Automatica

Published by: Elsevier

Published by

Elsevier
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Abstract

In this paper, we introduce a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical results characterizing the set of non-falsified parameters consistent with energy-bounded disturbances. We derive a semidefinite program which computes an exploration strategy that guarantees a desired accuracy of the parameter estimate. This design is based on sufficient conditions on the spectral content of the exploration data that robustly account for initial parametric uncertainty. Finally, we highlight the applicability of the exploration strategy through a numerical example involving a nonlinear system.

Keywords

Experiment design
;
Optimization under uncertainties
;
Uncertainty quantification
;
Data-driven control
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Janani Venkatasubramanian received the M.Sc. degree in electrical engineering and Ph.D. degree in mechanical engineering from the Delft University of Technology, The Netherlands, in 2018, and the University of Stuttgart, Stuttgart, Germany, in 2025, respectively. She completed her Ph.D. as a member of the International Max Planck Research School for Intelligent Systems (IMPRS-IS). She is currently a Postdoctoral Researcher at the Institute of Control Systems, Hamburg University of Technology. Her research interests lie in the areas of learning-based control, data-driven control, system identification, and robust and stochastic predictive control.
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Johannes Köhler is an Assistant Professor at Imperial College London. He received the Ph.D. degree from the University of Stuttgart, Germany, in 2021. From 2021 to 2025, he was a postdoctoral researcher at ETH Zurich, Switzerland. He has received several awards including the 2021 European Systems & Control Ph.D. Thesis Award, the IEEE CSS George S. Axelby Outstanding Paper Award 2022, and the Journal of Process Control Paper Award 2023. His research interests include data-driven models and predictive control with applications to robotics, autonomous systems, and biomedical problems.
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Mark Cannon (Member, IEEE) received the M.Eng. degree in engineering science and D.Phil. degree in control engineering from the University of Oxford, Oxford, U.K., in 1993 and 1998, respectively, and the M.S. degree in mechanical engineering from the Massachusetts Institute of Technology, in 1995. He is currently Professor of Engineering Science at the University of Oxford and a Fellow of St. John’s College. His research interests include robust and stochastic predictive control, data-driven control and optimization, adaptive control, and aerospace, automotive, and biomedical engineering applications.
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Frank Allgöwer studied engineering cybernetics and applied mathematics in Stuttgart and at the University of California, Los Angeles (UCLA), CA, USA, respectively, and received the Ph.D. degree from the University of Stuttgart, Stuttgart, Germany. Since 1999, he has been the Director of the Institute for Systems Theory and Automatic Control and a professor with the University of Stuttgart. His research interests include predictive control, data-based control, networked control, cooperative control, and nonlinear control with application to a wide range of fields including systems biology. Dr. Allgöwer was the President of the International Federation of Automatic Control (IFAC) in 2017–2020 and the Vice President of the German Research Foundation DFG in 2012–2020.
Frank Allgöwer is thankful that his work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 - 390740016 and under grant 468094890. Frank Allgöwer was supported by the Stuttgart Center for Simulation Science (SimTech). Janani Venkatasubramanian was supported by the International Max Planck Research School for Intelligent Systems (IMPRS-IS). Johannes Köhler was supported by the Swiss National Science Foundation under NCCR Automation (grant agreement 51NF40 180545).The material in this paper was partially presented at IFAC Symposium on System Identification, Boston, USA, July 17–18, 2024. This paper was recommended for publication in revised form by Associate Editor Simone Formentin under the direction of Editor Alessandro Chiuso.