Stochastic control for linear systems driven by fractional noises
This paper is concerned with optimal control of stochastic linear systems involving fractional Brownian motion (FBM). First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are establis...
| Автори: | , |
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| Формат: | Journal article |
| Мова: | English |
| Опубліковано: |
2005
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| _version_ | 1826269698408316928 |
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| author | Yaozhong, H Zhou, X |
| author_facet | Yaozhong, H Zhou, X |
| author_sort | Yaozhong, H |
| collection | OXFORD |
| description | This paper is concerned with optimal control of stochastic linear systems involving fractional Brownian motion (FBM). First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. Then, three control models are formulated and studied. In the first two models, the state is scalar-valued and the control is taken as Markovian. Either the problems are completely solved based on a Riccati equation (for model 1, where the cost is a quadratic functional on state and control variables) or optimality is characterized (for model 2, where the cost is a power functional). The last control model under investigation is a general one, where the system involves the Stratonovich integral with respect to FBM, the state is multidimensional, and the admissible controls are not limited to being Markovian. A new Riccati-type equation, which is a backward stochastic differential equation involving both FBM and normal Brownian motion, is introduced. Optimal control and optimal value of the model are explicitly obtained based on the solution to this Riccati-type equation. © 2005 Society for Industrial and Applied Mathematics. |
| first_indexed | 2024-03-06T21:29:10Z |
| format | Journal article |
| id | oxford-uuid:441516fd-8e07-4ae8-b9db-ffdc2c19ad2a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:29:10Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:441516fd-8e07-4ae8-b9db-ffdc2c19ad2a2022-03-26T14:59:29ZStochastic control for linear systems driven by fractional noisesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:441516fd-8e07-4ae8-b9db-ffdc2c19ad2aEnglishSymplectic Elements at Oxford2005Yaozhong, HZhou, XThis paper is concerned with optimal control of stochastic linear systems involving fractional Brownian motion (FBM). First, as a prerequisite for studying the underlying control problems, some new results on stochastic integrals and stochastic differential equations associated with FBM are established. Then, three control models are formulated and studied. In the first two models, the state is scalar-valued and the control is taken as Markovian. Either the problems are completely solved based on a Riccati equation (for model 1, where the cost is a quadratic functional on state and control variables) or optimality is characterized (for model 2, where the cost is a power functional). The last control model under investigation is a general one, where the system involves the Stratonovich integral with respect to FBM, the state is multidimensional, and the admissible controls are not limited to being Markovian. A new Riccati-type equation, which is a backward stochastic differential equation involving both FBM and normal Brownian motion, is introduced. Optimal control and optimal value of the model are explicitly obtained based on the solution to this Riccati-type equation. © 2005 Society for Industrial and Applied Mathematics. |
| spellingShingle | Yaozhong, H Zhou, X Stochastic control for linear systems driven by fractional noises |
| title | Stochastic control for linear systems driven by fractional noises |
| title_full | Stochastic control for linear systems driven by fractional noises |
| title_fullStr | Stochastic control for linear systems driven by fractional noises |
| title_full_unstemmed | Stochastic control for linear systems driven by fractional noises |
| title_short | Stochastic control for linear systems driven by fractional noises |
| title_sort | stochastic control for linear systems driven by fractional noises |
| work_keys_str_mv | AT yaozhongh stochasticcontrolforlinearsystemsdrivenbyfractionalnoises AT zhoux stochasticcontrolforlinearsystemsdrivenbyfractionalnoises |