Towards targeted exploration for non-stochastic disturbances
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911969261387776 |
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| author | Venkatasubramanian, Janani Köhler, Johannes Cannon, Mark Allgöwer, Frank |
| author_facet | Venkatasubramanian, Janani Köhler, Johannes Cannon, Mark Allgöwer, Frank |
| contents | We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_05947 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards targeted exploration for non-stochastic disturbances Venkatasubramanian, Janani Köhler, Johannes Cannon, Mark Allgöwer, Frank Systems and Control We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example. |
| title | Towards targeted exploration for non-stochastic disturbances |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2312.05947 |