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Linear Quadratic Optimal Control Problems of Delayed Backward Stochastic Differential Equations
Applied Mathematics and Optimization ( IF 1.6 ) Pub Date : 2021-04-26 , DOI: 10.1007/s00245-021-09778-4
Weijun Meng , Jingtao Shi

This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past history and the expected value of the future state trajectory in a short period of time. To obtain the optimal feedback, a new class of delayed Riccati equations and delayed-advanced forward-backward stochastic differential equations are introduced. Furthermore, the unique solvability of their solutions are discussed in detail.



中文翻译:

时滞倒向随机微分方程的线性二次最优控制问题

本文关注的是时滞后向随机微分方程的线性二次最优控制问题。为最佳控制导出了一个明确的表示形式,它是整个过去历史和未来状态轨迹的期望值在短时间内的线性反馈。为了获得最佳反馈,引入了一类新的时滞Riccati方程和时滞先进的前向-后向随机微分方程。此外,详细讨论了其解决方案的独特可解性。

更新日期:2021-04-26
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