Combining Prior Knowledge and Data for Robust Controller Design

2022/10/26 by Julian Berberich, Carsten W. Scherer, Frank Allgöwer · 138 citations
Engineering · Mathematics · Physics and Astronomy · #Artificial intelligence #Computer science #Control (management) #Control Systems and Identification #Control engineering #Control system #Control theory (sociology) #Controller (irrigation) #Data mining #Data-driven #Engineering #Fault Detection and Control Systems #Linear matrix inequality #Linear system #Machine learning #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Nonlinear system #Robust control #Robustness (evolution) #Stability (learning theory)

paper · open access · doi:10.1109/tac.2022.3209342

published in IEEE Transactions on Automatic Control 68(8), 4618-4633 (Institute of Electrical and Electronics Engineers)

openalex publication_date 2022/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI)-based feasibility criteria that guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter, a novel and unifying disturbance description is employed. While large parts of the article focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input–output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.

Citations

• Data-driven simulation and control
• Data-Driven Model Predictive Control with Stability and Robustness Guarantees

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