A flexible protocol of finite-time consensus for second-order multi-agent systems with pinning control

In this paper, we consider the finite-time consensus problem for second-order multi-agent systems with pinning control. Unlike the existing finite-time consensus algorithms for second-order multi-agent systems in which all agents' velocities and positions are assumed to have common communication weights and nonlinear couplings, we allow communication weights, nonlinear couplings and the feedback gains to be inconsistent for each agent's velocity and position. A flexible continuous protocol is designed to solve the finite-time consensus problem. Based on the Lyapunov functional approach and finite-time stability analysis, it is proved that this model not only achieves finite-time consensus for every agent but also estimates the settling time depending on initial data without assuming that α₂=2α₁1+α₁. Moreover, some simulation examples are given to verify the effectiveness of the theoretical results.