Robust Feedback Stabilization of Interacting Multi-agent Systems Under Uncertainty

Applied Mathematics & Optimization, vol. 89

Abstract

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 $${\mathcal {H}}_\infty $$ H ∞ control strategies on the agent and mean field description of the system. We show a bound on the $${\mathcal {H}}_\infty $$ H ∞ 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.

Authors 3

1. Giacomo Albi

   University of Verona

   Affiliation as printed

   Department of Computer Science, University of Verona, Str. Le Grazie 15, 37134, Verona, Italy

2. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

   IGPM, RWTH Aachen University, Templergraben, 55, 52062, Aachen, Germany

3. Chiara Segala corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   IGPM, RWTH Aachen University, Templergraben, 55, 52062, Aachen, Germany