Decentralized adaptive synchronization of an uncertain complex delayed dynamical network
Tóm tắt
In this paper, we investigate the locally and globally adaptive synchronization problem for an uncertain complex dynamical network with time-varying coupling delays based on the decentralized control. The coupling terms here are bounded by high-order polynomials with known gains that are ubiquitous in a large class of complex dynamical networks. We generalize the usual technology of searching for an appropriate coordinates transformation to change the network dynamics into a series of decoupled lower-dimensional systems. Several adaptive synchronization criteria are derived by constructing the Lyapunov-Krasovskii functional and Barbalat lemma, and the proposed criteria are simple in form and convenient for the practical engineering design. Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed synchronization scheme.
Tài liệu tham khảo
P. Erdös, A. Rényi. On the evolution of random graphs[J]. Publication of the Mathematical Institute of the Hungarian Academy of Science, 1960, 5(1): 17–61.
D. J. Watts, S. H. Strogatz. Collective dynamics of small-world networks[J]. Nature, 1998, 393(6684): 440–442.
A. L. Barabási, R. Albert, H. Jeong, et al. Power-law distribution of the world wide web[J]. Science, 2000, 287(5461): 2115.
S. H. Strogatz. Exploring complex network[J]. Nature, 2001, 410(6825): 268–276.
C. Wu. Synchronization in an array of linearly coupled dynamical systems[J]. IEEE Transactions on Circuits and Systems I, 1995, 42(8):430–447.
A. Pogromsky, H. Nijmeijer. Cooperative oscillatory behavior of mutually coupled dynamical systems[J]. IEEE Transactions on Circuits and Systems I, 2001, 48(2): 152–162.
V. N. Belykh, I. Belykh, M. Hasler. Connection graph stability method for synchronized coupled chaotic systems[J]. Physics D, 2004, 195(1/2): 159–187.
X. Wang, G. Chen. Synchronization in scale-free dynamical networks: robustness and fragility[J]. IEEE Transactions on Circuits and Systems I, 2002, 49(1): 54–62.
X. Li, G. Chen. Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint[J]. IEEE Transactions on Circuits and Systems I, 2003, 50(11): 1381–1390.
J. Lü, X. Yu, G. Chen, et al. Characterizing the synchronizability of small-world dynamical networks[J]. IEEE Transactions on Circuits and Systems I, 2004, 51(4): 787–796.
J. Lü, G. Chen. A time-varying complex dynamical network model and its controlled synchronization criteria[J]. IEEE Transactions on Automatic Control, 2005, 50(6): 841–846.
Z. Li, G. Chen. Robust adaptive synchronization of uncertain dynamical networks[J]. Physics Letters A, 2004, 324(2/3): 166–178.
J. Zhou, J. Lu, J. Lü. Adaptive synchronization of an uncertain complex dynamical network[J]. IEEE Transactions on Automatic Control, 2006, 51(4): 652–656.
W. Wang, J. Cao. Synchronization in an array of linearly coupled networks with time-varying delay[J]. Physics A, 2006, 366(1): 197–211.
M. Chen. Some simple synchronzation criteria for complex dynamical networks[J]. IEEE Transactions on Circuits and Systems I, 2006, 53(11): 1185–1189.
G. Jiang, W. Tang, G. Chen. A state-observer-based approach for synchronization in complex dynamical networks[J]. IEEE Transactions on Circuits and Systems I, 2006, 53(12): 2739–2745.
C. Li, G. Chen. Synchronization in general complex dynamical networks with coupling delays[J]. Physics A, 2004, 343(15): 263–278.
J. Cao, P. Li, W. Wang. Global synchronization in arrays of delayded neural networks with constant and delayed coupling[J]. Physics Letters A, 2006, 353(4): 318–325.
J. Zhou, T. Chen. Synchronization in general complex delayed dynamical network[J]. IEEE Transactions on Circuits and Systems I, 2006, 53(3): 733–744.
P. Li, Z. Yi, L. Zhang. Global synchronization of a class of delayed complex networks[J]. Chaos, Solitons and Fractals, 2006, 30(4): 903–908.
W. Xiong, W. Xie, J. Cao. Adaptive exponential synchronization of delayed chaotic networks[J]. Physics A, 2006, 370(2): 832–842.
C. Hua, X. Guan, S. Peng. Decentralized robust model reference adaptive cotnrol for interconnected time-delay systems[J]. Journal of Computational and Applied Mathematics, 2006, 193(2): 383–396.
C. Chou, C. Cheng. A decentralized model reference adaptive variable structure controller for large-sacle time-varying delay systems[J]. IEEE Transactions on Automatic Control, 2003, 48(77): 1213–1217.