The delay feedback control for the McKean-Vlasov stochastic differential equations with common noise
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911925509554176 |
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| author | Chen, Xing Li, Xiaoyue Yuan, Chenggui |
| author_facet | Chen, Xing Li, Xiaoyue Yuan, Chenggui |
| contents | Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions of the system state such that the controlled system to be boundedness in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in [27] which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The Itô formula with respect to both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11703 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The delay feedback control for the McKean-Vlasov stochastic differential equations with common noise Chen, Xing Li, Xiaoyue Yuan, Chenggui Probability 60H10, 93D15, 60K35 Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of delay feedback control mechanisms. The aim of this paper is to design delay feedback control functions of the system state such that the controlled system to be boundedness in infinite horizon and further exponentially stable in the mean square. The designed controller, which depends only on the system state is easier to implement than that in [27] which was designed to depend on both system state and measure. The existence and uniqueness of the global solution of the controlled system is proved. The Itô formula with respect to both state and measure is derived. The proposed delay feedback control strategies are rendered viable for effective stabilization of MV-SDEs with common noise. Furthermore, the moment Lyapunov exponent, which is intricately linked to the time delays, is meticulously estimated. |
| title | The delay feedback control for the McKean-Vlasov stochastic differential equations with common noise |
| topic | Probability 60H10, 93D15, 60K35 |
| url | https://arxiv.org/abs/2311.11703 |