Study of a One-Dimensional Optimal Control Problem with a Purely State-Dependent Cost

被引：1

作者：

Dmitruk, A. V. ^{[1
,2
]}

Vdovina, A. K. ^{[2
]}

机构：

[1] Russian Acad Sci, Cent Econ & Math Inst, Moscow, Russia

[2] Lomonosov Moscow State Univ, Moscow, Russia

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2020年 / 28卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Optimal control; One-dimensional state; Unimodular integrand; State-dependent cost; Tchyaplygin comparison theorem; Pontryagin maximum principle;

D O I：

10.1007/s12591-016-0306-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A one-dimensional optimal control problem with a state-dependent cost and a unimodular integrand is considered. It is shown that, under some standard assumptions, this problem can be solved without using the Pontryagin maximum principle, by simple methods of the classical analysis, basing on the Tchyaplygin comparison theorem. However, in some modifications of the problem, the usage of Pontryagin's maximum principle is preferable. The optimal synthesis for the problem and for its modifications is obtained.

引用

页码：133 / 151

页数：19

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