First-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay

被引：1

作者：

Song, Teng ^{[1
]}

Liu, Bin ^{[2
]}

机构：

[1] Wuhan Univ Technol, Sch Sci, Wuhan 430070, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2022年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Discrete-time stochastic systems; necessary optimality conditions; discrete-time backward stochastic equations; quasi-singular control; 1ST; ANALOG;

D O I：

10.1093/imamci/dnac010

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with the first-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay under weak assumptions. Based on a characteristic method and a discrete-time backward stochastic equation, we establish the linearized discrete-time stochastic maximum principle and Euler-type necessary optimality condition. Moreover, by a new discrete-time backward stochastic matrix equation, we also obtain the necessary optimality condition of quasi-singular control and the pointwise second-order optimality condition.

引用

页码：731 / 750

页数：20

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