Model reference adaptive control of structurally perturbed second‐order distributed parameter systems

We consider a class of second-order distributed parameter systems with structured perturbations in which both partial position and partial velocity measurements are assumed available. The control objective is to design an adaptive controller so that the plant state follows the state of a second-order reference model despite the presence of the perturbation terms. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Marius Tucsnak,et al.  How to Get a Conservative Well-Posed Linear System Out of Thin Air. Part II. Controllability and Stability , 2003, SIAM J. Control. Optim..

[3]  Ruth F. Curtain,et al.  ADAPTIVE COMPENSATORS FOR PERTURBED POSITIVE REAL INFINITE-DIMENSIONAL SYSTEMS , 2003 .

[4]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[5]  P. Daoutidis,et al.  Robust control of hyperbolic PDE systems , 1998 .

[6]  Masahiro Oya,et al.  Stabilization of infinite-dimensional semilinear second-order systems by position feedback , 2005, IMA J. Math. Control. Inf..

[7]  David S. Gilliam,et al.  Global solvability for damped abstract nonlinear hyperbolic systems , 1997, Differential and Integral Equations.

[8]  J. Wloka,et al.  Partial differential equations: Strongly elliptic differential operators and the method of variations , 1987 .

[9]  Michael A. Demetriou,et al.  Model Reference Adaptive Control of Distributed Parameter Systems , 1998 .

[10]  Michael A. Demetriou,et al.  On-Line Parameter Estimation for Infinite-Dimensional Dynamical Systems , 1997 .

[11]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[12]  Kazufumi Ito,et al.  Adaptive observers for structurally perturbed positive real delay systems , 1998 .

[13]  Miroslav Krstic.  On global stabilization of Burgers’ equation by boundary control , 1999 .

[14]  Michael A. Demetriou,et al.  An adaptive control scheme for a class of second order distributed parameter systems with structured perturbations , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  Marius Tucsnak,et al.  How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance , 2003 .

[16]  Panagiotis D. Christofides,et al.  Robust output feedback control of quasi-linear parabolic PDE systems , 1999 .

[17]  Ruth F. Curtain,et al.  Adaptive observers for slowly time varying infinite dimensional systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[18]  B. Jacob,et al.  Minimum-Phase Infinite-Dimensional SISO Second-Order Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  Yury Orlov,et al.  Robust stabilization of infinite-dimensional systems using sliding-mode output feedback control , 2004 .

[20]  S. Reich,et al.  Existence and Uniqueness of Solutions to a Second Order Nonlinear Nonlocal Hyperbolic Equation , 2001 .

[21]  Toshihiro Kobayashi.  Low-gain adaptive stabilization of infinite-dimensional second-order systems , 2002 .

[22]  M. Krstić,et al.  Backstepping observers for a class of parabolic PDEs , 2005, Syst. Control. Lett..

[23]  Michael A. Demetriou,et al.  Natural second-order observers for second-order distributed parameter systems , 2004, Syst. Control. Lett..

[24]  Toshihiro Kobayashi.  Stabilization of infinite‐dimensional second‐order system by adaptive PI‐controllers , 2001 .

[25]  M. Krstić,et al.  Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation , 2001 .

[26]  Toshihiro Kobayashi,et al.  Adaptive Regulator Design for a Class of Infinite-Dimensional Second-Order Systems☆ , 2001 .

[27]  Kaïs Ammari,et al.  Stabilization of second order evolution equations by a class of unbounded feedbacks , 2001 .

[28]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[29]  Ephrahim Garcia,et al.  A Self-Sensing Piezoelectric Actuator for Collocated Control , 1992 .

[30]  Miroslav Krstic,et al.  Closed-form boundary State feedbacks for a class of 1-D partial integro-differential equations , 2004, IEEE Transactions on Automatic Control.

[31]  Michael A. Demetriou,et al.  Adaptive identification of second-order distributed parameter systems , 1994 .

[32]  Ruth F. Curtain,et al.  Adaptive observers for structurally perturbed infinite dimensional systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[33]  Harvey Thomas Banks,et al.  Smart material structures: Modeling, estimation, and control , 1996 .