Second-Order Coupled Clustering Systems Consensus via Small-World Network Pinning Control

This paper studies consensus control of second-order inter-coupled clustering systems based on the interactive topology of small-world network modeling. By means of pinning control, an improved control strategy is proposed: select the pinning nodes with respect to the node-degree indices, optimize the control actions by the linear quadratic regulator theory to control the motion state of the pinning nodes, and the other nodes follow their pinning-controlled nodes directly or indirectly in terms of the coupling weight, so as to achieve consensus among the nodes position and velocity. The pinning input is obtained by linear quadratic regulator (LQR). Numerical simulations are included, through which the relationships between small-world network parameters and convergence speed are observed and verified.