Finite-time flocking and collision avoidance for second-order multi-agent systems

This paper focuses on the problem of the finite-time flocking with uniform minimal distance for second-order multi-agent systems. The solutions of these issues can be viewed as the reasonable explanations of the bird flocks or fish schools. A new discontinuous protocol, which combines a singular communication function with a weighted sum of sign functions of the relative velocities among agents, is proposed to guarantee that the agents can attract and repel with each other. Since the communication weight is singular, the existence and uniqueness theorem cannot be applied directly. However, by imposing some suitable conditions on the initial states and using the skill of the proof by contradiction, the existence of the global smooth solution is obtained. Furthermore, employing a finite time stability theory and constructing a Lyapunov function ingeniously, a flocking with least distance for the multi-agent system is acquired within a finite-time. Moreover, the bound of settling time can be estimated by the parameters and the initial states and this relationship show that the more the number of particles, the larger the bound of convergence time. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.