TY - JOUR

T1 - A novel constraint-tightening approach for robust data-driven predictive control

AU - Klöppelt, Christian

AU - Berberich, Julian

AU - Allgöwer, Frank

AU - Müller, Matthias A.

N1 - Funding Information: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant MU3929/1‐2, AL316/12‐2‐279734922, EXC2075‐390740016, and under grant 468094890. We acknowledge the support by the Stuttgart Center for Simulation Science (SimTech). The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS‐IS) for supporting Julian Berberich.

PY - 2022/12/7

Y1 - 2022/12/7

N2 - In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a prestabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example.

AB - In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a prestabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example.

KW - data-driven MPC

KW - robust MPC

UR - http://www.scopus.com/inward/record.url?scp=85131745932&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2203.07055

DO - 10.48550/arXiv.2203.07055

M3 - Article

AN - SCOPUS:85131745932

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1049-8923

ER -