Distributed Control Design for Spatially Interconnected Systems

IEEE Transactions on Automatic Control

Volumn 48, Issue 9, 2003, Pages 1478-1495

  D'Andrea, Raffaello ^a   Dullerud, Geir E ^b  

^a Department of Population Medicine and Diagnostic Sciences   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Distributed control; H ; Interconnected systems; Linear matrix inequalities (LMIs)

Indexed keywords

CONTROL EQUIPMENT; DISCRETE TIME CONTROL SYSTEMS; MATRIX ALGEBRA;

DISTRIBUTED CONTROL DESIGN;

LARGE SCALE SYSTEMS;

EID: 0141750576     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.816954     Document Type: Article

References (44)

1. P. Apkarian and P. Gahinet, "A convex characterization of gain-scheduled H-infinity controllers," IEEE Trans. Automat, Contr., vol. 40, pp. 853-864, May 1995.
2. G. Balas, J. Doyle, K. Glover, A. Packard, and R. Smith, The μ Analysis and Synthesis Toolbox. Natick, MA: The MathWorks Inc., 1991.
3. B. Bamieh, R Paganini, and M. Dahleh, "Distributed control of spatially invariant systems," IEEE Trans. Automat. Contr., vol. 47, pp. 1091-1118, July 2002.
4. S. P. Banks, State-Space and Frequency Domain Methods in the Control of Distributed Parameter Systems. New York: Peter Peregrinus, 1983.
5. C. L. Beck and R. D'Andrea, "Simplification of spatially distributed systems," Proc. IEEE Conf. Decision Control, pp. 620-625, 1999.
6. B. Bollobas, Linear Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1990.
7. S. P. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994. SIAM studies in applied mathematics.
8. R. W. Brockett and J. L. Willems, "Discretized partial differential equations: Examples of control systems defined on modules," Automatica, vol. 10, pp. 507-515, 1974.
9. D. F. Chichka and J. L. Speyer, "Solar-powered, formation-enhanced aerial vehicle system for sustained endurance," in Proc. Amer. Control Conf., 1998, pp. 684-688.
10. R. F. Curtain and H. J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory. New York: Springer-Verlag, 1995.
11. R. D'Andrea, "A linear matrix inequality approach to decentralized control of distributed parameter systems," in Proc. Amer. Control Conf., 1998, pp. 1350-1354.
12. _, "Linear matrix inequalities, multidimensional system optimization, and control of spatially distributed systems: An example," in Proc. Amer. Control Conf., 1999, pp. 2713-2717.
13. _, "Software for modeling, analysis, and control design for multidimensional systems," Proc. IEEE Int. Symp. Computer-Aided Control System Design, pp. 24-27, 1999.
14. _, "Extension of Parrott's theorem lo nondefinite scalings," IEEE Trans. Automat. Contr., vol. 45, pp. 937-940, May 2000.
15. R. D'Andrea and C. Beck, "Temporal discretization of spatially distributed systems," Proc. IEEE Conf. Decision Control, pp. 197-202, 1999.
16. R. D'Andrea and R. S. Chandra, "Control of discrete time interconnected systems," Proc. IEEE Conf. Decision Control, pp. 240-245, 2002.
17. R. D'Andrea, C. Langbort, and R. Chandra, "A state space approach to control of interconnected systems," in Mathematical Systems Theory in Biology, Communication, Computation and Finance, ser. IMA Book Series, J. Rosenthal, Ed. New York: Springer-Verlag, 2003.
18. J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, "State-space solutions to standard H2 and H-infinity control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831-847, Aug. 1989.
19. G. Dullerud and R. D'Andrea, "Distributed control of inhomogeneous systems, with boundary conditions," Proc. IEEE Conf. Decision Control, pp. 186-190, 1999.
