Minimax dual control with finite-dimensional information state
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917667510681600 |
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| author | Kjellqvist, Olle |
| author_facet | Kjellqvist, Olle |
| contents | This article considers output-feedback control of systems where the function mapping states to measurements has a set-valued inverse. We show that if the set has a bounded number of elements, then minimax dual control of such systems admits finite-dimensional information states. We specialize our results to a discrete-time integrator with magnitude measurements and derive a surprisingly simple sub-optimal control policy that ensures finite gain of the closed loop. The sub-optimal policy is a proportional controller where the magnitude of the gain is computed offline, but the sign is learned, forgotten, and relearned online.
The discrete-time integrator with magnitude measurements captures real-world applications such as antenna alignment, and despite its simplicity, it defies established control-design methods. For example, whether a stabilizing linear time-invariant controller exists for this system is unknown, and we conjecture that none exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimax dual control with finite-dimensional information state Kjellqvist, Olle Optimization and Control This article considers output-feedback control of systems where the function mapping states to measurements has a set-valued inverse. We show that if the set has a bounded number of elements, then minimax dual control of such systems admits finite-dimensional information states. We specialize our results to a discrete-time integrator with magnitude measurements and derive a surprisingly simple sub-optimal control policy that ensures finite gain of the closed loop. The sub-optimal policy is a proportional controller where the magnitude of the gain is computed offline, but the sign is learned, forgotten, and relearned online. The discrete-time integrator with magnitude measurements captures real-world applications such as antenna alignment, and despite its simplicity, it defies established control-design methods. For example, whether a stabilizing linear time-invariant controller exists for this system is unknown, and we conjecture that none exists. |
| title | Minimax dual control with finite-dimensional information state |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2312.05156 |