A State Space Approach to Control of Interconnected Systems

We present a state space approach to controlling systems with a highly structured interconnection topology. It is shown that by capturing these systems as fractional transformations on temporal and spatial operators, many standard results in control — such as the bounded real lemma, H-infinity optimization, and robustness analysis — can be generalized accordingly. The state space formulation yields conditions that can be expressed as linear matrix inequalities.

[1]  Raffaello D'Andrea,et al.  Imposing boundary conditions for a class of spatially-interconnected systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[2]  Xing-Gang Yan,et al.  Decentralized Output Feedback Robust Control for Nonlinear Large-scale Systems , 1998, Autom..

[3]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

[4]  Graeme B. Shaw,et al.  The generalized information network analysis methodology for distributed satellite systems , 1999 .

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

[6]  Max Donath,et al.  American Control Conference , 1993 .

[7]  Peter Seiler,et al.  Mesh stability of look-ahead interconnected systems , 2002, IEEE Trans. Autom. Control..

[8]  R. D'Andrea,et al.  Distributed control of close formation flight , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Geir E. Dullerud,et al.  A new approach for analysis and synthesis of time-varying systems , 1999, IEEE Trans. Autom. Control..

[10]  J. Hedrick,et al.  String stability of interconnected systems , 1996, IEEE Trans. Autom. Control..

[11]  R. D'Andrea,et al.  Software for modeling, analysis, and control design for multidimensional systems , 1999, Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404).

[12]  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).

[13]  M. Fliess,et al.  QUELQUES PROPRIETES STRUCTURELLES DES SYSTEMES LINEAIRES A RETARDS CONSTANTS , 1994 .

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

[15]  Gregory E. Stewart.  Two dimensional loop shaping controller design for paper machine cross-directional processes , 2000 .

[16]  R. D'Andrea,et al.  Control of interconnected systems of finite spatial extent , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[17]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  D. F. Chichka,et al.  Solar-powered, formation-enhanced aerial vehicle systems for sustained endurance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[19]  G.E. Dullerud,et al.  Distributed control of inhomogeneous systems, with boundary conditions , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  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).

[21]  Stephen P. Banks.  State-Space and Frequency Domain Methods in the Control of Distributed Parameter Systems , 1983 .

[22]  Geir E. Dullerud,et al.  Distributed control design for spatially interconnected systems , 2003, IEEE Trans. Autom. Control..

[23]  R. D'Andrea,et al.  Temporal discretization of spatially distributed systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[24]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[25]  R. D'Andrea.  Linear matrix inequalities, multidimensional system optimization, and control of spatially distributed systems: an example , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[26]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[27]  Richard D. Braatz,et al.  Robust performance of cross-directional basis-weight control in paper machines , 1993, Autom..

[28]  O. Toker,et al.  On the complexity of purely complex μ computation and related problems in multidimensional systems , 1998, IEEE Trans. Autom. Control..

[29]  Bassam Bamieh,et al.  Modeling and observer design for an array of electrostatically actuated microcantilevers , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[30]  R. D'Andrea,et al.  Control of spatially varying distributed systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[31]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[32]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

[33]  Martín Velasco-Villa,et al.  The disturbance decoupling problem for time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[34]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[35]  Andrew Packard,et al.  The complex structured singular value , 1993, Autom..

[36]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[37]  Petros A. Ioannou,et al.  Vehicle Following Control Design for Automated Highway Systems [25 Years Ago] , 1996, IEEE Control Systems.

[38]  Martín Velasco-Villa,et al.  The structure of nonlinear time delay systems , 2000, Kybernetika.

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

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

[41]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[42]  Pramod P. Khargonekar,et al.  On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings , 1981, CDC 1981.

[43]  Raffaello D'Andrea,et al.  Extension of Parrott's theorem to nondefinite scalings , 2000, IEEE Trans. Autom. Control..

[44]  Geir E. Dullerud,et al.  Distributed control of heterogeneous systems , 2004, IEEE Transactions on Automatic Control.

[45]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[46]  R. Brockett,et al.  Discretized partial differential equations: Examples of control systems defined on modules , 1974, Autom..

[47]  G. Stein,et al.  Structured uncertainty analysis of robust stability for spatially distributed systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[48]  M. Morari,et al.  Computational complexity of μ calculation , 1994, IEEE Trans. Autom. Control..