Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916675291447296 |
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| author | Li, Tongxin Yang, Ruixiao Qu, Guannan Shi, Guanya Yu, Chenkai Wierman, Adam Low, Steven H. |
| author_facet | Li, Tongxin Yang, Ruixiao Qu, Guannan Shi, Guanya Yu, Chenkai Wierman, Adam Low, Steven H. |
| contents | We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances \textit{"consistency"}, which measures the competitive ratio when predictions are accurate, and \textit{"robustness"}, which bounds the competitive ratio when predictions are inaccurate. We propose a novel $λ$-confident policy and provide a competitive ratio upper bound that depends on a trust parameter $λ\in [0,1]$ set based on the confidence in the predictions and some prediction error $\varepsilon$. Motivated by online learning methods, we design a self-tuning policy that adaptively learns the trust parameter $λ$ with a competitive ratio that depends on $\varepsilon$ and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by $ 1+{O(\varepsilon)}/({Θ(1)+Θ(\varepsilon)})+O(μ_{\mathsf{Var}})$ where $μ_\mathsf{Var}$ measures the variation of perturbations and predictions. It implies that when the variations of perturbations and predictions are small, by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error $\varepsilon$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_09659 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions Li, Tongxin Yang, Ruixiao Qu, Guannan Shi, Guanya Yu, Chenkai Wierman, Adam Low, Steven H. Systems and Control Optimization and Control We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances \textit{"consistency"}, which measures the competitive ratio when predictions are accurate, and \textit{"robustness"}, which bounds the competitive ratio when predictions are inaccurate. We propose a novel $λ$-confident policy and provide a competitive ratio upper bound that depends on a trust parameter $λ\in [0,1]$ set based on the confidence in the predictions and some prediction error $\varepsilon$. Motivated by online learning methods, we design a self-tuning policy that adaptively learns the trust parameter $λ$ with a competitive ratio that depends on $\varepsilon$ and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by $ 1+{O(\varepsilon)}/({Θ(1)+Θ(\varepsilon)})+O(μ_{\mathsf{Var}})$ where $μ_\mathsf{Var}$ measures the variation of perturbations and predictions. It implies that when the variations of perturbations and predictions are small, by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error $\varepsilon$. |
| title | Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2106.09659 |