Regularity results for a time-optimal control problem in the space of probability measures

Cavagnari, Giulia

doi:10.3934/mcrf.2017007

Cited by 10 publications

(15 citation statements)

References 14 publications

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“…[18]. Instead, more recent developments in the non-linear case (based on generalization of differential inclusions) have been recently described in [14,15,16].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Minimal time problem for discrete crowd models with a localized vector field

Duprez

Morancey

Rossi

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set.We give a characterization of the minimal time both for microscopic and macroscopic descriptions of a crowd. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control region to feed the desired final configuration.The construction of the control is explicit, providing a numerical algorithm for computing it. We finally give some numerical simulations.

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“…[18]. Instead, more recent developments in the non-linear case (based on generalization of differential inclusions) have been recently described in [14,15,16].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…We now give an example in the 2D case. Consider the initial data µ 0 and the target µ 1 defined by µ 0 := 1 8 × 1 (0,4)×(1,3) dx, µ 1 := 1 16 × 1 (8,14)×(0,4)\(9,13)×(1,3) dx.…”

Section: Example 2: the 2d Casementioning

confidence: 99%

Minimal time problem for discrete crowd models with a localized vector field

Duprez

Morancey

Rossi

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…A time-optimal control problem in the space of probability measures endowed with the topology induced by the Wasserstein metric has been introduced in [9,10,11,12], where the dynamics is given by a controlled continuity equation in the space of probability measures, which naturally arises as an infinite-dimensional counterpart of a finite-dimensional differential inclusion.…”

Section: Giulia Cavagnari Antonio Marigonda and Benedetto Piccolimentioning

confidence: 99%

“…Statement of the problem and preliminary results. We define now the objects considered in the present study, recalling the definition of admissible masspreserving trajectory stated in [9,10,11,12].…”

Section: Definition 22 (Standing Assumptionsmentioning

confidence: 99%

Optimal synchronization problem for a multi-agent system

Cavagnari

Marigonda

Piccoli

2017

Networks &Amp; Heterogeneous Media

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In this paper we investigate a time-optimal control problem in the space of positive and finite Borel measures on R d , motivated by applications in multi-agent systems. We provide a definition of admissible trajectory in the space of Borel measures in a particular non-isolated context, inspired by the so called optimal logistic problem, where the aim is to assign an initial amount of resources to a mass of agents, depending only on their initial position, in such a way that they can reach the given target with this minimum amount of supplies. We provide some approximation results connecting the microscopical description with the macroscopical one in the mass-preserving setting, we construct an optimal trajectory in the non isolated case and finally we are able to provide a Dynamic Programming Principle.

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“…In this appendix section, we recall some estimates used throughout the paper, borrowed from [13,16] (Lemma 2 and Lemma 3.1 respectively).…”

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confidence: 99%

Generalized dynamic programming principle and sparse mean-field control problems

Cavagnari

Marigonda

Piccoli

2020

Journal of Mathematical Analysis and Applications

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In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian velocity field is affine w.r.t. some variables. Our aim is to minimize a cost functional which includes a control norm, thus enforcing a control sparsity constraint. More precisely, we consider a nonlocal restriction on the total amount of control that can be used depending on the overall state of the evolving mass. We treat in details two main cases: an instantaneous constraint on the control applied to the evolving mass and a cumulative constraint, which depends also on the amount of control used in previous times. For both constraints, we prove the existence of optimal trajectories for general cost functions and that the value function is viscosity solution of a suitable Hamilton-Jacobi-Bellmann equation. Finally, we discuss an abstract Dynamic Programming Principle, providing further applications in the Appendix.

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Regularity results for a time-optimal control problem in the space of probability measures

Cited by 10 publications

References 14 publications

Minimal time problem for discrete crowd models with a localized vector field

Minimal time problem for discrete crowd models with a localized vector field

Optimal synchronization problem for a multi-agent system

Generalized dynamic programming principle and sparse mean-field control problems

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