Minimax Adaptive Control for a Finite Set of Linear Systems
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911828648394752 |
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| author | Rantzer, Anders |
| author_facet | Rantzer, Anders |
| contents | An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_10814 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Minimax Adaptive Control for a Finite Set of Linear Systems Rantzer, Anders Optimization and Control An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control. |
| title | Minimax Adaptive Control for a Finite Set of Linear Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2011.10814 |