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

TL;DR

This paper demonstrates that data-driven model predictive control using extended dynamic mode decomposition can ensure practical asymptotic stability for nonlinear systems, with theoretical error bounds and numerical validation.

Contribution

It provides the first proof of practical stability guarantees for EDMD-based MPC, including novel error bounds and stability preservation under cost controllability.

Findings

Proves practical asymptotic stability of EDMD-based MPC.

Derives bounds on estimation error proportional to state and control norms.

Numerical simulations confirm theoretical stability results.

Abstract

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.