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Analysis and Design of Interconnected Systems: A Systems and Control Perspective

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10500))

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Abstract

Hybrid and cyber-physical systems are at the intersection of the theory of concurrent processes and of systems and control theory. This paper reviews some ideas from systems and control theory, which can be considered to be fruitful for the study of such systems. Particular emphasis is on the use of dissipative systems theory for the analysis of interconnected systems, and on the ‘control by interconnection’ problem using an extension of the notion of (bi-)simulation to the realm of continuous dynamics. Furthermore, the paper surveys a definition of hybrid systems, which treats the continuous and discrete dynamics on an equal footing.

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Notes

  1. 1.

    Note that in the sequel we will also use the notations l, x, a, w for time-functions, mapping for each time instant t to elements \(l(t) \in \mathcal {L}, x(t) \in \mathcal {X}, a(t) \in \mathcal {A}, w(t) \in \mathcal {W}\), respectively.

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Acknowledgements

After my collaboration with Hans Schumacher at the CWI on the topic of hybrid systems, I was very fortunate to be close to the Formal Methods and Tools group at the Computer Science department of the University of Twente, headed by Ed Brinksma. I happily remember the enjoyable and very stimulating conversations with especially Ed Brinksma, Rom Langerak and Joost-Pieter Katoen, also involving Jan Willem Polderman from the mathematics side. Among others this led to the celebrated NWO-CASH project. I still regard this collaboration as an exemplary case of open and fruitful collaboration. It is a great pleasure to dedicate this paper, which is heavily inspired by this collaboration, to Ed at the occasion of his 60th birthday. Happy birthday Ed!

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Authors and Affiliations

  1. Jan C. Willems Center for Systems and Control, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

    Arjan van der Schaft

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  1. Arjan van der Schaft
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Correspondence to Arjan van der Schaft .

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Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  2. University of Twente, Enschede, The Netherlands

    Rom Langerak

  3. University of Twente, Enschede, The Netherlands

    Arend Rensink

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van der Schaft, A. (2017). Analysis and Design of Interconnected Systems: A Systems and Control Perspective. In: Katoen, JP., Langerak, R., Rensink, A. (eds) ModelEd, TestEd, TrustEd. Lecture Notes in Computer Science(), vol 10500. Springer, Cham. https://doi.org/10.1007/978-3-319-68270-9_16

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  • DOI: https://doi.org/10.1007/978-3-319-68270-9_16

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