Robust Adaptive Control of a Class of Nonlinear Systems and Its Applications

This paper addresses a global robust adaptive control problem for a class of uncertain nonlinear systems by output feedback control. The problem will be solved by the internal model design method. As our problem formulation includes the chaotic control and synchronization problem of some typical nonlinear systems as special cases, a direct application of our main result will lead to the solution of some interesting control problems such as the global disturbance rejection of the FitzHugh–Nagumo system and the robust output synchronization of the generalized Lorenz system and the harmonic system.

[1]  X. Guan,et al.  Adaptive control for chaotic systems , 2004 .

[2]  Antonio Loria,et al.  ADAPTIVE CONTROLLED SYNCHRONIZATION OF CHAOTIC SYSTEMS , 2006 .

[3]  Xiaohua Xia,et al.  Adaptive Synchronization for Generalized Lorenz Systems , 2008, IEEE Transactions on Automatic Control.

[4]  Jie Huang,et al.  Parameter convergence and minimal internal model with an adaptive output regulation problem , 2009, Autom..

[5]  D. Obradovic,et al.  Global control of Lorenz chaos , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[6]  Jie Huang,et al.  Remarks on the robust output regulation problem for nonlinear systems , 2001, IEEE Trans. Autom. Control..

[7]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[8]  Henrikus J. C. Huijberts,et al.  Linear Controllers for the Stabilization of Unknown Steady States of Chaotic Systems , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Sunil K. Agrawal,et al.  Differential flatness and cooperative tracking in the Lorenz system , 2003, Proceedings of the 2003 American Control Conference, 2003..

[10]  Antonio Loría,et al.  Adaptive Tracking Control of Chaotic Systems With Applications to Synchronization , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[12]  Lorenzo Marconi,et al.  Semi-global nonlinear output regulation with adaptive internal model , 2001, IEEE Trans. Autom. Control..

[13]  Yu Liang,et al.  Gain Scheduling Synchronization Method for Quadratic Chaotic Systems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  A. Isidori,et al.  Semiglobal nonlinear output regulation with adaptive internal model , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[15]  E. Lorenz Deterministic nonperiodic flow , 1963 .

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

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

[18]  Frank L. Lewis,et al.  An Asymptotic Tracking Problem and Its Application , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  C. Byrnes Output Regulation of Uncertain Nonlinear Systems , 1997 .

[20]  John Rinzel,et al.  A Formal Classification of Bursting Mechanisms in Excitable Systems , 1987 .

[21]  C.-J. Richard Shi,et al.  Sliced Message Passing: High Throughput Overlapped Decoding of High-Rate Low-Density Parity-Check Codes , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Jordi Madrenas,et al.  Implementation of compact VLSI FitzHugh-Nagumo neurons , 2008, 2008 IEEE International Symposium on Circuits and Systems.

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

[24]  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.

[25]  Xinghuo Yu,et al.  Adaptive control of chaotic dynamical systems using invariant manifold approach , 2000 .

[26]  Moez Feki Model-Independent Adaptive Control of Chua's System with cubic Nonlinearity , 2004, Int. J. Bifurc. Chaos.

[27]  Julio R. Banga,et al.  Robust feed-back control of travelling waves in a class of reaction–diffusion distributed biological systems , 2008 .

[28]  Wen Yu Passive equivalence of chaos in Lorenz system , 1999 .