Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees

TL;DR

This paper introduces a kernel EDMD-based data-driven MPC approach for nonlinear systems, providing stability guarantees without requiring invariant sets, and demonstrates its effectiveness through numerical simulations.

Contribution

It develops a kernel EDMD method for control that ensures practical stability in MPC without the need for stabilizing terminal conditions.

Findings

Practical asymptotic stability of the closed-loop system is proven.

The method avoids restrictive invariance conditions.

Numerical simulations confirm the theoretical results.

Abstract

Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a recently-introduced kernel EDMD method for control systems for data-driven model predictive control. Building upon pointwise error bounds proportional in the state, we rigorously show practical asymptotic stability of the origin w.r.t. the MPC closed loop without stabilizing terminal conditions. The key novelty is that we avoid restrictive invariance conditions. Last, we verify our findings by numerical simulations.