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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/2411.04548 |
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| _version_ | 1866910907898003456 |
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| author | Song, Bowen Wu, Chenxuan Iannelli, Andrea |
| author_facet | Song, Bowen Wu, Chenxuan Iannelli, Andrea |
| contents | This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the region of exponential convergence of both algorithms. In the case where there is uncertainty on the value of the system matrices, we provide input-to-state stability results capturing the effect of model parameter uncertainties. Our findings offer new insights into these algorithms at the heart of several approximate dynamic programming schemes, highlighting their convergence and robustness behaviors. Numerical examples illustrate the significance of some of the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence and Robustness of Value and Policy Iteration for the Linear Quadratic Regulator Song, Bowen Wu, Chenxuan Iannelli, Andrea Systems and Control 49N10 This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the region of exponential convergence of both algorithms. In the case where there is uncertainty on the value of the system matrices, we provide input-to-state stability results capturing the effect of model parameter uncertainties. Our findings offer new insights into these algorithms at the heart of several approximate dynamic programming schemes, highlighting their convergence and robustness behaviors. Numerical examples illustrate the significance of some of the theoretical results. |
| title | Convergence and Robustness of Value and Policy Iteration for the Linear Quadratic Regulator |
| topic | Systems and Control 49N10 |
| url | https://arxiv.org/abs/2411.04548 |