SCIENCE CHINA Information Sciences, Volume 60 , Issue 11 : 110204(2017) https://doi.org/10.1007/s11432-017-9146-1

Multi-leader multi-follower coordination with cohesion, dispersion, and containment control via proximity graphs

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  • ReceivedApr 11, 2017
  • AcceptedJun 23, 2017
  • PublishedOct 10, 2017



This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61473240, 61528301), National Natural Science Foundation of Fujian Province (Grant No. 2017J01119), 111 Project (Grant No. B17048), and State Key Laboratory of Intelligent Control and Decision of Complex Systems.


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  • Figure 1

    An illustration of the function $r_{ij}$ with the parameters: $r_{\rm~F}=1$, $d_2=0.4$, $a_1=0.84$, $a_2=-1$.

  • Figure 2

    Snapshots for the stationary leaders case. The leaders are denoted by “$\diamond$”, while the followers are denoted by “*”. The parameters are specified as follows: $r_{\rm~L}=5$, $r_{\rm~F}=1$, $d_1=0.8$, $d_2=0.4$, $a_2=-1$, $a_1=a_2(d_2^2-r_{\rm~F}^2)$, $b_{ik}=1$ for all $i~\in~\mathcal{V}_{\rm~F}$ and $k~\in~\left(\mathcal{N}_i~\cap~\mathcal{V}_{\rm~L}\right)$. (a) $t=0~{\rm~s}$; (b) $t=0.25~{\rm~s}$; (c) $t=0.75~{\rm~s}$; (d) $t=1~{\rm~s}$.

  • Figure 3

    (Color online) Stationary leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~F}$ and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=d_1$.

  • Figure 4

    (Color online) Stationary leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~L}$, and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=r_{\rm~L}$.

  • Figure 5

    Snapshots for the moving leaders case. (a) $t=0~{\rm~s}$; (b) $t=0.25~{\rm~s}$; (c) $t=0.75~{\rm~s}$; (d) $t=1~{\rm~s}$.

  • Figure 7

    (Color online) Moving leaders: the trajectory of $\|x_i-x_j\|$ for $(i,j)~\in~\mathcal{E}(0)$, $i~\in~\mathcal{V}_{\rm~L}$, and $j~\in~\mathcal{V}_{\rm~F}$ with the dashed line $\|x_i-x_j\|=r_{\rm~L}$.