Details
| Original language | English |
|---|---|
| Article number | 9109670 |
| Pages (from-to) | 1702-1717 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 66 |
| Issue number | 4 |
| Publication status | Published - 5 Jun 2020 |
Abstract
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.
Keywords
- Data-driven control, predictive control for linear systems, robust control, uncertain systems
ASJC Scopus subject areas
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Computer Science Applications
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In: IEEE Transactions on Automatic Control, Vol. 66, No. 4, 9109670, 05.06.2020, p. 1702-1717.
Research output: Contribution to journal › Article › Research
}
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 -