An algorithm to prove contraction, consensus, and network synchronization

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 1, Issue PART 1, 2009, Pages 60-65

  Di Bernardo, Mario ^a   Russo, Giovanni ^a   Slotine, Jean Jacques ^b  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Consensus; Contraction theory; Networked control systems; Synchronization

Indexed keywords

CONSENSUS; CONTRACTION THEORY; NETWORK SYNCHRONIZATION; NETWORKED CONTROL SYSTEMS; NOVEL STRATEGIES;

ALGORITHMS; CONTROL SYSTEMS; DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS;

SYNCHRONIZATION;

EID: 79960951245     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20090924-3-IT-4005.0053     Document Type: Conference Paper

References (26)

1. Angeli, D. (2002). A Lyapunov approach to incremental stability properties. IEEE Transactions on Automatic Control, 47, 410-421. (Pubitemid 34536795)
2. Bertsekas, D. and Tsitsiklis, J. (1989). Parallel and Distributed Computation: Numerical Methods. Prentice-Hall (Englewood Cliffs, NJ, USA).
3. Chung, S.J. and Slotine, J.J.E. (2007). Nonlinear model reduction and decentralized control of tethered formation flight. Journal of Guidance, Control and Dynamics, 30, 390-400.
4. Cortes, J. and Bullo, F. (2005). Coordination and geometric optimization via distributed dynamical systems. SIAM J. Control Optim., 44, 1543-1574.
5. Del Vecchio, D., Ninfa, A.J., and Sontag, E.D. (2008). Modular cell biology: Retroactivity and insulation. Nature Molecular Systems Biology, 4, 161.
6. di Bernardo, M., Russo, G., and J.J.E. Slotine (2009). A novel algorithm to prove contraction of nonlinear dynamical systems: theory and applications. In preparation.
7. Elowitz, M.B. and Leibler, S. (2000). A synthetic oscillatory network of transcriptional regulators. Nature, 403, 335-338. (Pubitemid 30062393)
8. Garcia-Ojalvo, J., Elowitz, M.B., and Strogatz, S.H. (2004). Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing. Proc. of the Natl. Acad. of Sci., 101, 10955-10960. (Pubitemid 38989566)
9. Hartman, P. (1961). On stability in the large for systems of ordinary differential equations. Canadian Journal of Mathematics, 13, 480-492.
10. Hui, Q. and Haddad, W.H. (2008). Distributed nonlinear control algorithms for network consensus. Automatica, 44, 2375-2381.
11. Lewis, D.C. (1949). Metric properties of differential equations. American Journal of Mathematics, 71, 294-312.
12. Lohmiller, W. and Slotine, J.J. (2005). Contraction analysis of non-linear distributed systems. International Journal of Control, 78, 678-688. (Pubitemid 41657403)
13. Lohmiller, W. and Slotine, J.J.E. (1998). On contraction analysis for non-linear systems. Automatica, 34, 683-696. (Pubitemid 128400392)
14. Newman, M.E. (2003). The structure and function of complex networks. SIAM Review, 45, 167-256.
15. Olfati-Saber, R. and Murray, R.M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49, 1520-1533.
16. Pavlov, A., Pogromvsky, A., van de Wouv, N., and Nijmeijer, H. (2004). Convergent dynamics, a tribute to Boris Pavlovich Demidovich. Systems and Control Letters, 52, 257-261.
17. Pham, Q.C. and Slotine, J.J.E. (2007). Stable concurrent synchronization in dynamic system networks. Neural Networks, 20, 62-77.
18. Pham, Q.C., Tabareau, N., and Slotine, J.J.E. (2009). A contraction theory approach to stochastic incremental stability. IEEE Transactions on Automatic Control, 54.
19. Russo, G. and di Bernardo, M. (2009a). An algorithm for the construction of synthetic self synchronizing biological circuits. In International Symposium on Circuits and Systems, 305-308.
20. Russo, G. and di Bernardo, M. (2009b). Contraction theory and the master stability function: linking two approaches to study synchronization in complex networks. IEEE Transactions on Circuit and Systems II, 56, 177-181.
21. Russo, G. and di Bernardo, M. (2009c). How to synchronize biological clocks. Journal of Computational Biology, 16, 379-393.
22. Russo, G., Sontag, E.D., and di Bernardo, M. (2009). Global entrainment of transcriptional systems to periodic inputs. Submitted to PLoS Computational Biology.
23. Slotine, J. J., and Li,W. (1991). Applied nonlinear control. Prentice Hall (Englewood Cliffs, NJ, USA).
24. Tabareau, N., Slotine, J. J. and Pham, Q. C. (2009). How synchronization protects from noise. Available at http://arxiv.org/abs/0801.0011.
25. Vidyasagar, M. (1993). Nonlinear systems analysis (2nd Ed.). Pretice-Hall (Englewood Cliffs, NJ, USA).
26. Wang, W. and Slotine, J.J.E. (2005). On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics, 92, 38-53. (Pubitemid 40134701)