Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes

arXiv (Cornell University), pp. 324–335

Abstract

Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution in the controller synthesis. The result is a more informed and, thus, more efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system's stability.Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.

Authors 3

1. Alexander von Rohr Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Matthias Neumann-Brosig

   Technische Universität Braunschweig · Ingenieurgesellschaft Auto und Verkehr (Germany)

   Affiliation as printed

   Ingenieurgesellschaft Auto und Verkehr (IAV)

   Institut Analysis und Algebra , TU Braunschweig , Germany

3. Sebastian Trimpe Aachen Institut for Data Science in Mechanical Engineering

   RWTH Aachen University · Max Planck Institute for Intelligent Systems

   Affiliation as printed

   Institut for Data Science in Mechanical Engineering , RWTH Aachen University , Germany

   Max Planck Institute for Intelligent Systems , Tübingen/ Stuttgart , Germany

   RWTH Aachen University