Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems

We propose a method of robust nonlinear H/sub /spl infin// master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the L/sub 2/-gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite L/sub 2/-gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.

[1]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[2]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[3]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[4]  P. Moylan,et al.  Connections between finite-gain and asymptotic stability , 1980 .

[5]  Elijah Polak,et al.  Nondifferentiable optimization algorithm for designing control systems having singular value inequalities , 1982, Autom..

[6]  L. Chua,et al.  The double scroll family , 1986 .

[7]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[8]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[9]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[10]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .

[11]  Peter E. Kloeden,et al.  The Numerical Solution of Nonlinear Stochastic Dynamical Systems: a Brief Introduction , 1991 .

[12]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[13]  Leon O. Chua,et al.  Stability analysis of generalized cellular neural networks , 1993, Int. J. Circuit Theory Appl..

[14]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[15]  Leon O. Chua,et al.  The CNN paradigm , 1993 .

[16]  Leon O. Chua,et al.  TRANSITIONS IN DYNAMICAL REGIMES BY DRIVING: A UNIFIED METHOD OF CONTROL AND SYNCHRONIZATION OF CHAOS , 1993 .

[17]  L. Chua,et al.  HYPERCHAOTIC ATTRACTORS OF UNIDIRECTIONALLY-COUPLED CHUA’S CIRCUITS , 1994 .

[18]  M. Hasler.  Synchronization principles and applications , 1994 .

[19]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[20]  Leon O. Chua,et al.  Chua's circuit 10 years later , 1994, Int. J. Circuit Theory Appl..

[21]  L. Chua,et al.  A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS , 1994 .

[22]  Johan A. K. Suykens,et al.  Artificial Neural Networks for Modeling and Control of Non-Linear Systems , 1995 .

[23]  Leon O. Chua,et al.  ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS , 1996 .

[24]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[25]  J. Suykens,et al.  Nonlinear H/sub /spl infin// synchronization of Lur'e systems: dynamic output feedback case , 1997 .

[26]  L. Chua,et al.  Absolute Stability Theory and the Synchronization Problem , 1997 .

[27]  J. Suykens,et al.  n-Double Scroll Hypercubes in 1-D CNNs , 1997 .

[28]  J. Suykens,et al.  Absolute stability theory and master-slave synchronization , 1997 .

[29]  Leon O. Chua,et al.  A family of n-scroll attractors from a generalized Chua's circuit , 1997 .

[30]  J. Suykens,et al.  Nonlinear H∞ Synchronization of Chaotic Lur'e Systems , 1997 .

[31]  J. Suykens,et al.  Master-slave synchronization using dynamic output feedback , 1997 .

[32]  Leon O. Chua,et al.  Nonlinear H$_{\infty}$ synchronization of chaotic Lur'e systems , 1997 .