Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis
Conference Paper
Overview
Overview
abstract
This paper studies the online optimal control problem with time-varying convex stage costs for a time-invariant linear dynamical system, where a finite look-ahead window with accurate predictions of the stage costs is available at each time. We design online algorithms, Receding Horizon Gradient-based Control (RHGC), that utilizes the predictions through finite steps of gradient computations. We study the algorithm performance measured by dynamic regret: the online performance minus the optimal performance in hindsight. It is shown that the dynamic regret of RHGC decays exponentially with the size of the look-ahead window. In addition, we provide a fundamental limit of the dynamic regret for any online algorithms by considering linear quadratic tracking problems. The regret upper bound of one RHGC method almost reaches the fundamental limit, demonstrating the effectiveness of the algorithm. Finally, we numerically test our algorithms for both linear and nonlinear systems to show the effectiveness and generality of our RHGC.
