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arXiv · 1510.05076

A categorical approach to open and interconnected dynamical systems

Brendan Fong·Paolo Rapisarda·Paweł Sobociński
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Abstract

We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous work, these are understood as multi-input multi-output transducers that process streams with an \emph{infinite past} as well as an infinite future. This extended semantics features non-controllable systems, and we develop a novel, structural characterisation of controllability. Our approach is formalised through the theory of props, extending the work of Bonchi, Zanasi and the third author.

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Brendan Fong, Paolo Rapisarda, Paweł Sobociński. 2015-10-17. A categorical approach to open and interconnected dynamical systems. https://doi.org/10.1145/2933575.2934556

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