Results 1 
3 of
3
SPARSE CONTROL OF ALIGNMENT MODELS IN HIGH DIMENSION
"... ABSTRACT. For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct lowdimensional representations of the dynamical system, which allow the learning of nearly optimal control strategies in high dimension with overwhel ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
ABSTRACT. For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct lowdimensional representations of the dynamical system, which allow the learning of nearly optimal control strategies in high dimension with overwhelming confidence. In this paper we present an instance of this general statement tailored to the sparse control of models of consensus emergence in high dimension, projected to lower dimensions by means of random linear maps. We show that one can steer, nearly optimally and with high probability, a highdimensional alignment model to consensus by acting at each switching time on one agent of the system only, with a control rule chosen essentially exclusively according to information gathered from a randomly drawn lowdimensional representation of the control system.
MeanField Pontryagin Maximum Principle
, 2015
"... We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasovtype. Such problems arise naturally as Γlimits of optimal control problems subject to ODE constraints, modeling, for instance, external interventions on crowd d ..."
Abstract
 Add to MetaCart
(Show Context)
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasovtype. Such problems arise naturally as Γlimits of optimal control problems subject to ODE constraints, modeling, for instance, external interventions on crowd dynamics. We obtain these firstorder optimality conditions in the form of Hamiltonian flows in the Wasserstein space of probability measures with forwardbackward boundary conditions with respect to the first and second marginals, respectively. In particular, we recover the equations and their solutions by means of a constructive procedure, which can be seen as the meanfield limit of the Pontryagin Maximum Principle applied to the discrete optimal control problems, under a suitable scaling of the adjoint variables.
Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences (ÖAW)
, 2014
"... (Un)conditional consensus emergence under perturbed and decentralized feedback controls Powered by TCPDF (www.tcpdf.org) (Un)conditional consensus emergence under perturbed and decentralized feedback controls Mattia Bongini∗, Massimo Fornasier†, and Dante Kalise‡ ..."
Abstract
 Add to MetaCart
(Un)conditional consensus emergence under perturbed and decentralized feedback controls Powered by TCPDF (www.tcpdf.org) (Un)conditional consensus emergence under perturbed and decentralized feedback controls Mattia Bongini∗, Massimo Fornasier†, and Dante Kalise‡