Robust Learning-Based Control via Bootstrapped Multiplicative Noise
Benjamin Gravell, Tyler Summers, L4DC 2020
Keywords: Optimal, robust, adaptive, control, reinforcement learning, system identification, stochastic parameters
Summary
We propose a robust adaptive control algorithm that explicitly accounts for inherent non-asymptotic uncertainties arising from models estimated with finite, noisy data. The algorithm has three components: (1) a least-squares nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method using an optimal linear quadratic regulator (LQR) with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Numerical experiments show significant improvements over the certainty equivalent controller on both expected regret and measures of regret risk.
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