TY - JOUR

T1 - Data-Driven Model Predictive Control with Stability and Robustness Guarantees

AU - Berberich, Julian

AU - Koehler, Johannes

AU - Müller, Matthias A.

AU - Allgower, Frank

N1 - Funding information: Manuscript received November 20, 2019; revised May 4, 2020; accepted May 26, 2020. Date of publication June 5, 2020; date of current version March 29, 2021. This work was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy—EXC 2075—390740016. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting Julian Berberich, and the International Research Training Group Soft Tissue Robotics (GRK 2198/1). Recommended by Associate Editor E. C. Kerrigan. (Corresponding author: Julian Berberich.) Julian Berberich, Johannes Köhler, and Frank Allgöwer are with the Institute for Systems Theory and Automatic Control, University of Stuttgart 70550, Stuttgart, Germany (e-mail: julian.berberich@ist. uni-stuttgart.de; johannes.koehler@ist.uni-stuttgart.de; frank.allgower@ ist.uni-stuttgart.de).

PY - 2020/6/5

Y1 - 2020/6/5

N2 - We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input-output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

AB - We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input-output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

KW - Data-driven control

KW - predictive control for linear systems

KW - robust control

KW - uncertain systems

UR - http://www.scopus.com/inward/record.url?scp=85103441657&partnerID=8YFLogxK

U2 - 10.1109/TAC.2020.3000182

DO - 10.1109/TAC.2020.3000182

M3 - Article

VL - 66

SP - 1702

EP - 1717

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 4

M1 - 9109670

ER -