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Mathematics > Optimization and Control

arXiv:2210.01699 (math)
[Submitted on 4 Oct 2022 (v1), last revised 5 Oct 2022 (this version, v2)]

Title:Robust feedback stabilization of interacting multi-agent systems under uncertainty

Authors:Giacomo Albi, Michael Herty, Chiara Segala
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Abstract:We consider control strategies for large-scale interacting agent systems under uncertainty. The particular focus is on the design of robust controls that allow to bound the variance of the controlled system over time. To this end we consider $\mathcal{H}_\infty$ control strategies on the agent and mean field description of the system. We show a bound on the $\mathcal{H}_\infty$ norm for a stabilizing controller independent on the number of agents. Furthermore, we compare the new control with existing approaches to treat uncertainty by generalized polynomial chaos expansion. Numerical results are presented for one-dimensional and two-dimensional agent systems.
Comments: 27 pages, 10 figures
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
MSC classes: 49K15, 49M25, 93-10, 93D09, 35Q70, 35Q93
Cite as: arXiv:2210.01699 [math.OC]
  (or arXiv:2210.01699v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.01699

Submission history

From: Chiara Segala [view email]
[v1] Tue, 4 Oct 2022 15:53:01 UTC (658 KB)
[v2] Wed, 5 Oct 2022 08:03:02 UTC (658 KB)
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