On synchronous steady states and internal models of diffusively coupled systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 43, Issue 21, 2010, Pages 1-10

  Wieland, Peter ^a   Allgöwer, Frank ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COUPLINGS; DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

COUPLED SYSTEMS; DIFFUSIVE COUPLING; INDIVIDUAL SYSTEMS; INTERNAL MODELING; INTERNAL MODELS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; OUTPUT REGULATION; SYSTEMS POSSESSING;

PROBLEM SOLVING;

EID: 84871330272     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20100915-3-IT-2017.00081     Document Type: Conference Paper

References (35)

1. Bennett, M., Schatz, M.F., Rockwood, H., and Wiesenfeld, K. (2002). Huygens's clocks. Proceedings of the Royal Society A, 458(2019), 563-579.
2. Buck, J.B. (1988). Synchronous rhythmic flashing of fireflies. II. The Quaterly Review of Biology, 63(3), 265- 289.
3. Byrnes, C.I. and Isidori, A. (1998). Output regulation for nonlinear systems: An overview. In Proceedings of the 37th IEEE Conference on Decision and Control, 3069- 3074.
4. Byrnes, C.I. and Isidori, A. (2003). Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation. IEEE Transactions on Automatic Control, 48(10), 1712-1723.
5. Coddington, E.A. and Levinson, N. (1955). Theory of Ordinary Differential Equations. International Series in Pure and Applied Mathematics. McGraw-Hill Book Company.
6. Fax, J.A. and Murray, R.M. (2004). Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 49(9), 1465-1476.
7. Francis, B.A. and Wonham, W.M. (1976). The internal model principle of control theory. Automatica, 12, 457- 465.
8. Hahn, W. (1967). Stability of Motion. Springer.
9. Hale, J.K. (1997). Diffusive coupling, dissipation, and synchronization. Journal of Dynamics and Differential Equations, 9(1), 1-52.
10. Hale, J.K., Magalhaes, L.T., and Oliva, W.M. (2002). Dynamics in Infinite Dimensions, volume 47 of Applied Mathematical Sciences. Springer, 2nd edition.
11. Helbing, D., Farkas, I., and Vicsek, T. (2000). Simulating dynamical features of escape panic. Nature, 407, 487- 490.
12. Isidori, A. and Byrnes, C.I. (2008). Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection. Annual Reviews in Control, 32, 1-16.
13. Izhikevich, E.M. (2007). Dynamical Systems in Neuro- science: The Geometry of Excitability and Bursting. Computational Neuroscience. MIT Press.
14. Jadbabaie, A., Lin, J., and Morse, A.S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988-1001.
15. Kuramoto, Y. (1975). Self-entrainment of a population of coupled non-linear oscillators. In H. Araki (ed.), International Symposium on Mathematical Problems in Theoretical Physics, volume 39 of Lecture Notes in Physics, 420-422. Springer.
16. Mischaikow, K., Smith, H., and Thieme, H.R. (1995). Asymptotically autonomous semiflows: Chain reccurence and Lyapunov functions. Transactions of the American Mathematical Society, 347(5), 1669-1685.
17. Moreau, L. (2005). Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2), 169-182.
18. Nair, S. and Leonard, N.E. (2008). Stable synchronization of mechanical system networks. SIAM Journal on Control and Optimization, 47(2), 234-265.
19. Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control, 51(3), 401-420.
20. Pikovsky, A., Rosenblum, M., and Kurths, J. (2001). Synchronization. A universal concept in nonlinear sciences, volume 12 of Cambridge Nonlinear Science Series. Cambridge University Press.
21. Ren, W., Beard, R.W., and Atkins, E.M. (2007). Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine, 27(2), 71-82.
22. Reynolds, C.W. (1987). Flocks, herds, and schools: A distributed behavioral model. In Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, 25-34. ACM.
23. Sarlette, A. (2009). Geometry and Symmetries in Coordination Control. Ph.D. thesis, Department of Electrical Engineering and Computer Science, University of Liege, Belgium.
24. Sarlette, A. and Sepulchre, R. (2009). Consensus on homogeneous manifolds. In Proceedings of the joint 48th IEEE Conference on Decision and Control and Chinese Control Conference, 6438-6443.
25. Schmidt, G.S., Muenz, U., and Allgower, F. (2009). Multiagent speed consensus via delayed position feedback with application to kuramoto oscillators. In Proceedings of the European Control Conference, 2464-2469.
26. Sepulchre, R., Paley, D.A., and Leonard, N.E. (2008). Stabilization of planar collective motion with limited communication. IEEE Transactions on Automatic Con- trol, 53(3), 706-719.
27. Strauss, A. and Yorke, J.A. (1967). On asymptotically autonomous differential equations. Mathematical Systems Theory, 1(2), 175-182.
28. Strogatz, S. (2003). Sync. The emerging science of spontaneous order. Penguin Books.
29. Tanner, H.G., Jadbabaie, A., and Pappas, G.J. (2003). Coordination of multiple autonomous vehicles. In Proceedings of the 11th IEEE Mediterranean Conference on Control and Automation.
30. Tanner, H.G., Jadbabaie, A., and Pappas, G.J. (2007). Flocking in fixed and switching networks. IEEE Transactions on Automatic Control, 52(5), 863-868.
31. Vicsek, T., Cziŕok, A., Ben-Jacob, E., Cohen, I., and Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(7), 1226-1229.
32. Wieland, P. and Allgower, F. (2009a). An internal model principle for consensus in heterogeneous linear multiagent systems. In Proceedings of the 1st IFAC Workshop on Distributed Estimation and Control in Networked Systems, 7-12.
33. Wieland, P. and Allgower, F. (2009b). An internal model principle for synchronization. In Proceedings of the 7th IEEE International Conference on Control and Automation, 285-290.
34. Wieland, P., Schmidt, G.S., Sepulchre, R., and Allgower, F. (2010). Phase synchronization through entrainment by a consensus input. In Proceedings of the 49th IEEE Conference on Decision and Control. Submitted.
35. Wieland, P., Sepulchre, R., and Allgower, F. (2009). An internal model principle is necessary and sufficient for linear output synchronization. Automatica. Submitted.