Periodic Exponential Turnpike Phenomenon in Mean-Field Stochastic Linear-Quadratic Optimal Control
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916336136880128 |
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| author | Sun, Jingrui Yuan, Lvning Zhang, Jiaqi |
| author_facet | Sun, Jingrui Yuan, Lvning Zhang, Jiaqi |
| contents | The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and detectability for stochastic linear systems. Then, the long-term behavior of the associated Riccati equations is analyzed under stabilizability and detectability conditions.Subsequently, a periodic mean-field stochastic LQ problem is formulated and solved. Finally, a linear transformation of the periodic extension of its optimal pair is shown to be the turnpike limit of the initial optimal control problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic Exponential Turnpike Phenomenon in Mean-Field Stochastic Linear-Quadratic Optimal Control Sun, Jingrui Yuan, Lvning Zhang, Jiaqi Optimization and Control 49N10, 49N20, 49N80, 93E20 The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and detectability for stochastic linear systems. Then, the long-term behavior of the associated Riccati equations is analyzed under stabilizability and detectability conditions.Subsequently, a periodic mean-field stochastic LQ problem is formulated and solved. Finally, a linear transformation of the periodic extension of its optimal pair is shown to be the turnpike limit of the initial optimal control problem. |
| title | Periodic Exponential Turnpike Phenomenon in Mean-Field Stochastic Linear-Quadratic Optimal Control |
| topic | Optimization and Control 49N10, 49N20, 49N80, 93E20 |
| url | https://arxiv.org/abs/2407.17926 |