• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>Annual ACM/IEEE Symposium on Logic in Computer Science >A categorical approach to open and interconnected dynamical systems
【24h】

A categorical approach to open and interconnected dynamical systems

机译：开放和相互联系的动力系统的一种分类方法

获取原文
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

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：威廉姆斯（Willems）在1986年的《自动化》（Automatica）论文中，通过研究线性时不变（LTI）离散动力系统，介绍了有影响的行为方法来控制理论。行为方法将开放系统置于其中心，通过撕裂，缩放和链接进行建模。我们证明了这些想法自然是用对称单项式类别的语言表达的。我们的主要结果给出了直观的声音和完全完整的弦图代数，用于对LTI系统进行推理。这些字符串图与经典的信号流图概念密切相关，信号流图具有多输入多输出换能器的语义，可处理具有无限过去和无限未来的离散流。在分类层次上，代数表征是相关性的支撑。使用此框架，我们得出了可控性的新型结构表征，从而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网络分析系统中出现的问题提供优雅，简单和有效的解决方案，这是控制理论和计算机科学交叉发展的活跃领域。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号