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A categorical approach to open and interconnected dynamical systems

机译：打开和互连动态系统的分类方法

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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 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 characterisation 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 systems over networks, a vibrant research area at the crossing of control theory and computer science.
机译：在1986年，自动纸质威廉斯介绍了控制理论的有影响力的行为方法，并考虑了线性时间不变（LTI）离散动力系统。行为方法将开放系统位于其中心，通过撕裂，缩放和链接建模。我们表明这些想法自然以对称的单面类别的语言表达。您的主要结果给出了直观的声音和完全完整的弦图代数，了解LTI系统。这些字符串图与信号流程图的经典概念密切相关，赋予语义为多输入多输出传感器，该传感器处理具有无限流的离散流以及无限的未来。在分类层面，代数表征是支持本框架的支持。我们推导出一种新的结构表征可控性，因此提供了一种用于分析网络和互连系统的可控性的方法。我们认为这有可能为在网络上分析系统分析，在控制理论和计算机科学的交叉路中提供充满活力的研究区域，提供优雅，简单，有效的解决方案。

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