Sparse control in microscopic and mean-field leader-follower models
Optimization and Control
2025-03-19 v1
Abstract
This work investigates the decay properties of Lyapunov functions in leader-follower systems seen as a sparse control framework. Starting with a microscopic representation, we establish conditions under which the total Lyapunov function, encompassing both leaders and followers, exhibits exponential decay. The analysis is extended to a hybrid setting combining a mean-field description for followers and a microscopic model for leaders. We identify sufficient conditions on control gain and interaction strengths that guarantee stabilization of the linear system towards a target state. The results highlight the influence of sparse control and interaction parameters in achieving coordinated behavior in multi-agent systems.
Cite
@article{arxiv.2503.14113,
title = {Sparse control in microscopic and mean-field leader-follower models},
author = {Melanie Harms and Michael Herty and Chiara Segala and Eva Zerz},
journal= {arXiv preprint arXiv:2503.14113},
year = {2025}
}