Averaged time-optimal control problem in the space of positive Borel measures

Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We introduce a time-optimal control theory in the space M + (R d) of positive and finite Borel measures. We prove some natural results, such as a dynamic programming principle, the existence of optimal trajectories, regularity results and an HJB equation for the value function in this infinite-dimensional setting. The main tool used is the superposition principle (by Ambrosio-Gigli-Savaré) which allows to represent the trajectory in the space of measures as weighted superposition of classical characteristic curves in ? d.

Original languageEnglish (US)
Pages (from-to)721-740
Number of pages20
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume24
Issue number2
DOIs
StatePublished - Apr 1 2018

Fingerprint

Time-optimal Control
Borel Measure
Superposition
Optimal Control Problem
Trajectories
HJB Equation
Dynamic Programming Principle
Characteristic Curve
Optimal Trajectory
Optimal Control Theory
Control theory
Dynamic programming
Value Function
Regularity
Trajectory

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

Keywords

  • Differential inclusions
  • Dynamic programming
  • Multi-agent systems
  • Optimal transport
  • Time-optimal control

Cite this

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Averaged time-optimal control problem in the space of positive Borel measures. / Cavagnari, Giulia; Marigonda, Antonio; Piccoli, Benedetto.

In: ESAIM - Control, Optimisation and Calculus of Variations, Vol. 24, No. 2, 01.04.2018, p. 721-740.

Research output: Contribution to journalArticle

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AU - Piccoli, Benedetto

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AB - We introduce a time-optimal control theory in the space M + (R d) of positive and finite Borel measures. We prove some natural results, such as a dynamic programming principle, the existence of optimal trajectories, regularity results and an HJB equation for the value function in this infinite-dimensional setting. The main tool used is the superposition principle (by Ambrosio-Gigli-Savaré) which allows to represent the trajectory in the space of measures as weighted superposition of classical characteristic curves in ? d.

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