Minimum time control problems for non-autonomous differential equations

O. Bokanowski; A. Briani; H. Zidani

doi:10.1016/j.sysconle.2009.08.003

Minimum time control problems for non-autonomous differential equations

O. Bokanowski
, A. Briani
, H. Zidani

École Polytechnique

UPMC Université de Paris VI
Laboratoire de Probabilités et Modèles Aléatoires
University of Pisa

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function. Two simple numerical examples are given to illustrate our approach.

Original language	English
Pages (from-to)	742-746
Number of pages	5
Journal	Systems and Control Letters
Volume	58
Issue number	10-11
DOIs	https://doi.org/10.1016/j.sysconle.2009.08.003
Publication status	Published - 1 Oct 2009

Keywords

Hamilton-Jacobi-Bellman equation
Minimum time problem
Non-autonomous differential equations
Reachability set
Target problem

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10.1016/j.sysconle.2009.08.003

Cite this

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abstract = "In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function. Two simple numerical examples are given to illustrate our approach.",

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AU - Zidani, H.

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AB - In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function. Two simple numerical examples are given to illustrate our approach.

KW - Hamilton-Jacobi-Bellman equation

KW - Minimum time problem

KW - Non-autonomous differential equations

KW - Reachability set

KW - Target problem

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JF - Systems and Control Letters

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ER -

Minimum time control problems for non-autonomous differential equations

Abstract

Keywords

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