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arXiv · 2503.14113

Sparse control in microscopic and mean-field leader-follower models

Melanie Harms·Michael Herty·Chiara Segala·Eva Zerz
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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.

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Melanie Harms, Michael Herty, Chiara Segala, Eva Zerz. 2025-03-18. Sparse control in microscopic and mean-field leader-follower models. https://arxiv.org/abs/2503.14113

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