Infinite-Horizon Distributionally Robust Regret-Optimal Control
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913386359422976 |
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| author | Kargin, Taylan Hajar, Joudi Malik, Vikrant Hassibi, Babak |
| author_facet | Kargin, Taylan Hajar, Joudi Malik, Vikrant Hassibi, Babak |
| contents | We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret-the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite-Horizon Distributionally Robust Regret-Optimal Control Kargin, Taylan Hajar, Joudi Malik, Vikrant Hassibi, Babak Optimization and Control Systems and Control We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret-the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting. |
| title | Infinite-Horizon Distributionally Robust Regret-Optimal Control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2406.07248 |