# Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations

arXiv: https://arxiv.org/abs/2311.05360 · HTML: https://mlsanity.com/paper/2311.05360/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 9 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [A trajectory-based framework for data-driven system analysis and control](https://mlsanity.com/paper/1903.10723/) (2019)
- [Bridging direct & indirect data-driven control formulations via regularizations and relaxations](https://mlsanity.com/paper/2101.01273/) (2021)
- [Robust and Kernelized Data-Enabled Predictive Control for Nonlinear Systems](https://mlsanity.com/paper/2206.01866/) (2022)
- [Linear tracking MPC for nonlinear systems Part II: The data-driven case](https://mlsanity.com/paper/2105.08567/) (2021)
- [Nonlinear Data-Enabled Prediction and Control](https://mlsanity.com/paper/2101.03187/) (2021)
- [Koopman based data-driven predictive control](https://mlsanity.com/paper/2102.05122/) (2021)
- [On the design of terminal ingredients for data-driven MPC](https://mlsanity.com/paper/2101.05573/) (2021)
- [Data-Driven Predictive Control for Linear Parameter-Varying Systems](https://mlsanity.com/paper/2103.16160/) (2021)
- [Data-driven Nonlinear Predictive Control for Feedback Linearizable Systems](https://mlsanity.com/paper/2211.06339/) (2022)

## Built on by (most cited first, 5 of 5)

- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [Deep Operator Neural Network Model Predictive Control](https://mlsanity.com/paper/2505.18008/) (2025)
- [Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees](https://mlsanity.com/paper/2405.01292/) (2024)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)

## Abstract (arXiv)

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis functions DeePC behavioral predictor and we identify necessary and sufficient conditions for equivalence with a corresponding basis functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.