Data-driven Koopman MPC using Mixed Stochastic-Deterministic Tubes

TL;DR

This paper introduces a data-driven stochastic MPC method for nonlinear systems using Koopman operator theory and a mixed stochastic-deterministic tube approach, ensuring constraint satisfaction with finite sample guarantees.

Contribution

It develops a novel Koopman-based stochastic MPC framework with mixed tubes and provides finite sample error bounds, advancing data-driven control for nonlinear systems.

Findings

Effective regulation of nonlinear systems demonstrated in simulations.

Finite sample error bounds established for the proposed tubes.

Combines stochastic and deterministic approaches for robust constraint satisfaction.

Abstract

This paper presents a novel data-driven stochastic MPC design for discrete-time nonlinear systems with additive disturbances by leveraging the Koopman operator and a distributionally robust optimization (DRO) framework. By lifting the dynamical system into a linear space, we achieve a finite-dimensional approximation of the Koopman operator. We explicitly account for the modeling approximation and additive disturbance error by a mixed stochastic-deterministic tube for the lifted linear model. This ensures the regulation of the original nonlinear system while complying with the prespecified constraints. Stochastic and deterministic tubes are constructed using a DRO and a hyper-cube hull, respectively. We provide finite sample error bounds for both types of tubes. The effectiveness of the proposed approach is demonstrated through numerical simulations.