# Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes

arXiv: https://arxiv.org/abs/2105.07668 · HTML: https://mlsanity.com/paper/2105.07668/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 17 May 2021.

## Builds on (most cited first, 9 of 9)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Variational Gaussian Process State-Space Models](https://mlsanity.com/paper/1406.4905/) (2014)
- [Actively Learning Gaussian Process Dynamics](https://mlsanity.com/paper/1911.09946/) (2019)
- [Computationally Efficient Bayesian Learning of Gaussian Process State Space Models](https://mlsanity.com/paper/1506.02267/) (2015)
- [Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes](https://mlsanity.com/paper/2004.11238/) (2020)
- [Event-triggered Learning for Linear Quadratic Control](https://mlsanity.com/paper/1910.07732/) (2019)
- [Learning convex bounds for linear quadratic control policy synthesis](https://mlsanity.com/paper/1806.00319/) (2018)

## Built on by (most cited first, 4 of 4)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [On the Consistency of Kernel Methods with Dependent Observations](https://mlsanity.com/paper/2406.06101/) (2024)
- [Improving the Performance of Robust Control through Event-Triggered Learning](https://mlsanity.com/paper/2207.14252/) (2022)

## Abstract (arXiv)

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.