DYNAMIC PROGRAMMING FOR OPTIMAL CONTROL PROBLEMS WITH DELAYS IN THE CONTROL VARIABLE

被引：16

作者：

Federico, Salvatore ^{[1
]}

Tacconi, Elisa ^{[2
]}

机构：

[1] Univ Milan, DEMM, I-20122 Milan, Italy

[2] Univ Luigi Bocconi, Dept Finance, I-20126 Milan, Italy

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 02期

关键词：

Hamilton-Jacobi-Bellman equation; optimal control; delay equations; viscosity solutions; regularity; verification theorem; HAMILTON-JACOBI EQUATIONS; BOUNDARY CONTROL-PROBLEMS; TIME-TO-BUILD; DIFFERENTIAL-EQUATIONS; STATE CONSTRAINTS; EVOLUTION-EQUATIONS; QUADRATIC CONTROL; HILBERT-SPACES; LINEAR-SYSTEMS; HJB EQUATIONS;

D O I：

10.1137/110840649

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 study a class of optimal control problems with state constraint, where the state equation is a differential equation with delays in the control variable. This class of problems arises in some economic applications, in particular in optimal advertising problems. The optimal control problem is embedded in a suitable Hilbert space, and the associated Hamilton-Jacobi-Bellman (HJB) equation is considered in this space. It is proved that the value function is continuous with respect to a weak norm and that it solves in the viscosity sense the associated HJB equation. The main results are the proof of a directional C-1-regularity for the value function and the feedback characterization of optimal controls.

引用

页码：1203 / 1236

页数：34

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[2]

[Anonymous], 1983, HAMILTON JACOBI EQUA

[3]

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