## Flocking motion of multi-agent system by dynamic pinning control

The flocking motion in multi-agent system with switching topology is investigated in this study. A dynamic pinning control algorithm (DPCA) is developed to generate a stable flocking motion for all the agents without the assumption of connectivity or initial connectivity of the network. For the switching network, the network topology may be varied with time. All the agents at each topology switching time are regrouped into some connected subgroups, and the agent with the highest degree in each subgroup is selected as the informed agents. Based on LaSalle Invariance Principle, it is proved that the proposed DPCA ensures that the velocities of all the agents approach to that of the virtual leader asymptotically, no collision happens between the agents, and the system approaches to a configuration that minimises the global potentials. Moreover, the convergent rate and the computational cost of the proposed algorithm are investigated. The proposed DPCA is also applied to the situation where the virtual leader travels with a varying velocity. Numerical simulations demonstrate the stability and efficiency of the proposed algorithm.