# Data-driven MPC with stability guarantees using extended dynamic mode decomposition

arXiv: https://arxiv.org/abs/2308.00296 · HTML: https://mlsanity.com/paper/2308.00296/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2023.

## Built on by (most cited first, 7 of 7)

- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees](https://mlsanity.com/paper/2405.01292/) (2024)
- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)
- [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)
- [Safety-Critical Contextual Control via Online Riemannian Optimization with World Models](https://mlsanity.com/paper/2604.19639/) (2026)
- [Learning to control switching nonlinear systems with Koopman operator regression](https://mlsanity.com/paper/2607.11344/) (2026)
- [SAMpLE: A SystemC-AMS Machine LEarning-based Framework for Virtual Prototyping](https://mlsanity.com/paper/2608.25910/) (2026)

## Abstract (arXiv)

For nonlinear (control) systems, extended dynamic mode decomposition (EDMD) is a popular method to obtain data-driven surrogate models. Its theoretical foundation is the Koopman framework, in which one propagates observable functions of the state to obtain a linear representation in an infinite-dimensional space. In this work, we prove practical asymptotic stability of a (controlled) equilibrium for EDMD-based model predictive control, in which the optimization step is conducted using the data-based surrogate model. To this end, we derive novel bounds on the estimation error that are proportional to the norm of state and control. This enables us to show that, if the underlying system is cost controllable, this stabilizablility property is preserved. We conduct numerical simulations illustrating the proven practical asymptotic stability.