# A categorical approach to open and interconnected dynamical systems

@article{Fong2016ACA, title={A categorical approach to open and interconnected dynamical systems}, author={Brendan Fong and Paolo Rapisarda and Pawel Soboci'nski}, journal={2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}, year={2016}, pages={1-10} }

In his 1986 Automatica paper Willems introduced the influential behavioural approach to control theory with an investigation of linear time-invariant (LTI) discrete dynamical systems. The behavioural approach places open systems at its centre, modelling by tearing, zooming, and linking. We show that these ideas are naturally expressed in the language of symmetric monoidal categories.Our main result gives an intuitive sound and fully complete string diagram algebra for reasoning about LTI…

## 37 Citations

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It is shown to axiomatise a category of open Petri nets, in the style of the connector algebras of nets with boundaries first studied by Bruni, Melgratti, Montanari and Sobociński.

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Bialgebraic Semantics for String Diagrams

- Computer ScienceCONCUR
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This work uses the bialgebraic approach to derive well-behaved structural operational semantics of string diagrams, a graphical syntax that is increasingly used in the study of interacting systems across different disciplines.

37 : 2 Bialgebraic Semantics for String Diagrams

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This work provides bialgebraic compositional semantics for a versatile string diagrammatic language which has been used to model both signal flow graphs and Petri nets, and reveals a correspondence between two different interpretations of the Frobenius equations on string diagrams.

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The resource calculus is introduced, a string diagrammatic language for concurrent systems that uses the same syntax and operational semantics as the signal flow calculus --- an algebraic formalism for signal flow graphs, which is a combinatorial model of computation of interest in control theory.

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- 2019

This work has shown how to extend graphical linear/affine algebra with a connector for affine behaviour, which can model systems with richer patterns of behaviour such as mutual exclusion when R = N and non-passive electrical components—when R = R(x).

Rewriting with Frobenius

- Computer ScienceLICS
- 2018

A DPO rewriting formalism which is able to absorb multiple Frobenius structures, thus sensibly simplifying diagrammatic reasoning in the analysis of compound systems in a compositional, resource-sensitive manner.

The algebra of open and interconnected systems

- Computer Science
- 2016

This thesis develops the theory of hypergraph categories and introduces the tools of decorated cospans and corelations, a more powerful version that permits construction of all hyper graph categories and hypergraph functors.

Categories in Control: Applied PROPs

- Mathematics
- 2016

Author(s): Erbele, Jason | Advisor(s): Baez, John | Abstract: Control theory uses `signal-flow diagrams' to describe processes where real-valued functions of time are added, multiplied by scalars,…

Rewriting modulo symmetric monoidal structure

- Computer Science2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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This paper interprets diagrams combinatorially as typed hypergraphs and establishes the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hyper graphs, subject to a soundness condition called convexity, on the other.

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