A PDE viewpoint on basic properties of coordination algorithms with symmetries

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 5139-5144

  Sarlette, Alain ^a   Sepulchre, Rodolphe ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL ENGINEERING;

CONTROL APPLICATIONS; COORDINATION ALGORITHMS; DISCRETE APPROXIMATION; DISTRIBUTED SYSTEMS; FUNDAMENTAL PROPERTIES; INTERACTION MATRICES; LOCAL INTERACTIONS; SPATIAL INVARIANCE;

DISTRIBUTED DATABASE SYSTEMS;

EID: 77950824982     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400570     Document Type: Conference Paper

References (27)

1. B. Bamieh, M. Jovanovic, P. Mitra, and S. Patterson. Effect of topological dimension on rigidity of vehicle formations: fundamental limitations of local feedback. Proc. 48th IEEE Conf. Decision and Control, pages 369-374, 2008.
2. B. Bamieh, F. Paganini, and M.A. Dahleh. Distributed control of spatially invariant systems. IEEE Trans. Automatic Control, 47(7):1091-1107, 2002.
3. Ch. Bastin, A. Sarlette, R. Sepulchre, M. Dimmler, T. Erm, B. Bauvir, and B. Sedghi. European extremely large telescope M1 control strategies study. ESO Internal report E-TRE-ULG-0449-0007, 2009.
4. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah. Randomized gossip algorithms. IEEE Trans. Information Theory (Special issue), 52(6):2508-2530, 2006.
5. R.W. Brockett and J.L. Willems. Discretized partial differential equations: Examples of control systems defined on modules. Automatica, 10(5):507-515, 1974.
6. Kai Chung Chu. Decentralized control of high speed vehicle strings. Transportation Research, pages 361-383, June 1974.
7. J.P. Desai, J.P. Ostrowski, and V. Kumar. Modeling and control of formations of nonholonomic mobile robots. IEEE Trans. Robotics and Automation, 17(6):905-908, 2001.
8. S.R. Duncan and G.F. Bryant. The spatial bandwidth of cross-directional control systems for web processes. Automatica, 33(2):139-153, 1997.
9. J.A. Essers. Partial differential equations: characterization for numerical solution and the finite differences method. Master degree course at Florida State University / University of Liège, 1988 / 2004.
10. F. Fagnani and J.C. Willems. Interconnections and symmetries of linear differential systems. Mathematics of Control, Signals and Systems, 7(2):167-186, 1994.
11. J. Fax and R.M. Murray. Information flow and cooperative control of vehicle formations. IEEE Trans. Automatic Control, 49(9):1465-1476, 2004.
12. L. Galbusera, M.P.E. Marciandi, P. Bolzern, and G. Ferrari-Trecate. Control schemes based on the wave equation for consensus in multi-agent systems with double-integrator dynamics. Proc. 46th IEEE Conf. Decision and Control, pages 1498-1503, 2007.
13. D.M. Gorinevsky, S.P. Boyd, and G. Stein. Design of low-bandwidth spatially ditributed feedback. IEEE Trans. Automatic Control, 53(2):257-272, 2008.
14. W.P. Heath. Orthogonal functions for cross-directional control of web forming processes. Automatica, 32(2):183-198, 1996.
15. J.M. Hendrickx, B.D.O. Anderson, J.C. Delvenne, and V.D. Blondel. Directed graphs for the analysis of rigidity and persistence in autonomous agents systems. International journal of robust and nonlinear control, 17(10):960-981, 2007.
16. J.H. Kim, M. West, S. Lall, E. Scholte, and A. Banaszuk. Stochastic multiscale approaches to consensus problems. Proc. 48th IEEE Conf. Decision and Control, pages 5551-5557, 2008.
17. J.R. Lawton and R.W. Beard. Synchronized multiple spacecraft rotations. Automatica, 38:1359-1364, 2002.
18. N.E. Leonard, D. Paley, F. Lekien, R. Sepulchre, D. Frantantoni, and R. Davis. Collective motion, sensor networks and ocean sampling. Proc. IEEE, 95(1):48-74, 2007.
19. K.W. Morton and D.F. Mayers. Numerical solution of partial differential equations, an introduction. Cambridge University Press, 2005.
20. R. Olfati-Saber, J.A. Fax, and R.M. Murray. Consensus and cooperation in networked multi-agent systems. Proc. IEEE, 95(1):215-233, 2007.
21. A. Olshevsky and J.N. Tsitsiklis. Convergence rates in distributed consensus and averaging. Proc. 45th IEEE Conf. Decision and Control, pages 3387-3392, 2006.
22. L. Peppard. String stability of relative-motion PID vehicle control. IEEE Trans. Automatic Control, 19(5):579-581, 1974.
23. Wei Ren and R.W. Beard. Distributed Consensus in Multi-vehicle Cooperative Control. Communications and Control Engineering. Springer, 2008.
24. G. Stein and D.M. Gorinevsky. Design of surface shape control for large two-dimensional arrays. IEEE Trans. Control Systems Technology, 13:422-433, 2005.
25. G.E. Stewart, D.M. Gorinevsky, and G.A. Dumont. Two-dimensional loop-shaping. Automatica, 39(5):779-792, 2003.
26. D. Swaroop and J.K. Hedrick (advisor). String stability of interconnected systems: an application to platooning in automated highway systems. PhD Thesis, University of California Berkeley, 1994.
27. J.N. Tsitsiklis and M. Athans (advisor). Problems in decentralized decision making and computation. PhD Thesis, MIT, 1984.