Hamilton-Jacobi-Bellman Equation for a Time-Optimal Control Problem in the Space of Probability Measures - Inria - Institut national de recherche en sciences et technologies du numérique
Conference Papers Year : 2016

Hamilton-Jacobi-Bellman Equation for a Time-Optimal Control Problem in the Space of Probability Measures

Abstract

In this paper we formulate a time-optimal control problem in the space of probability measures endowed with the Wasserstein metric as a natural generalization of the correspondent classical problem in $${\mathbb {R}}^d$$ where the controlled dynamics is given by a differential inclusion. The main motivation is to model situations in which we have only a probabilistic knowledge of the initial state. In particular we prove first a Dynamic Programming Principle and then we give an Hamilton-Jacobi-Bellman equation in the space of probability measures which is solved by a generalization of the minimum time function in a suitable viscosity sense.
Fichier principal
Vignette du fichier
447583_1_En_18_Chapter.pdf (339.54 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01626919 , version 1 (31-10-2017)

Licence

Identifiers

Cite

Giulia Cavagnari, Antonio Marigonda, Giandomenico Orlandi. Hamilton-Jacobi-Bellman Equation for a Time-Optimal Control Problem in the Space of Probability Measures. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.200-208, ⟨10.1007/978-3-319-55795-3_18⟩. ⟨hal-01626919⟩
94 View
457 Download

Altmetric

Share

More