Model-free stochastic linear quadratic design by semidefinite programming
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913623023026176 |
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| author | Guo, Jing Jiang, Xiushan Zhang, Weihai |
| author_facet | Guo, Jing Jiang, Xiushan Zhang, Weihai |
| contents | In this article, we study a model-free design approach for stochastic linear quadratic (SLQ) controllers. Based on the convexity of the SLQ dual problem and the Karush-Kuhn-Tucker (KKT) conditions, we find the relationship between the optimal point of the dual problem and the Q-function, which can be used to develop a novel model-free semidefinite programming (SDP) algorithm for deriving optimal control gain. This study provides a new optimization perspective for understanding Q-learning algorithms and lays a theoretical foundation for effective reinforcement learning (RL) algorithms. Finally, the effectiveness of the proposed model-free SDP algorithm is demonstrated by two case simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model-free stochastic linear quadratic design by semidefinite programming Guo, Jing Jiang, Xiushan Zhang, Weihai Optimization and Control In this article, we study a model-free design approach for stochastic linear quadratic (SLQ) controllers. Based on the convexity of the SLQ dual problem and the Karush-Kuhn-Tucker (KKT) conditions, we find the relationship between the optimal point of the dual problem and the Q-function, which can be used to develop a novel model-free semidefinite programming (SDP) algorithm for deriving optimal control gain. This study provides a new optimization perspective for understanding Q-learning algorithms and lays a theoretical foundation for effective reinforcement learning (RL) algorithms. Finally, the effectiveness of the proposed model-free SDP algorithm is demonstrated by two case simulations. |
| title | Model-free stochastic linear quadratic design by semidefinite programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.17230 |