H ∞ analysis of cooperative multi-agent systems by adaptive interpolation

Zoran Tomljanović

Applications of Mathematics (2025)

  • Issue: 3, page 367-386
  • ISSN: 0862-7940

Abstract

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We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the H ∞ norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient H ∞ norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the H ∞ norm.

How to cite

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Tomljanović, Zoran. "$H_{\infty }$ analysis of cooperative multi-agent systems by adaptive interpolation." Applications of Mathematics (2025): 367-386. <http://eudml.org/doc/299989>.

@article{Tomljanović2025,
abstract = {We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the $H_\{\infty \}$ norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient $H_\{\infty \}$ norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the $H_\{\infty \}$ norm.},
author = {Tomljanović, Zoran},
journal = {Applications of Mathematics},
keywords = {multi-agent system; $H_\{\infty \}$ norm; network robustness; adaptive interpolation},
language = {eng},
number = {3},
pages = {367-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$H_\{\infty \}$ analysis of cooperative multi-agent systems by adaptive interpolation},
url = {http://eudml.org/doc/299989},
year = {2025},
}

TY - JOUR
AU - Tomljanović, Zoran
TI - $H_{\infty }$ analysis of cooperative multi-agent systems by adaptive interpolation
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 3
SP - 367
EP - 386
AB - We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the $H_{\infty }$ norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient $H_{\infty }$ norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the $H_{\infty }$ norm.
LA - eng
KW - multi-agent system; $H_{\infty }$ norm; network robustness; adaptive interpolation
UR - http://eudml.org/doc/299989
ER -

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