Zusammenfassung
High-Gain-Beobachter werden häufig verwendet, um den aktuellen internen Zustand nichtlinearer Systeme zu schätzen. Der Ansatz beruht auf der Transformation in die Beobachtbarkeitsnormalform und mitunter auf der Einbettung des Systems in einen höherdimensionalen Raum. Obwohl dies Vorteile in Bezug auf Existenzbedingungen und Konvergenz bieten kann, sind die rechnerischen und implementierungsbezogenen Aufgaben oft abschreckend. In diesem Beitrag gehen wir einige dieser Herausforderungen an, indem wir neuronale Netze und automatisches Differenzieren verwenden, um die erforderlichen Funktionen für die Implementierung des Beobachters zu approximieren. Dies bietet einen pragmatischen Ansatz, um einige der mit der Einbettung von Beobachtern verbundenen Probleme zu umgehen.
Abstract
High gain observers are frequently utilized to estimate the current internal state of nonlinear systems. The approach relies on transforming the system into the observability canonical form and occasionally embedding it into a higher dimensional space. While this can offer advantages in terms of existence conditions and convergence, the computational and implementation tasks are often daunting. In this paper, we address some of these challenges by using neural networks and automatic differentiation to approximate the necessary functions for implementing the observer. This offers a pragmatic approach to bypassing some of the problems associated with embedding observers.
Über die Autoren
Dipl.-Ing. Julius Fiedler ist wissenschaftlicher Mitarbeiter am Institut für Regelungs- und Steuerungstheorie an der Fakultät Elektrotechnik und Informationstechnik der Technischen Universität Dresden. Er beschäftigt sich mit formaler Repräsentation von Wissen, mit Fokus auf Anwendungen in der Regelungstechnik und maschinellem Lernen.
Dipl.-Ing. Daniel Gerbet ist wissenschaftlicher Mitarbeiter am Institut für Regelungs- und Steuerungstheorie an der Fakultät Elektrotechnik und Informationstechnik der Technischen Universität Dresden. Er beschäftigt sich mit dem Reglerentwurf durch Methoden aus der algebraischen Geometrie und der Quantorenelimination.
Prof. Dr.-Ing. habil. Dipl.-Math. Klaus Röbenack ist Direktor des Instituts für Regelungs- und Steuerungstheorie an der Fakultät Elektrotechnik und Informationstechnik der Technischen Universität Dresden. Seine Arbeitsgebiete umfassen den Entwurf nichtlinearer Regler und Beobachter sowie das wissenschaftliche Rechnen.
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Research ethics: Not applicable.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: The authors state no conflict of interest.
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Research funding: Partly funded by Deutsche Forschungsgemeinschaft (DFG) – 417698841.
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Data availability: The raw data can be obtained on request from the corresponding author.
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