PapersNo Access

DELAYED FEEDBACK CONTROL WITH STATE PREDICTOR FOR CONTINUOUS-TIME CHAOTIC SYSTEMS

HIROYUKI NAKAJIMA

Department of Electronic Engineering and Computer Science, School of Engineering, Kinki University, Higashi-Hiroshima, 739-2116, Japan

Search for more papers by this author

https://doi.org/10.1142/S0218127402004917Cited by:16 (Source: Crossref)

Abstract

We propose an application of state predictor to delayed feedback control (DFC) for continuous-time dynamical systems. First, we define the DFC for continuous-time systems clearly. Next, on the basis of this definition, we propose a DFC method with state-predictor to stabilize unstable equilibrium points in autonomous systems and derive a sufficient condition for stabilization. Then we extend this method to stabilizing unstable periodic orbits and also derive a sufficient condition for stabilization. Finally, we briefly discuss the relation between the conditions for stabilization of our methods and those of the dynamic DFC and the prediction-based feedback control for discrete-time systems.

Keywords:

References

M. Basso, R. Genesio and A. Tesi, IEEE Trans. CAS-I 44(10), 1023 (1997). Crossref, Google Scholar
M. Bassoet al., Int. J. Bifurcation and Chaos 8(8), 1699 (1998), DOI: 10.1142/S0218127498001376. Link, Web of Science, Google Scholar
M. E. Bleich and J. E. S. Socolar, Phys. Lett. A 210, 87 (1996). Crossref, Web of Science, Google Scholar
G. Chen and X. Yu, IEEE Trans. CAS-I 46(6), 767 (1999). Crossref, Google Scholar
T. Hino, S. Yamamoto and T. Ushio, Stabilization of unstable periodic orbits of chaotic discrete-time systems using prediction-based feedback control, Proc. AFSS2000 1 (2000) pp. 347–352. Google Scholar
M. Ikeda, H. Maeda and S. Kodama, SIAM J. Contr. 13(2), 304 (1975). Crossref, Web of Science, Google Scholar
W. Justet al., Phys. Rev. Lett. 78(2), 203 (1997). Crossref, Web of Science, Google Scholar
W. Justet al., Phys. Rev. Lett. 81(3), 562 (1998). Crossref, Web of Science, Google Scholar
W. Justet al., Phys. Rev. E 59(3), 2826 (1999). Crossref, Web of Science, Google Scholar
W. Justet al., Phys. Lett. A 254, 158 (1999). Crossref, Web of Science, Google Scholar
W. Justet al., Phys. Rev. E 61(5), 5045 (2000). Crossref, Web of Science, Google Scholar
H. Kokameet al., State difference feedback can stabilize uncertain steady states, Proc. American Control Conf. (2000) pp. 1370–1374. Google Scholar
K. Konishi and H. Kokame, Phys. Lett. A 248(5 & 6), 359 (1998). Crossref, Web of Science, Google Scholar
K. Konishi, M. Ishii and H. Kokame, IEEE Trans. CAS-I 46(10), 1285 (1999). Crossref, Google Scholar
A. Z. Manitius and A. W. Olbrot, IEEE Trans. AC-24(4), 541 (1979). Google Scholar
H. Nakajima, Phys. Lett. A 232(3 & 4), 207 (1997). Crossref, Web of Science, Google Scholar
H. Nakajima and Y. Ueda, Physica D 111, 143 (1998). Crossref, Web of Science, Google Scholar
H. Nakajima and Y. Ueda, Phys. Rev. E 58(2-A), 1757 (1998). Crossref, Web of Science, Google Scholar
H. Nakajima, A generalization of the extended delayed feedback control for chaotic systems, Proc. COC2000 2 (2000) pp. 209–212. Google Scholar
K. Pyragas, Phys. Lett. A 170, 421 (1992). Crossref, Web of Science, Google Scholar
K. Pyragas, Phys. Lett. A 206, 323 (1995). Crossref, Web of Science, Google Scholar
K. Pyragas, Phys. Rev. Lett. 86(11), 2265 (2001). Crossref, Web of Science, Google Scholar
H. G. Schuster and M. B. Stemmler, Phys. Rev. E 56(6), 6410 (1997). Crossref, Web of Science, Google Scholar
J. E. S. Socolar, D. W. Sukow and D. J. Gauthier, Phys. Rev. E 50(4), 3245 (1994). Crossref, Web of Science, Google Scholar
Y. P. Tian and X. Yu, J. Franklin Instit. 337, 771 (2000). Crossref, Web of Science, Google Scholar
Y. P. Tian and G. Chen, Phys. Lett. A 284, 31 (2001). Crossref, Web of Science, Google Scholar
T. Ushio, IEEE Trans. CAS-I 43(9), 815 (1996). Crossref, Google Scholar
T. Ushio and S. Yamamoto, Phys. Lett. A 247, 112 (1998). Crossref, Web of Science, Google Scholar
T. Ushio and S. Yamamoto, Phys. Lett. A 264, 30 (1999). Crossref, Web of Science, Google Scholar
Watanabe, K. [1993] "Control for systems with time-delay," SICE (in Japanese) . Google Scholar
D. Xu and S. R. Bishop, Phys. Lett. A 210, 273 (1996). Crossref, Web of Science, Google Scholar
Yamamoto, S., Hino, T. & Ushio, T. [1999] "Controlling chaos by dynamic delayed feedback," Technical Report of IEICE NLP99-28, 17–22 (in Japanese) . Google Scholar
S. Yamamoto, T. Hino and T. Ushio, IEEE Trans. CAS-I 48(6), 785 (2001). Crossref, Google Scholar
X. Yu, IEEE Trans. CAS-I 46(11), 1408 (1999). Google Scholar