Pontryagin's maximum principle for dynamic systems on time scales

被引：14

作者：

Bohner, Martin ^{[1
]}

Kenzhebaev, Kenzhegaly ^{[2
]}

Lavrova, Olga ^{[3
]}

Stanzhytskyi, Oleksandr ^{[3
]}

机构：

[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO USA

[2] K Zhubanov Aktobe Reg State Univ, Dept Fundamental & Appl Math, Aktobe, Kazakhstan

[3] Taras Shevchenko Natl Univ Kyiv, Dept Math, Kiev, Ukraine

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2017年 / 23卷 / 07期

基金：

美国国家卫生研究院; 英国医学研究理事会;

关键词：

Time scale; optimal control; Lagrange function; Lagrange multiplier; needle-like variations; right-scattered point; right-dense point; CALCULUS; OBSERVABILITY; THEOREM;

D O I：

10.1080/10236198.2017.1284829

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, an analogue of Pontryagin's maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontryagin maximum principles and extending them to other cases 'in between'. We generalize known results to the case when a certain set of admissible values of the control is not necessarily closed (but convex) and the attainable set is not necessarily convex. At the same time, we impose an additional condition on the graininess of the time scale. For linear systems, sufficient conditions in the form of the maximum principle are obtained.

引用

页码：1161 / 1189

页数：29

共 55 条

[1] Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales [J].