The Power of Predictions in Online Control

Abstract

We study the impact of predictions in online Linear Quadratic Regulator control with both stochastic and adversarial disturbances in the dynamics. In both settings, we characterize the optimal policy and derive tight bounds on the minimum cost and dynamic regret. Perhaps surprisingly, our analysis shows that the conventional greedy MPC approach is a near-optimal policy in both stochastic and adversarial settings. Specifically, for length-$T$ problems, MPC requires only $O(\log T)$ predictions to reach $O(1)$ dynamic regret, which matches (up to lower-order terms) our lower bound on the required prediction horizon for constant regret.

References in corpus (8)

• Neural Lander: Stable Drone Landing Control using Learned Dynamics
• Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator
• Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis
• Online Control with Adversarial Disturbances
• Logarithmic Regret for Online Control
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Cited by in corpus (4)

• Online Robust Control of Nonlinear Systems with Large Uncertainty
• On the Regret Analysis of Online LQR Control with Predictions
• On the Value of Preview Information For Safety Control
• Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory