Data-Driven Model Predictive Control With Stability and Robustness Guarantees

• Published in: IEEE transactions on automatic control Vol. 66; no. 4; pp. 1702 - 1717
• Main Authors: Berberich, Julian, Kohler, Johannes, Muller, Matthias A., Allgower, Frank
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loops; Control stability; Control theory; Data-driven control; Linear systems; Noise; Noise levels; Noise measurement; Predictive control; predictive control for linear systems; Regularization; Robust control; Stability analysis; System theory; Systems theory; Time invariant systems; Trajectory; Trajectory measurement; uncertain systems; Upper bounds
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3000182

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.