Collective behavior in discontinuous second-order consensus model with collision avoidance

We propose a new multi-agent second-order system with a discontinuous vector field representing flocking, cohesion, and collision avoidance forces. Unlike traditional approaches that use continuous vector fields, we employ Filippov's differential inclusion framework to address the dynamics at discontinuity points. We provide suitable sufficient conditions concerning initial data, system parameters, and kernel functions to ensure asymptotic flocking and collision avoidance within the system.