Mean-Field, Infinite Horizon, Optimal Control of Nonlinear Stochastic Delay System Governed by Teugels Martingales Associated with Levy Processes

被引：2

作者：

Muthukumar, P. ^{[1
]}

Deepa, R. ^{[1
]}

机构：

[1] Deemed Univ, Gandhigram Rural Inst, Dept Math, Dindigul 624302, Tamil Nadu, India

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2019年 / 7卷 / 02期

关键词：

Backward stochastic delay differential equation; Infinite horizon; Levy processes; Mean-field; Stochastic maximum principle; Teugels martingales;

D O I：

10.1007/s40304-018-0143-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper focuses on optimal control of nonlinear stochastic delay system constructed through Teugels martingales associated with Levy processes and standard Brownian motion, in which finite horizon is extended to infinite horizon. In order to describe the interacting many-body system, the expectation values of state processes are added to the concerned system. Further, sufficient and necessary conditions are established under convexity assumptions of the control domain. Finally, an example is given to demonstrate the application of the theory.

引用

页码：163 / 180

页数：18

共 50 条

[41] Stochastic differential equations in infinite dimensional Hilbert space and its optimal control problem with Levy processes [J].

Wang, Meijiao ;

Shi, Qiuhong ;

Tang, Maoning ;

Meng, Qingxin .

AIMS MATHEMATICS, 2022, 7 (02) :2427-2455

[42] OPTIMAL CONTROL PROBLEM FOR RISK-SENSITIVE MEAN-FIELD STOCHASTIC DELAY DIFFERENTIAL EQUATION WITH PARTIAL INFORMATION [J].

Ma, Heping ;

Liu, Bin .

ASIAN JOURNAL OF CONTROL, 2017, 19 (06) :2097-2115

[43] A mean-field maximum principle for optimal control of forward–backward stochastic differential equations with Poisson jump processes [J].

Hafayed M. .

Hafayed, Mokhtar (hafayedmokhtar@yahoo.com), 2013, Springer Science and Business Media Deutschland GmbH (01) :300-315

[44] Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control [J].

Maoning TANG ;

Qingxin MENG ;

Meijiao WANG .

ChineseAnnalsofMathematics,SeriesB, 2019, (04) :515-540

[45] Stochastic maximum principle for discrete time mean-field optimal control problems [J].

Ahmadova, Arzu ;

Mahmudov, Nazim I. I. .

OPTIMAL CONTROL APPLICATIONS & METHODS, 2023, 44 (06) :3361-3378

[46] Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control [J].

Tang, Maoning ;

Meng, Qingxin ;

Wang, Meijiao .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2019, 40 (04) :515-540

[47] Forward and Backward Mean-Field Stochastic Partial Differential Equation and Optimal Control [J].

Maoning Tang ;

Qingxin Meng ;

Meijiao Wang .

Chinese Annals of Mathematics, Series B, 2019, 40 :515-540

[48] A Partially Observed Optimal Control Problem for Mean-Field Type Forward-Backward Stochastic System [J].

Wang Guangchen ;

Wu Zhen ;

Zhang Chenghui .

PROCEEDINGS OF THE 35TH CHINESE CONTROL CONFERENCE 2016, 2016, :1781-1786

[49] Necessary and sufficient conditions for optimal control of stochastic systems associated with Levy processes [J].

Meng QingXin ;

Tang MaoNing .

SCIENCE IN CHINA SERIES F-INFORMATION SCIENCES, 2009, 52 (11) :1982-1992

[50] Optimal Control for Mean-field System: Discrete-time Case [J].

Zhang, Huanshui ;

Qi, Qingyuan .

2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC), 2016, :4474-4480

← 1 2 3 4 5 →