Chua’s Circuit Regulation Using a Nonlinear Adaptive Feedback Technique

Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.





References:
[1] E. J. Altman, "Bifurcation analysis of Chua-s circuit with applications
for low-level visual sensing," J. Circuits Syst. Comput., vol. 3, pp. 63-
92, Mar. 1993.
[2] Leon 0. Chua, Chai Wah Wu, Anshan Huang, and Guo-Qun Zhong, "A
Universal Circuit for Studying and Generating Chaos" IEEE Tra. On
circuit and system-I: VOL. 40, NO. IO, october 1993. pp 732-744.
[3] B. R. Andrievskii and A. L. Fradkov, "Control of Chaos: Methods and
Applications. I. Methods" Automation and Remote Control, Vol. 64, No.
5, 2003, pp. 673-713.
[4] A. Razminia "Adaptive Control of Chaotic systems, case study: Chua-s
circuit" M.S thesis, Submitted in Shahrood University of technology.
Fall 2006.
[5] Huang W. Stabilizing nonlinear dynamical systems by an adaptive
adjustment mechanism. Phys Rev E 2000;61:R1012-5.
[6] Y. Zheng," Controlling chaos based on an adaptive adjustment
mechanism" Chaos, Solitons and Fractals , Elsevier 2005.
[7] T. Matsumoto, "A chaotic attractor from ChuaÔÇÿs circuit," IEEE Trans.
Circuits Sysr., vol. CAS-31, pp. 1055-1058, 1984.
[8] L. 0. Chua, "The genesis of Chua-s circuit," Archiv Elektronik
Ubertragungstechnik, vol. 46, no. 4, pp. 250-257, 1992.
[9] G. Q. Zhong and F. Ayrom, "Experimental confirmation of chaos from
Chua-s circuit," Inr. J. Circuit Theory Applications, vol. 13, no. 1, pp.
93-98, 1985.
[10] G. Q. Zhong and F. Ayrom, "Periodicity and chaos in ChuaÔÇÿs circuit,"
IEEE Trans. Circuits Sys., vol. CAS-32, pp. 501-503, 1985.
[11] T. Matsumoto, L. 0. Chua, and M. Komuro, "The double scroll," IEEE
Trans. Circuits Sys., vol. CAS-32, pp. 797-818, 1985.
[12] M. Komuro, R. Tokunaga, T. Matsumoto, L. 0. Chua, and A. Hotta,
"Global bifurcation analysis of the double scroll circuit," Int. J.
Bifurcation Chaos, vol. 1, no. 1, pp, 139-182, 1991.
[13] L. 0. Chua, M. Komuro, and T. Matsumoto, "The double scroll family,
parts I and 11," IEEE Trans. Circuits Sys., vol. CAS-33, pp. 1073-1 118,
1986.
[14] L. P. Shil-nikov, "Chua-s circuit: Rigorous results and future problems,"
IEEE Trans. Circuits Sys. -I: Fundamental Theory Applications, this
issue.
[15] V. N. Belykh and L. 0. Chua, "New type of strange attractor related to
the Chua-s circuit," J. Circuits Sysr. Comput., vol. 3, pp. 361-374, June
1993.
[16] L. 0. Chua and G. N. Lin, "Canonical realization of Chua-s circuit
family," IEEE Trans. Circuits Syst., vol. 37, pp. 885-902, 1990.