Practical synchronization on complex dynamical networks via optimal pinning control.
We consider practical synchronization on complex dynamical networks under linear feedback control designed by optimal control theory. The control goal is to minimize global synchronization error and control strength over a given finite time interval, and synchronization error at terminal time. By utilizing the Pontryagin's minimum principle, and based on a general complex dynamical network, we obtain an optimal system to achieve the control goal. The result is verified by performing some numerical simulations on Star networks, Watts-Strogatz networks, and Barabási-Albert networks. Moreover, by combining optimal control and traditional pinning control, we propose an optimal pinning control strategy which depends on the network's topological structure. Obtained results show that optimal pinning control is very effective for synchronization control in real applications.
School of Mathematics and Computing Science, Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin 541004, People's Republic of China.
Kezan
K
Li
Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Hangzhou 310018, People's Republic of China.
Weigang
W
Sun
School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia 6009, Australia.
Michael
M
Small
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China.
Xinchu
X
Fu