We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances consistency, which measures the competitive ratio when predictions are accurate, and robustness, which bounds the competitive ratio when predictions are inaccurate. We propose a novel 𝜆-confident controller and prove that it maintains a competitive ratio upper bound of 1 + min{𝑂 (𝜆 2 𝜀) + 𝑂 (1 − 𝜆) 2 , 𝑂 (1) + 𝑂 (𝜆 2 )} where 𝜆 ∈ [0, 1] is a trust parameter set based on the confidence in the predictions, and 𝜀 is the prediction error. Further, we design a self-tuning policy that adaptively learns the trust parameter 𝜆 with a competitive ratio that depends on 𝜀 and the variation of system perturbations and predictions.CCS Concepts: • Theory of computation → Online learning algorithms; Regret bounds.

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances consistency, which measures the competitive ratio when predictions are accurate, and robustness, which bounds the competitive ratio when predictions are inaccurate.

Machine-learned black-box policies are ubiquitous for nonlinear control problems. Meanwhile, crude model information is often available for these problems from, e.g., linear approximations of nonlinear dynamics. We study the problem of certifying a black-box control policy with stability using model-based advice for nonlinear control on a single trajectory. We first show a general negative result that a naive convex combination of a black-box policy and a linear model-based policy can lead to instability, even if the two policies are both stabilizing. We then propose an adaptive λ-confident policy, with a coefficient λ indicating the confidence in a black-box policy, and prove its stability. With bounded nonlinearity, in addition, we show that the adaptive λ-confident policy achieves a bounded competitive ratio when a black-box policy is near-optimal. Finally, we propose an online learning approach to implement the adaptive λ-confident policy and verify its efficacy in case studies about the Cart-Pole problem and a real-world electric vehicle (EV) charging problem with covariate shift due to COVID-19.INDEX TERMS black-box policy, stability, nonlinear control, covariate shift

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances "consistency'', which measures the competitive ratio when predictions are accurate, and "robustness'', which bounds the competitive ratio when predictions are inaccurate. We propose a novel λ-confident controller and prove that it maintains a competitive ratio upper bound of 1 + min {O(λ2ε)+ O(1-λ)2,O(1)+O(λ2)} where λ∈ [0,1] is a trust parameter set based on the confidence in the predictions, and ε is the prediction error. Further, 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 ε and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by 1+O(ε) /(Θ)(1)+Θ(ε))+O(μVar) where μVar measures the variation of perturbations and predictions. It implies that by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error ε.