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| Explicit solution to forward and backward stochastic differential equations with state delay and its application to optimal control |
| TianfuMa1,JuanjuanXu1,HuanshuiZhang2 |
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| (1 Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;2 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, Shandong, China) |
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| 摘要: |
| This paper is concerned with linear forward–backward stochastic differential equations (FBSDEs) with state delay, the
solvability which is much more complex than the case of no delay or input delay caused by the prediction of the backward
processes of the future time. To overcome this difficulty, we innovatively establish the non-homogeneous relationship between
the backward and forward processes with the help of the corresponding discrete-time system. The main contribution is to
give the explicit solution to the FBSDEs with state delay in terms of partial Riccati equations for the first time. The presented
results form the basis to solve the challenging problem of linear quadratic optimal control for multiplicative-noise stochastic
systems with state delay. |
| 关键词: FBSDEs · State delay · Analytical solution · Discrete-time system |
| DOI：https://doi.org/10.1007/s11768-022-00106-x |
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| 基金项目: |
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| Explicit solution to forward and backward stochastic differential equations with state delay and its application to optimal control |
| Tianfu Ma1,Juanjuan Xu1,Huanshui Zhang2 |
| (1 Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;2 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, Shandong, China) |
| Abstract: |
| This paper is concerned with linear forward–backward stochastic differential equations (FBSDEs) with state delay, the
solvability which is much more complex than the case of no delay or input delay caused by the prediction of the backward
processes of the future time. To overcome this difficulty, we innovatively establish the non-homogeneous relationship between
the backward and forward processes with the help of the corresponding discrete-time system. The main contribution is to
give the explicit solution to the FBSDEs with state delay in terms of partial Riccati equations for the first time. The presented
results form the basis to solve the challenging problem of linear quadratic optimal control for multiplicative-noise stochastic
systems with state delay. |
| Key words: FBSDEs · State delay · Analytical solution · Discrete-time system |
