Feedback approaches for set-point stabilization of interacting particle systems

Abstract

We explore the problem of asymptotically stabilizing a class of interacting particle systems to a prescribed particle configuration with zero velocity. The class of interacting particle systems is motivated by the Cucker-Smale model on the mean-field level. Rather than designing a feedback by manually solving an IDA-PBC matching equation, we derive a feedback using an instantaneous rolling horizon control algorithm. We show that this feedback preserves the port-Hamiltonian structure of the interacting particle system and therefore allows for an interpretation in the IDA-PBC framework. Additionally, the energy balance of the closed-loop Hamiltonian provides an important tool to prove convergence of the particles' velocities and interaction forces in discrete and continuous time. If the control operator is surjective, we additionally prove convergence of the particle positions to the prescribed configuration.