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

Melanie Harms; Michael Herty; Chiara Segala; Eva Zerz; Melanie Harms; Michael Herty; Chiara Segala; Eva Zerz

doi:10.3934/math.2025856

AIMS Mathematics

2025, Volume 10, Issue 8: 19147-19172. doi: 10.3934/math.2025856

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

1.
Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Aachen, Germany
2.
Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany
3.
Faculty of Informatics, Università della Svizzera Italiana – USI, Lugano, Switzerland

Received: 16 March 2025 Revised: 05 June 2025 Accepted: 17 June 2025 Published: 22 August 2025
MSC : 93C10, 34D05, 49K20, 37N40, 82C22

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.
- sparse control,
- Lyapunov decay,
- leader-follower systems,
- mean-field approximation,
- multi-agent dynamics,
- stabilization
Citation: Melanie Harms, Michael Herty, Chiara Segala, Eva Zerz. Sparse control in microscopic and mean-field leader-follower models[J]. AIMS Mathematics, 2025, 10(8): 19147-19172. doi: 10.3934/math.2025856

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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, 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.

References

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