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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.13227 |
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| _version_ | 1866914876311470080 |
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| author | Yan, Fei Gao, Jie Feng, Tao Liu, Jianxing |
| author_facet | Yan, Fei Gao, Jie Feng, Tao Liu, Jianxing |
| contents | In this paper, the discrete-time modified algebraic Riccati equation (MARE) is solved when the system model is completely unavailable. To achieve this, firstly a brand new iterative method based on the standard discrete-time algebraic Riccati equation (DARE) and its input weighting matrix is proposed to solve the MARE. For the single-input case, the iteration can be initialized by an arbitrary positive input weighting if and only if the MARE has a stabilizing solution; nevertheless a pre-given input weighting matrix of a sufficiently large magnitude is used to perform the iteration for the multi-input case when the characteristic parameter belongs to a specified subset. Benefit from the developed specific iteration structure, the Q-learning (QL) algorithm can be employed to subtly solve the MARE where only the system input/output data is used thus the system model is not required. Finally, a numerical simulation example is given to verify the effectiveness of the theoretical results and the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving the Model Unavailable MARE using Q-Learning Algorithm Yan, Fei Gao, Jie Feng, Tao Liu, Jianxing Systems and Control In this paper, the discrete-time modified algebraic Riccati equation (MARE) is solved when the system model is completely unavailable. To achieve this, firstly a brand new iterative method based on the standard discrete-time algebraic Riccati equation (DARE) and its input weighting matrix is proposed to solve the MARE. For the single-input case, the iteration can be initialized by an arbitrary positive input weighting if and only if the MARE has a stabilizing solution; nevertheless a pre-given input weighting matrix of a sufficiently large magnitude is used to perform the iteration for the multi-input case when the characteristic parameter belongs to a specified subset. Benefit from the developed specific iteration structure, the Q-learning (QL) algorithm can be employed to subtly solve the MARE where only the system input/output data is used thus the system model is not required. Finally, a numerical simulation example is given to verify the effectiveness of the theoretical results and the algorithm. |
| title | Solving the Model Unavailable MARE using Q-Learning Algorithm |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2407.13227 |