Exponential stability of data-driven nonlinear MPC based on input/output models

TL;DR

This paper proves exponential stability for data-driven nonlinear MPC schemes that use input-output data and surrogate models, under certain conditions, and demonstrates practical applicability through numerical examples.

Contribution

It establishes exponential stability for nonlinear MPC using input-output data and kernel interpolation, a novel theoretical result in data-driven control.

Findings

Exponential stability is achieved with sufficiently long prediction horizons.

Kernel interpolation effectively verifies the approximation condition.

Numerical example demonstrates practical applicability to nonlinear systems.

Abstract

We consider nonlinear model predictive control (MPC) schemes using surrogate models in the optimization step based on input-output data only. We establish exponential stability for sufficiently long prediction horizons assuming exponential stabilizability and a proportional error bound. Moreover, we verify the imposed condition on the approximation using kernel interpolation and demonstrate the practical applicability to nonlinear systems with a numerical example.