General linear forward and backward Stochastic difference equations with applications
In this paper, we consider a class of general linear forward and, backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/137853 |
| _version_ | 1811691053076447232 |
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| author | Xu, Juanjuan Zhang, Huanshi Xie, Lihua |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Xu, Juanjuan Zhang, Huanshi Xie, Lihua |
| author_sort | Xu, Juanjuan |
| collection | NTU |
| description | In this paper, we consider a class of general linear forward and, backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS. |
| first_indexed | 2024-10-01T06:13:46Z |
| format | Journal Article |
| id | ntu-10356/137853 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:13:46Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1378532020-04-16T04:59:39Z General linear forward and backward Stochastic difference equations with applications Xu, Juanjuan Zhang, Huanshi Xie, Lihua School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Forward and Backward Stochastic Difference Equations Stochastic Optimal Control In this paper, we consider a class of general linear forward and, backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS. 2020-04-16T04:59:39Z 2020-04-16T04:59:39Z 2018 Journal Article Xu, J., Zhang, H., & Xie, L. (2018). General linear forward and backward Stochastic difference equations with applications. Automatica, 96, 40-50. doi:10.1016/j.automatica.2018.06.031 0005-1098 https://hdl.handle.net/10356/137853 10.1016/j.automatica.2018.06.031 2-s2.0-85048943455 96 40 50 en Automatica © 2018 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Electrical and electronic engineering Forward and Backward Stochastic Difference Equations Stochastic Optimal Control Xu, Juanjuan Zhang, Huanshi Xie, Lihua General linear forward and backward Stochastic difference equations with applications |
| title | General linear forward and backward Stochastic difference equations with applications |
| title_full | General linear forward and backward Stochastic difference equations with applications |
| title_fullStr | General linear forward and backward Stochastic difference equations with applications |
| title_full_unstemmed | General linear forward and backward Stochastic difference equations with applications |
| title_short | General linear forward and backward Stochastic difference equations with applications |
| title_sort | general linear forward and backward stochastic difference equations with applications |
| topic | Engineering::Electrical and electronic engineering Forward and Backward Stochastic Difference Equations Stochastic Optimal Control |
| url | https://hdl.handle.net/10356/137853 |
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