689	RWTH Publication No: 1009791        2025
TITLE	Sparse control in microscopic and mean-field leader-follower models
AUTHORS	Melanie Harms, Michael Herty, Chiara Segala, Eva Zerz
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.
KEYWORDS	Sparse control, Lyapunov decay, leader-follower systems, mean-field approximation, multi-agent dynamics, stabilization