Distributed control of spatially reversible interconnected systems with boundary conditions

SIAM Journal on Control and Optimization

Volumn 44, Issue 1, 2006, Pages 1-28

  Langbort, Cédric ^a   D'Andrea, Raffaello ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b School of Chemical and Molecular Engineering   (United States)

Author keywords

Boundary conditions; Spatially distributed control; Symmetric systems

Indexed keywords

FINITE EXTENT SYSTEMS; WELL-POSEDNESS;

PARTIAL DIFFERENTIAL EQUATIONS; SYSTEM STABILITY;

LARGE SCALE SYSTEMS;

EID: 33244484833     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902415803     Document Type: Article

References (22)

1. B. BAMIEH, F. PAGANINI, AND M. DAHLEH, Distributed control of spatially invariant systems, IEEE Trans. Automat. Control, 47 (2002), pp. 1091-1118.
2. H. T. BANKS, R. C. SMITH, AND Y. WANG, Smart Material Structures Modeling, Estimation and Control, John Wiley and Sons, New York, 1996.
3. R. W. BROCKETT AND J. L. WILLEMS, Discretized partial differential equations: Examples of control systems defined on modules, Automatica, 10 (1974), pp. 507-515.
4. R. F. CURTAIN AND H. J. ZWART, An Introduction to Infinite-Dimensional Linear System Theory, Texts in Applied Mathematics 21, Springer-Verlag, Berlin, New York, 1995.
5. R. D'ANDREA AND G. E. DULLERUD, Distributed control of spatially interconnected systems, IEEE Trans. Automat. Control, 48 (2003), pp. 1478-1495.
6. B. DIONNE, M. GOLUBITSKY, AND I. STEWART, Coupled cells with internal symmetry I and II, Nonlinearity, 9 (1996), pp. 559-599.
7. G. E. DULLERUD AND F. PAGANINI, A Course in Robust Control Theory, Texts in Applied Mathematics 36, Springer-Verlag, Berlin, New York, 1999.
8. G. E. DULLERUD, R. D'ANDREA, AND S. G. LALL, Control of spatially varying distributed systems, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 1889-1893.
9. L. C. EVANS, Partial Differential Equations, Graduate Studies in Mathematics 19, AMS, Providence, RI, 1998.
10. F. FAGNANI AND J. C. WILLEMS, Representations of symmetric linear dynamical systems, SIAM J. Control Optim., 31 (1993), pp. 1267-1293.
11. V. KAPILA, A. G. SPARKS, J. BUFFINGTON, AND Q. YAN, Spacecraft formation flying: Dynamics and control, in Proceedings of the American Control Conference, San Diego, CA, 1999, pp. 4137-4141.
12. P. P. KHARGONEKAR, K. POOLLA, AND A. TANNENBAUM, Robust control of linear time-invariant plants using periodic compensation, IEEE Trans. Automat. Control, 27 (1982), pp. 627-638.
13. D. LAUGHLIN, M. MORARI, AND R. D. BRAATZ, Robust performance of cross-directional basis-weight control in paper machines, Automatica, 29 (1993), pp. 1395-1410.
14. ∞ robustification of a paper machine cross-directional control system, in Proceedings of the American Control Conference, 2001, Arlington, VA, pp. 2203-2209.
15. F. PAGANINI AND B. BAMIEH, Decentralization properties of optimal distributed controllers, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 1877-1882.
16. L. QIU, On the robustness of symmetric systems, Systems Control Lett., 27 (1996), pp. 187-190.
17. E. D. SONTAG, Linear systems over commutative rings: A survey, Ricerche Automat., 7 (1976), pp. 1-34.
18. G. E. STEWART, Analysis and Design of Boundary Conditions for a Spatially Distributed Control System, Tech. report, Honeywell Industrial Control, 2001.
19. D. SWAROOP AND J. K. HEDRICK, Constant spacing strategies for platooning in automated highway systems, J. Dynam. Systems, Measurement Control, 121 (1999), pp. 462-470.
20. M. E. TAYLOR, Partial Differential Equations I: Basic Theory, Springer-Verlag, Berlin, New York, 1996.
21. G. YANG, J. L. WANG, AND Y. C. SOH, Decentralized fixed modes of symmetric systems, in Proceedings of the American Control Conference, Arlington, VA, 2001, pp. 3134-3135.
22. J. D. WOLFE, D. F. CHICHKA, AND J. L. SPEYER, Decentralized Controllers for Unmanned Aerial Vehicle Formation Flight, Tech. report 96-3833, American Institute of Aeronautics and Astronautics, Reston, VA, 1996.