Stability of data-driven Koopman MPC with terminal conditions

TL;DR

This paper establishes stability conditions for data-driven Koopman MPC with terminal constraints, ensuring asymptotic stability despite approximation errors, using kernel EDMD models.

Contribution

It provides a theoretical framework for stability of Koopman-based MPC with terminal conditions, including error bounds and practical data-driven modeling techniques.

Findings

Proves recursive feasibility and stability under proportional error bounds.

Demonstrates the framework on a numerical case study.

Shows that kernel EDMD models can satisfy stability conditions for nonlinear systems.

Abstract

This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular, we prove recursive feasibility and asymptotic stability if a proportional error bound holds, where proportional means that the bound is linear in the norm of the state and the input. For a broad class of nonlinear systems, this condition can be satisfied using data-driven surrogate models generated by kernel Extended Dynamic Mode Decomposition (kEDMD) using the Koopman operator. Last, the applicability of the proposed framework is demonstrated in a numerical case study.