# Data-Enabled Predictive Control: In the Shallows of the DeePC

arXiv: https://arxiv.org/abs/1811.05890 · HTML: https://mlsanity.com/paper/1811.05890/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2018.

## Built on by (most cited first, 30 of 38)

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- [Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems](https://mlsanity.com/paper/2509.18404/) (2025)
- [Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information](https://mlsanity.com/paper/2106.10533/) (2021)
- [Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning](https://mlsanity.com/paper/2205.15703/) (2022)
- [Analysis and Detectability of Offline Data Poisoning Attacks on Linear Dynamical Systems](https://mlsanity.com/paper/2211.08804/) (2022)
- [Urban traffic congestion control: a DeePC change](https://mlsanity.com/paper/2311.09851/) (2023)
- [Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study](https://mlsanity.com/paper/2401.04508/) (2024)
- [Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2510.04591/) (2025)
- [Receding-Horizon Control via Drifting Models](https://mlsanity.com/paper/2604.04528/) (2026)
- [Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems](https://mlsanity.com/paper/2102.09111/) (2021)
- [Achievement and Fragility of Long-term Equitability](https://mlsanity.com/paper/2206.12333/) (2022)
- [LMI-based Data-Driven Robust Model Predictive Control](https://mlsanity.com/paper/2303.04777/) (2023)
- [Data-Driven Adversarial Online Control for Unknown Linear Systems](https://mlsanity.com/paper/2308.08138/) (2023)
- [Uncertainty Quantification of Data-Driven Output Predictors in the Output Error Setting](https://mlsanity.com/paper/2404.15098/) (2024)
- [Data-Driven Predictive Control of Nonholonomic Robots Based on a Bilinear Koopman Realization: Data Does Not Replace Geometry](https://mlsanity.com/paper/2411.07192/) (2024)
- [Enforcing Cooperative Safety for Reinforcement Learning-based Mixed-Autonomy Platoon Control](https://mlsanity.com/paper/2411.10031/) (2024)
- [Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis](https://mlsanity.com/paper/2508.17142/) (2025)

## Abstract (arXiv)

We consider the problem of optimal trajectory tracking for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioural systems theory approach to learn a non-parametric system model used to predict future trajectories. The DeePC algorithm is shown to be equivalent to the classical and widely adopted Model Predictive Control (MPC) algorithm in the case of deterministic linear time-invariant systems. In the case of nonlinear stochastic systems, we propose regularizations to the DeePC algorithm. Simulations are provided to illustrate performance and compare the algorithm with other methods.