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

Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli

Research output: Contribution to journalArticle

9 Scopus citations

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

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

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