Maximum Principle for Control System driven by Mixed Fractional Brownian Motion
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916540811575296 |
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| author | Li, Yuhang Han, Yuecai |
| author_facet | Li, Yuhang Han, Yuecai |
| contents | In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin calculus and introducing a disturbance control region, we obtain a modified maximum principle. Through martingale representation theorem, we obtain the adjoint backward stochastic differential equation in a natural way. Furthermore, corresponding to [1], a significant result is that the necessary condition is simplified by only containing one equality. As an application, the linear quadratic case is investigated to illustrate the main results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_11893 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximum Principle for Control System driven by Mixed Fractional Brownian Motion Li, Yuhang Han, Yuecai Optimization and Control Probability In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin calculus and introducing a disturbance control region, we obtain a modified maximum principle. Through martingale representation theorem, we obtain the adjoint backward stochastic differential equation in a natural way. Furthermore, corresponding to [1], a significant result is that the necessary condition is simplified by only containing one equality. As an application, the linear quadratic case is investigated to illustrate the main results. |
| title | Maximum Principle for Control System driven by Mixed Fractional Brownian Motion |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2312.11893 |