Infinite Horizon Mean-Field Linear-Quadratic Optimal Control Problems with Switching and Indefinite-Weighted Costs
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912287013470208 |
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| author | Mei, Hongwei Wang, Rui Wei, Qingmeng Yong, Jiongmin |
| author_facet | Mei, Hongwei Wang, Rui Wei, Qingmeng Yong, Jiongmin |
| contents | This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from [17], the cost functionals do not have positive-definite weights here. When the problems are merely finite, we construct a sequence of asymptotic optimal controls and derive their closed-loop representations. For the solvability, an equivalence result between the open-loop and closed-loop cases is established through algebraic Riccati equations and infinite horizon backward stochastic differential equations. It can be seen that the research in [17] with positive-definite weights is a special case of the current paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Horizon Mean-Field Linear-Quadratic Optimal Control Problems with Switching and Indefinite-Weighted Costs Mei, Hongwei Wang, Rui Wei, Qingmeng Yong, Jiongmin Optimization and Control This paper is concerned with an infinite horizon stochastic linear quadratic (LQ, for short) optimal control problems with conditional mean-field terms in a switching environment. Different from [17], the cost functionals do not have positive-definite weights here. When the problems are merely finite, we construct a sequence of asymptotic optimal controls and derive their closed-loop representations. For the solvability, an equivalence result between the open-loop and closed-loop cases is established through algebraic Riccati equations and infinite horizon backward stochastic differential equations. It can be seen that the research in [17] with positive-definite weights is a special case of the current paper. |
| title | Infinite Horizon Mean-Field Linear-Quadratic Optimal Control Problems with Switching and Indefinite-Weighted Costs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.17622 |