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.
Related
- Feedback Stabilization for Sampled Linear Systems with Control-linear Noise
- Successive design of backstepping observers for parabolic PDE-ODE systems and its duality to state feedback stabilization
- Semi-global exact prescribed-time stabilization of linear systems by bounded linear time-varying feedback
- Parameter estimation for graphon-interacting particle systems from discrete observations
- Almost sure exponential stabilization of linear stochastic systems driven by a general α-stable process via discrete-time state feedback
BibTeX
@misc{happ2026feedback,
title = {{Feedback approaches for set-point stabilization of interacting particle systems}},
author = {Daniel Jannik Happ and Birgit Jacob and Claudia Totzeck},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17222},
eprint = {2608.17222},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17222},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feedback approaches for set-point stabilization of interacting particle systems
AU - Daniel Jannik Happ
AU - Birgit Jacob
AU - Claudia Totzeck
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2608.17222
UR - https://arxiv.org/abs/2608.17222
AB - 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.
ER -