Data-Enabled Predictive Control for Nonlinear Systems Based on a Koopman Bilinear Realization

TL;DR

This paper introduces a data-driven control approach for nonlinear systems using Koopman bilinear realization, eliminating the need for system identification and improving robustness and optimality over traditional Koopman methods.

Contribution

It extends Willems' Fundamental Lemma to nonlinear systems via Koopman bilinear realization, enabling direct data-driven control without EDMD-based system identification.

Findings

Achieves improved optimality over conventional Koopman methods.

Demonstrates robustness to finite Koopman approximation errors.

Provides a practical data-enabled predictive control framework for nonlinear systems.

Abstract

This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in conventional Koopman-based methods and design controllers for nonlinear systems directly from data. Leveraging this result, we develop a Data-Enabled Predictive Control (DeePC) framework for nonlinear systems with unknown dynamics. A case study demonstrates that our direct data-driven control method achieves improved optimality compared to conventional Koopman-based methods. Furthermore, in examples where an exact Koopman realization with a finite-dimensional lifting function set of the controlled nonlinear system does not exist, our method exhibits advanced robustness to finite Koopman approximation errors compared to existing methods.