[en] In this paper. we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others Computer science
Author, co-author :
Scardovi, Luca
Sarlette, Alain ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Blondel V.D., Hendrickx J.M., Olshevsky A., and Tsitsiklis J.N. Convergence in multiagent coordination, consensus, and flocking. Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. Seville, Spain (2005) 2996-3000
Cortes J., Martinez S., Karatas T., and Bullo F. Coverage control for mobile sensing networks. IEEE Trans. Robotics Automat. 20 2 (2004) 243-255
Jadbabaie A., Lin J., and Morse S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003) 988-1001
Jadbabaie A., Motee N., and Barahona M. On the stability of the Kuramoto model of coupled nonlinear oscillators. Proceedings of the 42nd IEEE American Control Conference. Boston, Ma (2004) 4296-4301
Khalil H.K. Nonlinear Systems (2001), Prentice-Hall, Englewood Cliffs, NJ
Kuramoto Y. Chemical Oscillations, Waves and Turbulence (1984), Springer, Berlin
N. Leonard, D. Paley, F. Lekien, R. Sepulchre, D. Frantoni, R. Davis, Collective motion, sensor networks and ocean sampling, Proc. IEEE (2007), to appear.
Mischaikow K., Smith H., and Thieme H. Asymptotically autonomous semiflows; chain recurrence and Lyapunov functions. Trans. Amer. Math. Soc. 347 (1995) 1669-1685
Moreau L. Stability of continuous-time distributed consensus algorithms. Proceedings of the 43rd IEEE Conference on Decision and Control. Atlantis, Paradise Island, Bahamas (2004) 3998-4003
Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Automat. Control 50 (2005) 169-182
Olfati-Saber R., and Murray R. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control 49 (2004) 1520-1533
Sarlette A., Sepulchre R., and Leonard N. Discrete-time synchronization on the N-torus. Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Kyoto, Japan (2006) 2408-2411
L. Scardovi, R. Sepulchre, Collective optimization over average quantities, in: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, 2006, to appear.
R. Sepulchre, D. Paley, N. Leonard, Stabilization of planar collective motion with all-to-all communication, IEEE Trans. Automat. Control, accepted for publication.
R. Sepulchre, D. Paley, N. Leonard, Stabilization of planar collective motion with limited communication, IEEE Trans. Automat. Control, 2006, submitted for publication.
R. Sepulchre, D. Paley, N. Leonard, Group coordination and cooperative control of steered particles in the plane, in: K.Y. Pettersen, J. Gravdahl, H. Nijmeijer (Eds.), Group Coordination and Cooperative Control, Lecture Notes in Control and Information Sciences, vol. 336, Springer, Berlin, 2006, pp. 217-232.
Strogatz S.H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143 (2000) 1-20
Strogatz S.H. Sync: The Emerging Science of Spontaneous Order (2003), Hyperion Press, New York
Vicsek T., Czirok A., Ben-jacob E., Cohen I., and Shochet O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75 (1995) 1226-1229
Willems J.C. Lyapunov functions for diagonally dominant systems. Automatica J. IFAC 12 (1976) 519-523
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
