, 170, 421-428, (1992)
[8] Fuh, C.C.; Tung, C.P., Controlling chaos using differential geometric method, Phys. rev. lett., 75, 16, 2952-2955, (1995)
[9] Gallegos, J.A., Nonlinear regulation of a Lorenz system by feedback linearization techniques, Dyn. contr., 4, 277-298, (1994) · Zbl 0825.93547
[10] Vincent, T.L.; Yu, J., Control of a chaotic system, Dyn. contr., 1, 35-52, (1991) · Zbl 0747.93071
[11] Gallias, Z., New method for stabilizing of unstable periodic orbits in chaotic systems, Int. J. bifurcat. chaos, 5, 1, 281-295, (1995) · Zbl 0885.58047
[12] Yu, X.; Chen, G.; Xia, Y.; Song, Y.; Cao, Z., An invariant-manifold-based method for chaos control, IEEE trans. circ. syst. I, 48, 8, 930-937, (2001) · Zbl 1003.93041
[13] Yamamoto, S.; Hino, T.; Ushio, T., Dynamic delayed feedback controllers for chaotic discrete time systems, IEEE trans. circ. syst. I, 48, 6, 785-789, (2001) · Zbl 1159.93329
[14] Lu, J.; Wei, R.; Wang, X.; Wang, Z., Backstepping control of discrete time chaotic systems with application to the henon systems, IEEE trans. circ. syst. I, 48, 11, 1359-1363, (2001) · Zbl 0994.37017
[15] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives, and applications, (1998), World Scientific Singapore
[16] Ott, E.; Grebogi, C.; Yorke, J.A., Controlling chaos, Phys. rev. lett., 64, 11, 1196-1199, (1990) · Zbl 0964.37501
[17] Tanaka, K.; Ikeda, T.; Wang, H.O., A unified approach to controlling chaos via LMI-based fuzzy control system design, IEEE trans. circ. syst. I, 45, 1021-1040, (1998) · Zbl 0951.93046
[18] Zeng, Y.; Singh, S.N., Adaptive control of chaos in Lorenz systems, Dyn. contr., 7, 143-154, (1997) · Zbl 0875.93191
[19] Ge SS, Lee TH, Wang C. Adaptive backstepping control of a class of chaotic systems. In: Proceedings of 38th IEEE conference on decision and control, Phoenix, Arizona, 1999. p. 714-9
[20] Narendra, K.S.; Annaswamy, A.M., Stable adaptive systems, (1989), Prentice Hall New Jersey · Zbl 0758.93039
[21] Middleton, R.; Goodwin, G.C.; Hill, D.; Mayne, D., Design issues in adaptive control, IEEE trans. automat. contr., 33, 50-58, (1988) · Zbl 0637.93040
[22] Feng, G., Analysis of a new algorithm for continuous time robust adaptive control, IEEE trans. automat. contr., 44, 1764-1768, (1999) · Zbl 0957.93075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.