# Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guarantees

arXiv: https://arxiv.org/abs/2105.03397 · HTML: https://mlsanity.com/paper/2105.03397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 12 of 12)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Deterministic error bounds for kernel-based learning techniques under bounded noise](https://mlsanity.com/paper/2008.04005/) (2020)
- [Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes](https://mlsanity.com/paper/2004.11238/) (2020)
- [Provably Robust Learning-Based Approach for High-Accuracy Tracking Control of Lagrangian Systems](https://mlsanity.com/paper/1804.01031/) (2018)
- [Combining Prior Knowledge and Data for Robust Controller Design](https://mlsanity.com/paper/2009.05253/) (2020)
- [Robust data-driven state-feedback design](https://mlsanity.com/paper/1909.04314/) (2019)
- [Bayesian Safe Learning and Control with Sum-of-Squares Analysis and Polynomial Kernels](https://mlsanity.com/paper/2004.00662/) (2020)
- [Verifying dissipativity properties from noise-corrupted input-state data](https://mlsanity.com/paper/2004.07270/) (2020)

## Built on by (most cited first, 2 of 2)

- [Lipschitz and H"older Continuity in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2310.18078/) (2023)
- [Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors](https://mlsanity.com/paper/2307.04415/) (2023)

## Abstract (arXiv)

The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.