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SCIENCE CHINA Information Sciences, Volume 61, Issue 5: 052203(2018) https://doi.org/10.1007/s11432-016-9099-x

Guaranteed cost boundary control for cluster synchronization of complex spatio-temporal dynamical networks with community structure

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  • ReceivedNov 23, 2016
  • AcceptedApr 20, 2017
  • PublishedNov 20, 2017

Abstract

This paper discusses the problem for cluster synchronization control of a nonlinear complex spatio-temporal dynamical network (CSDN) with community structure. Initially, a collocated boundary controller with boundary measurement is studied to achieve the cluster synchronization of the CSDN. After that, a guaranteed cost boundary controller is further developed based on the obtained results. Furthermore, the suboptimal control design is addressed by minimizing an upper bound of the cost function. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573096, 61272530, 61703193), Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012741), Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2017MF022, ZR2015FL0 21), Youth Project of National Education Science Fund in the 13th Five-year Plan (Grant No. EIA160450), “333 Engineering” Foundation of Jiangsu Province of China (Grant No. BRA2015286) and National Priority Research Project NPRP funded by Qatar National Research Fund (Grant No. 9 166-1-031).


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  • Figure 1

    (Color online) The open-loop trajectories of synchronization errors $\left\|~{e_i~(\cdot,~t)}\right\|~$, $i\in~\{1,~2,~\ldots,~6\}$. (a) $\left\|~{e_{i,1}(\cdot,~t)}\right\|,~i\in~V_1$; (b) $\left\|~{e_{i,2}(\cdot,~t)}\right\|,~i\in~V_1$; (c) $\left\|~{e_{i,1}(\cdot,~t)}\right\|,~i\in~V_2$; (d) $\left\|~{e_{i,2}(\cdot,~t)}\right\|,~i\in~V_2$.

  • Figure 2

    (Color online) The closed-loop profiles of synchronization errors $e_i~(X,~t),~i\in~\{1,~2,~\ldots,~6\}$.

  • Figure 3

    (Color online) The trajectories of control inputs $u_i~(t)$, $i\in~\{1,~2,~\ldots,~6\}$.

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