@article{Harms2025, 
author = {Melanie Harms and Michael Herty and Chiara Segala and Eva Zerz},
title = {Sparse control in microscopic and mean-field leader-follower models},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19147-19172},
keywords = {sparse control, Lyapunov decay, leader-follower systems, mean-field approximation, multi-agent dynamics, stabilization},
url = {https://www.sciopen.com/article/10.3934/math.2025856},
doi = {10.3934/math.2025856},
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, is decaying. 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.}
}