Applications of Mathematics, first online, pp. 1-20
$H_{\infty}$ analysis of cooperative multi-agent systems by adaptive interpolation
Zoran Tomljanović
Received September 9, 2024. Published online June 17, 2025.
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.
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Affiliations: Zoran Tomljanović, School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, 31000 Osijek, Croatia, e-mail: ztomljan@mathos.hr
