Asymptotic Target Tracking in Discontinuous Dynamical Systems: Applications of Filippov's Inclusion Framework

We propose two novel multiagent systems characterized by discontinuous vector fields, designed to track a given moving or stationary target while ensuring collision avoidance. Unlike traditional approaches that employ continuous vector fields, we adopt Filippov's differential inclusion framework to model the dynamics at discontinuity points. For each model, we present an admissible set of initial conditions, system parameters, kernel functions, and a target configuration that guarantees both qualitative and quantitative asymptotic tracking of a prescribed target while avoiding collisions.