# Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees

arXiv: https://arxiv.org/abs/2405.01292 · HTML: https://mlsanity.com/paper/2405.01292/

## Key facts

- Cited by 2 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 2 May 2024.

## 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)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Deep Identification of Nonlinear Systems in Koopman Form](https://mlsanity.com/paper/2110.02583/) (2021)
- [Koopman Form of Nonlinear Systems with Inputs](https://mlsanity.com/paper/2207.12132/) (2022)
- [Robust Tube-based Model Predictive Control with Koopman Operators--Extended Version](https://mlsanity.com/paper/2108.13011/) (2021)
- [Data-driven MPC with stability guarantees using extended dynamic mode decomposition](https://mlsanity.com/paper/2308.00296/) (2023)
- [State space models vs. multi-step predictors in predictive control: Are state space models complicating safe data-driven designs?](https://mlsanity.com/paper/2203.15471/) (2022)
- [Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations](https://mlsanity.com/paper/2311.05360/) (2023)
- [Koopman based data-driven predictive control](https://mlsanity.com/paper/2102.05122/) (2021)
- [On the design of persistently exciting inputs for data-driven control of linear and nonlinear systems](https://mlsanity.com/paper/2303.08707/) (2023)
- [Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version](https://mlsanity.com/paper/2203.01073/) (2022)

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

- [Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator](https://mlsanity.com/paper/2410.01057/) (2024)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)

## Abstract (arXiv)

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.