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A categorical approach to open and interconnected dynamical systems

A categorical approach to open and interconnected dynamical systems
A categorical approach to open and interconnected dynamical systems
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 be- havioural approach places open systems at its centre, modelling by tearing, zooming, and linking. We show that these ideas are natu- rally 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 systems. These string diagrams are closely related to the classical notion of signal flow graphs, endowed with semantics as multi-input multi-output transducers that process discrete streams with an infinite past as well as an infinite future. At the categorical level, the algebraic characterisation is that of the prop of corelations.

Using this framework, we derive a novel structural characterisa- tion of controllability, and consequently provide a methodology for analysing controllability of networked and interconnected systems. We argue that this has the potential of providing elegant, simple, and efficient solutions to problems arising in the analysis of sys- tems over networks, a vibrant research area at the crossing of con- trol theory and computer science.
Fong, Brendan
468ef8f4-7a57-4499-88b4-02e9bf754c8a
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Fong, Brendan
468ef8f4-7a57-4499-88b4-02e9bf754c8a
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b

Fong, Brendan, Sobocinski, Pawel and Rapisarda, Paolo (2016) A categorical approach to open and interconnected dynamical systems. LiCS 2016: 31st Annual ACM/IEEE Symposium on Logic in Computer Science, United States. 05 - 08 Jul 2016. 10 pp.

Record type: Conference or Workshop Item (Paper)

Abstract

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 be- havioural approach places open systems at its centre, modelling by tearing, zooming, and linking. We show that these ideas are natu- rally 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 systems. These string diagrams are closely related to the classical notion of signal flow graphs, endowed with semantics as multi-input multi-output transducers that process discrete streams with an infinite past as well as an infinite future. At the categorical level, the algebraic characterisation is that of the prop of corelations.

Using this framework, we derive a novel structural characterisa- tion of controllability, and consequently provide a methodology for analysing controllability of networked and interconnected systems. We argue that this has the potential of providing elegant, simple, and efficient solutions to problems arising in the analysis of sys- tems over networks, a vibrant research area at the crossing of con- trol theory and computer science.

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e-pub ahead of print date: July 2016
Venue - Dates: LiCS 2016: 31st Annual ACM/IEEE Symposium on Logic in Computer Science, United States, 2016-07-05 - 2016-07-08
Organisations: Electronic & Software Systems

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Local EPrints ID: 393995
URI: https://eprints.soton.ac.uk/id/eprint/393995
PURE UUID: a7cec7a6-48ca-4e22-92f5-1c787315e349

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Date deposited: 26 May 2016 13:03
Last modified: 09 Jan 2018 18:08

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Contributors

Author: Brendan Fong
Author: Pawel Sobocinski
Author: Paolo Rapisarda

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