L2 norm performance index of synchronization and optimal control synthesis of complex networks

Chao Liu; Zhisheng Duan; Guanrong Chen; Lin Huang

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arXiv · 0710.2736

L2 norm performance index of synchronization and optimal control synthesis of complex networks

Chao Liu·Zhisheng Duan·Guanrong Chen·Lin Huang

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Abstract

In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means that the network synchronizes faster with lower-overshoot. The L2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L2 norm of the error vector e and the H2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H2 norm of the transfer function G is analyzed. Finally, an optimal controller is designed, according to the so-called LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L2 norm of the output of the linearized network.

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BibTeX RIS

Chao Liu, Zhisheng Duan, Guanrong Chen, Lin Huang. 2007-10-15. L2 norm performance index of synchronization and optimal control synthesis of complex networks. https://arxiv.org/abs/0710.2736

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