Convex synthesis of localized controllers for spatially invariant systems

A method is presented to impose localization in controller design for distributed arrays with underlying spatial invariance. The method applies to either state or output feedback problems where the performance objective (e.g., stabilization, H"2 or H"~ control) can be stated in terms of the search for a suitable Lyapunov matrix over spatial frequency. By restricting this matrix to be constant across frequency, controller localization can be naturally imposed. Thus, we obtain sufficient conditions for the existence of a controller with the desired localization and performance, which take the form of linear matrix inequalities (LMIs) over spatial frequency. For one-dimensional arrays, we further show how to convert these conditions exactly to finite-dimensional LMIs by means of the Kalman-Yakubovich-Popov Lemma; extensions to the multi-dimensional case are also discussed.

[1]  P. Khargonekar,et al.  Mixed H/sub 2//H/sub infinity / control: a convex optimization approach , 1991 .

[2]  Thomas Bewley,et al.  Flow control: new challenges for a new Renaissance , 2001 .

[3]  Dimitry M. Gorinevsky,et al.  Performance analysis of cross-direction process control using multivariable and spectral models , 2000, IEEE Trans. Control. Syst. Technol..

[4]  Fernando Paganini,et al.  Distributed control of spatially invariant systems , 2002, IEEE Trans. Autom. Control..

[5]  C. Scherer,et al.  Lecture Notes DISC Course on Linear Matrix Inequalities in Control , 1999 .

[6]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[7]  Izumi Masubuchi,et al.  LMI-based controller synthesis: A unified formulation and solution , 1998 .

[8]  A. Rantzer.  On the Kalman-Yakubovich-Popov lemma , 1996 .

[9]  Geir E. Dullerud,et al.  Convex ` 2 Synthesis for Multidimensional SystemsRa aello , 1998 .

[10]  Fernando Paganini.  A recursive information flow system for distributed control arrays , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Chih-Ming Ho,et al.  REVIEW: MEMS and Its Applications for Flow Control , 1996 .

[12]  F. Paganini,et al.  Decentralization properties of optimal distributed controllers , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[13]  van der,et al.  Finite difference methods for solving partial differential equations , 1968 .

[14]  S. Lall,et al.  Convex /spl Lscr//sub 2/ synthesis for multidimensional systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[15]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[16]  Kun Li,et al.  Large segmented telescopes , 2000 .

[17]  Mario Innocenti,et al.  Autonomous formation flight , 2000 .

[18]  R. D'Andrea,et al.  A linear matrix inequality approach to decentralized control of distributed parameter systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[19]  S. Melzer,et al.  Optimal regulation of systems described by a countably infinite number of objects , 1971 .

[20]  Jian-Xin Xu,et al.  Controller design for a single-link flexible smart materials robot with experimental tests , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).