AVERAGED TIME-OPTIMAL CONTROL PROBLEM IN THE SPACE OF POSITIVE BOREL MEASURES

被引：7

作者：

Cavagnari, Giulia ^{[1
]}

Marigonda, Antonio ^{[2
]}

Piccoli, Benedetto ^{[1
]}

机构：

[1] Rutgers Univ Camden, Dept Math Sci, 311 N 5th St, Camden, NJ 08102 USA

[2] Univ Verona, Dept Comp Sci, Str Le Grazie 15, I-37134 Verona, Italy

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2018年 / 24卷 / 02期

关键词：

Time-optimal control; dynamic programming; optimal transport; differential inclusions; multi-agent systems;

D O I：

10.1051/cocv/2017060

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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-Savare) which allows to represent the trajectory in the space of measures as weighted superposition of classical characteristic curves in Rd.

引用

页码：721 / 740

页数：20

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