Abstract
Delays in feedback dynamics of coupled dynamical systems arise regularly, especially in embedded control where the physical plant and the controller continuously interact through digital networks. Systems featuring delays are however notoriously difficult to analyze. Consequently, formal analysis often addresses simplified, delay-free substitute models, risking negligence of the adverse impact of delay on control performance. In this ongoing work, we demonstrate that for continuous systems such as delay differential equations, a major part of the delay-induced complexity can be reduced effectively when adding natural constraints to the model of the delayed feedback channel, namely that it transports a band-limited signal and implements a non-punctual, distributed delay. The reduction is based on a sampling approach which is applicable when the above conditions on the feedback are satisfied. We further discuss the possibilities of lifting this method to mixed discrete-continuous dynamics of delayed hybrid systems and the open issues thereof.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: DFG GRK 1765/2
Funding statement: This work is supported by the German Research Foundation (DFG) through the Research Training Group SCARE: System Correctness under Adverse Conditions (DFG GRK 1765/2).
About the authors
Erzana Berani Abdelwahab studied Mathematics and received her B. S. degree from Fatih University and her M. S. degree from Bilkent University in Turkey. She has started her PhD in Computer Science at the University of Oldenburg in October 2018 as part of the Research Training Group SCARE under the supervision of Prof. Dr. Martin Fränzle. Her current research interests include formal modeling and verification methods for hybrid systems.
Prof. Dr. Martin Fränzle has been Professor for Hybrid Systems within the Department of Computing Science at the University of Oldenburg since 2004 and the university’s Vice President for Research, Transfer, and Digitalization since 2020. He holds a diploma and a doctoral degree in Computer Science from the University of Kiel and was an associate professor and later a Velux visiting professor at the Technical University of Denmark. Further visiting professorships and extended research stays led him to Freiburg and Saarbrücken (both Germany), Copenhagen (Denmark), Tallinn (Estonia), Grenoble (France), Oxford (UK), and the Chinese Academy of Sciences. Fränzle’s research focuses on the mathematical modelling as well as the verification and synthesis of secure and reliable cyber-physical systems, i. e., the merging of physical objects with information technology into “smart” infrastructures such as autonomous vehicles, production facilities, or supply networks. His research interests thereby span from theoretical foundations to applications and industrial transfer, the latter often pursued within the associated research institute OFFIS e. V., where he is long-standing member of the executive board of the R&D division Transportation.
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