# Robust and Kernelized Data-Enabled Predictive Control for Nonlinear Systems

arXiv: https://arxiv.org/abs/2206.01866 · HTML: https://mlsanity.com/paper/2206.01866/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2022.

## Built on by (most cited first, 9 of 9)

- [Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations](https://mlsanity.com/paper/2311.05360/) (2023)
- [Offline Guarded Safe Reinforcement Learning for Medical Treatment Optimization Strategies](https://mlsanity.com/paper/2505.16242/) (2025)
- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [Data-driven Acceleration of MPC with Guarantees](https://mlsanity.com/paper/2511.13588/) (2025)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [Fine-tuning for Data-enabled Predictive Control of Noisy Systems by Reinforcement Learning](https://mlsanity.com/paper/2505.24572/) (2025)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)
- [A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2605.07052/) (2026)

## Abstract (arXiv)

This paper presents a robust and kernelized data-enabled predictive control (RoKDeePC) algorithm to perform model-free optimal control for nonlinear systems using only input and output data. The algorithm combines robust predictive control and a non-parametric representation of nonlinear systems enabled by regularized kernel methods. The latter is based on implicitly learning the nonlinear behavior of the system via the representer theorem. Instead of seeking a model and then performing control design, our method goes directly from data to control. This allows us to robustify the control inputs against the uncertainties in data by considering a min-max optimization problem to calculate the optimal control sequence. We show that by incorporating a proper uncertainty set, this min-max problem can be reformulated as a nonconvex but structured minimization problem. By exploiting its structure, we present a projected gradient descent algorithm to effectively solve this problem. Finally, we test the RoKDeePC on two nonlinear example systems - one academic case study and a grid-forming converter feeding a nonlinear load - and compare it with some existing nonlinear data-driven predictive control methods.