A Boltzmann approach to mean-field sparse feedback control

2016/11/12 by Albi, Giacomo, Fornasier, Massimo, Kalise, Dante · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1611.03988

Abstract

We study the synthesis of optimal control policies for large-scale multi-agent systems. The optimal control design induces a parsimonious control intervention by means of l-1, sparsity-promoting control penalizations. We study instantaneous and infinite horizon sparse optimal feedback controllers. In order to circumvent the dimensionality issues associated to the control of large-scale agent-based models, we follow a Boltzmann approach. We generate (sub)optimal controls signals for the kinetic limit of the multi-agent dynamics, by sampling of the optimal solution of the associated two-agent dynamics. Numerical experiments assess the performance of the proposed sparse design.

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• Hierarchical clustering and dimensional reduction for optimal control of large-scale agent-based models

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