Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes
This work addresses robustness issues in control systems for applications like robotics or autonomous vehicles, but it is incremental as it builds on existing linear quadratic control synthesis methods.
The paper tackles the challenge of robustness in learning-based control by incorporating Gaussian process posterior distributions into controller synthesis, resulting in a more efficient trade-off between performance and robustness compared to worst-case and certainty-equivalence designs.
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.