20. G. E. Dullerud and R. D'Andrea, "Distributed control of heterogeneous systems," IEEE Trans. Automat. Contr., submitted for publication.
21. G. E. Dullerud, R. D'Andrea, and S. Lall, "Control of spatially varying distributed systems," Proc. IEEE Conf. Decision Control, pp. 1889-1893, 1998.
22. J. M. Fowler and R. D'Andrea, "Distributed control of close formation flight," Proc. IEEE Conf. Decision Control, pp. 2972-2977, 2002.
23. _, "A formation flight experiment for research in control of interconnected systems," Control Syst. Mag., 2003, to be published.
24. P. Gahinet and P. Apkarian, "A linear matrix inequality approach to H-∞ control," Int. J. Robust Nonlinear Control, vol. 4, pp. 421-448, 1994.
25. P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, The LMI Control Toolbox. Natick, MA: The MathWorks, Inc., 1995.
26. D. Gorinevsky and G. Stein, "Structured uncertainty analysis of robust stability for spatially distributed systems," in Proc. IEEE Conf. Decision Control, 2000.
27. J. Kulkarni, R. D'Andrea, and B. Brandl, "Application of distributed control techniques to the adaptive secondary mirror of Cornell's large atacama telescope," presented at the SPIE Astronomical Telescopes Instrumentation Conf., 2002.
28. C. Langbort and R. D'Andrea, "Imposing boundary conditions for spatially interconnected systems," presented at the Amer. Control Conf., 2003.
29. J. M. Maciejowski, Multivariable Feedback Design. Reading, MA: Addison-Wesley, 1989.
30. S. M. Melzer and B. C. Kuo, "Optimal regulation of systems described by a countably infinite number of objects," Automatica, vol. 7, pp. 359-366, 1971.
31. M. Napoli and B. Bamieh, "Modeling and observed design for an array of electrostatically actuated microcantilevers," Proc. IEEE Conf. Decision. Control, pp. 4274-4279, 2001.
32. A. Packard, "Gain scheduling via linear fractional transformations," Syst. Control Lett., vol. 22, no. 2, pp. 79-92, 1994.
33. A. Packard and J. C. Doyle, "The complex structured singular value," Automatica, vol. 29, no. 1, pp. 71-109, 1993.
34. A. Packard, K. Zhou, P. Pandey, and G. Becker, "A collection of robust control problems leading to LMIs," Proc. IEEE Conf. Decision Control, pp. 1245-1250, 1991.
35. F. Paganini, "A recursive information flow system for distributed control arrays," in Proc. Amer. Control Conf., 1999, pp. 3821-3825.
36. A. Rantzer, "On the Kaiman-Yakubovich-Popov lemma," Syst. Control Lett., vol. 28, no. 1, pp. 7-10, 1996.
37. H. Raza and P. Ioannou, "Vehicle following control design for automated highway systems," IEEE Control Syst., vol. 16, pp. 43-60, June 1996.
38. M. G. Safonov and D. J. N. Limbeer, "Simplyfing the H-infinity theory via loop shifting," Proc. IEEE Conf. Decision Control, 1988.
39. G. B. Shaw, D. W. Miller, and D. E. Hastings, "The generalized information network analysis methodology for distributed satellite systems," Ph.D. dissertation, Mass. Inst. Technol., Cambridge, MA, 1998.
40. G. E. Stewart, "Two-dimensional loop shaping controller design for paper machine cross-directional processes," Ph.D. dissertation, Univ. British Columbia, Vancouver, BC, Canada, 2000.
41. M. E. Taylor, Partial Differential Equations I: Basic Theory. New York: Springer-Verlag. 1996.
42. J. D. Wolfe, D. F. Chichka, and J. L. Speyer, "Decentralized controllers for unmmaned aerial vehicle formation flight," Amer. Inst. Aeronautics Astronautics, 1996.
43. F. Wu and E. Yildizoglu, "A distributed gain-scheduling control design for a flexible beam problem," in Proc. Amer. Control Conf., 2002, pp. 3174-3179.
44. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River. NJ: Prentice-Hall, 1995.