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

AIMS Mathematics, vol. 10, pp. 19147–19172

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.

Authors 4

1. Melanie Harms Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie , RWTH Aachen University , Aachen , Germany

2. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Aachen , Germany

3. Chiara Segala

   Università della Svizzera italiana

   Affiliation as printed

   Faculty of Informatics , Università della Svizzera Italiana -USI , Lugano , Switzerland

4. Eva Zerz Aachen Institut für Geometrie und Praktische Mathematik Lehrstuhl für Algebra und Zahlentheorie

   Università della Svizzera italiana · RWTH Aachen University

   Affiliation as printed

   Faculty of Informatics, Università della Svizzera Italiana – USI, Lugano, Switzerland

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen University, Aachen, Germany