希尔伯特空间中倒向随机时滞微分方程的无限视界最优控制问题

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190207

H. Liang, Jianjun Zhou

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引用次数: 1

摘要

研究了Hilbert空间中由一类后向随机时滞微分方程驱动的无限视界最优控制问题。首先给出了状态方程解的先验估计，并以此证明了状态方程解的存在唯一性。同时，通过引入时间超前随机微分方程作为伴随方程，导出了无限视界上最优控制问题的充分必要条件。最后，将理论结果应用于一个线性二次控制问题。

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INFINITE HORIZON OPTIMAL CONTROL PROBLEMS OF BACKWARD STOCHASTIC DELAY DIFFERENTIAL EQUATIONS IN HILBERT SPACES

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).