An Asymptotic Tracking Problem and Its Application

This paper deals with an asymptotic tracking problem for the Chua's circuit. We first show that the control problem for the Chua's circuit can be formulated as the global robust output regulation problem for nonlinear systems in output feedback form. Then we show that the solvability conditions for the output regulation problem for the Chua's circuit are all satisfied. Finally, an output feedback control law is designed for the Chua's circuit. The control law enables, in the presence of large parameter variations, the output of the circuit to track a class of sinusoidal signals with arbitrary amplitudes and initial phases while maintaining the global stability of the closed-loop system.

[1]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

[2]  Jie Huang,et al.  Adaptive Robust Stabilization of Output Feedback Systems With Application to Chua's Circuit , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  G. Zhong.  Implementation of Chua's circuit with a cubic nonlinearity , 1994 .

[4]  Teh-Lu Liao,et al.  Control of Chua's circuit with a cubic nonlinearity via nonlinear linearization technique , 1998 .

[5]  Xudong Ye,et al.  Decentralized adaptive output regulation for a class of large-scale nonlinear systems , 2003, IEEE Trans. Autom. Control..

[6]  Gang Feng,et al.  Output regulation of discrete-time piecewise-linear systems with application to controlling chaos , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[8]  Jie Huang,et al.  A general framework for tackling the output regulation problem , 2004, IEEE Transactions on Automatic Control.

[9]  Sahjendra N. Singh,et al.  Adaptive Feedback Linearizing Control of Chua's Circuit , 2002, Int. J. Bifurc. Chaos.

[10]  Guanrong Chen,et al.  Controlling Chua's global unfolding circuit family , 1993 .

[11]  Gang Feng,et al.  Output Tracking of Piecewise-Linear Systems via Error Feedback Regulator With Application to Synchronization of Nonlinear Chua's Circuit , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  Guo-Ping Jiang,et al.  Stabilizing unstable equilibria of chaotic systems from a State observer approach , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[14]  L. Chua.  The Genesis of Chua's circuit , 1992 .

[15]  Jie Huang,et al.  Global robust output regulation for output feedback systems , 2003, IEEE International Conference on Robotics, Intelligent Systems and Signal Processing, 2003. Proceedings. 2003.

[16]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems. I. Linear parameterization , 1993, IEEE Trans. Autom. Control..

[17]  A. Isidori,et al.  Global robust output regulation for a class of nonlinear systems , 2000 .