Abstract
In this Chapter we discuss a novel decentralized adaptive strategy to synchronize complex networks. We present two alternative strategies. A vertex-based method where each node assigns an adaptive coupling strength to all its incoming links and an edge-based one where mutually coupled nodes negotiates their strengths according to the mismatch between their output functions. Proof of asymptotic stability is given using an appropriate Lyapunov function. The theoretical results are validated on a set of representative examples: the synchronization of a network of Chua’s circuits and the consensus of a network of integrators.
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References
Bartissol, P., Chua, L.O.: The double hook. IEEE Transactions on Circuits and Systems 35(12), 1512–1522 (1988)
Belykh, V.N., Verichev, N.N., Kocarev, L.J., Chua, L.O.: On chaotic synchronization in a linear array of Chua’s circuits. Journal of Circuits, Systems, and Computers 3(2), 579–589 (1993)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: structure and dynamics. Physics Reports 424, 175–308 (2006)
Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Transactions on Circuits and Systems 54, 1317–1326 (2007)
Chen, T., Liu, X.: Network synchronization with an adaptive coupling strenght (October 2006) arXiv:math/0610580
Chua, L.O., Itoh, M., Kocarev, L., Eckert, K.: Chaos synchronization in Chua’s circuit. Technical Report UCB/ERL M92/111, EECS Department, University of California, Berkeley (1992)
Chua, L.O., Kocarev, L., Eckert, K., Itoh, M.: Experimental chaos synchronization in Chua’s circuit. International Journal of Bifurcation and Chaos 2, 705–708 (1992)
Fewell, J.H.: Social insect networks. Science 301, 1867–1870 (2003)
Hugenii, C.: Horoloquium Oscilatorium. Apud F. Muguet (1673)
Kashiwagi, A., Urabe, I., Kaneko, K., Yomo, T.: Adaptive response of a gene network to environmental changes by fitness-induced attractor selection. PLoS ONE 1(e49) (2006)
Khalil, H.K.: Nonlinear systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2001)
Kuramoto, Y.: Chemical oscillations, waves and turbolence. Springer, Heidelberg (1984)
De Lellis, P., di Bernardo, M., Garofalo, F.: Novel decentralized adaptive strategies for the synchronization of complex networks. Accepted for Publication on Automatica (2008)
De Lellis, P., di Bernardo, M., Garofalo, F.: Synchronization of complex networks through local adaptive coupling. Chaos 18, 037110 (2008)
De Lellis, P., di Bernardo, M., Sorrentino, F., Tierno, A.: Adaptive synchronization of complex networks. International Journal of Computer Mathematics 85(8), 1189–1218 (2008)
Li, C., Chen, L., Aihara, K.: Stochastic synchronization of genetic oscillator networks. BMC Systems Biology (2007) doi:10.1186/1752-0509-1-6
Li, Q., Rus, D.: Global clock synchronization in sensor networks. IEEE Transactions on Computers 55(2), 214–226 (2006)
Matsumoto, T.: A chaotic attractor from Chua’s circuit. IEEE Transactions on Circuits and Systems 31(12), 1055–1058 (1984)
Moallemi, C.C., Van Roy, B.: Distributed optimization in adaptive networks. In: Thrun, S., Saul, L.K., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems (NIPS), vol. 16 (2004)
Murray, R.M., Olfati-Saber, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49(9), 1520–1533 (2004)
Newman, M.E.J., Barabàsi, A.L., Watts, D.J.: The structure and dynamics of complex networks. Princeton University Press, Princeton (2006)
Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95 (January 2007)
Pham, Q.-C., Slotine, J.-J.: Stable concurrent synchronization in dynamic system networks. Neural Networks 20(1), 62–77 (2007)
Russo, G., di Bernardo, M.: Contraction theory and the master stability function: linking two approaches to study synchronization. IEEE Transactions on Systems and Circuits II (in press, 2009)
Stanley, K.O., Bryant, B.D., Mikkulainen, R.: Evolving adaptive neural networks with and without adaptive synapses. In: The 2003 Congress on Evolutionary Computation. CEC 2003 (2003)
Wang, W., Slotine, J.-J.E.: On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics 92(1), 38–53 (2005)
Wang, X.F., Chen, G.: Synchronization in scale-free dynamical networks: Robustness and fragility (May 2001) arXiv:cond-mat/0105014v2
Wang, X.F., Chen, G.: Complex networks: small-world, scale-free and beyond. IEEE Circuits and Systems Magazine 3(1), 6–20 (2003)
Wu, C.W., Chua, L.O.: Synchronization in an array of linearly coupled dynamical systems. IEEE Transactions on Circuits and Systems 42(8), 430–447 (1995)
Wu, X., Cai, J., Zhao, Y.: Some new algebraic criteria for chaos synchronization of Chua’s circuits by linear state error feedback control. International Journal of Circuit Theory and Applications 34(3), 265–280 (2006)
Yalcin, M.E., Suykens, J.A.K., Vandewalle, J.P.L.: Cellular Neural Networks, Multi-Scroll Chaos and Synchronization, vol. 50. World Scientific Publishing Co. Pte Ltd., Singapore (2005)
Yamaguchi, S., Isejima, H., Matsuo, T., Okura, R., Yagita, K., Kobayashi, M., Okamura, H.: Synchronization of cellular clocks in the suprachiasmatic nucleus. Science 302(5649), 1408–1412 (2003)
Zhou, C., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Physical Review Letters 96, 164102 (2006)
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De Lellis, P., di Bernardo, M., Garofalo, F. (2009). Decentralized Adaptive Control for Synchronization and Consensus of Complex Networks. In: Chiuso, A., Fortuna, L., Frasca, M., Rizzo, A., Schenato, L., Zampieri, S. (eds) Modelling, Estimation and Control of Networked Complex Systems. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03199-1_2
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DOI: https://doi.org/10.1007/978-3-642-03199-1_2
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