Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees

TL;DR

This paper introduces a data-driven predictive control method for nonlinear systems using Koopman models, focusing on stability, feasibility, and error mitigation, demonstrated on a benchmark example.

Contribution

It proposes a novel Koopman-based predictive control approach with stability and feasibility guarantees, avoiding explicit model identification.

Findings

Successful control of a nonlinear benchmark system

Guarantees of recursive feasibility and stability

Effective error mitigation through regularization

Abstract

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.