Collaborative Research: A Coalgebraic Framework for Development and Composition of Hybrid Systems

协作研究：混合系统开发和组合的代数框架

• 批准号: 0208743
• 负责人: Michael Mislove
• 金额: $ 12万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2006-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0208743&HistoricalAwards=false
• 关键词: Collaborative; Research; Coalgebraic; Framework; Development

Mislove & PavlovicCCR-0208743--0209004This project focuses on mathematical foundations and design methodologies for embedded hybrid systems (EHS). The essential feature of such systems is that software components interact not only with each other, but also with the physical world, through sensors and actuators. The discrete dynamics of computation thus adds up with the continuous dynamics of physical systems. Hybrid systems are an attempt to capture this double dynamism in a unified framework. To limit the interference of the formidable complexities of dynamical systems of both types, the continuous trajectories are usually encapsulated into states, at the static points of the discrete computational paths. The methods of continuous mathematics are then simply combined with the methods of discrete mathematics to analyze such combined systems.The starting point of the planned research is a belief that the burgeoning field of coalgebra provides methods and techniques that will allow uniform representation and implementation methods for continuous and discrete objects and aspects. While algebraic methods allow specifying and programming of finite objects and inductive structures, such as expressions or well-founded trees, coalgebraic methods allow specifying and programming infinite objects, as coinductive structures: they include automata and various state machines on the one hand, as well as iterative function systems, analytic functions and operators, and real numbers on the other hand.In a real sense, coinduction permeates analysis just like inductionpermeates arithmetic. The difference is that the latter has been recognized as a fundamental logical principle a long time ago, whereas the the former has been recognized only recently, although it has appeared implicitly for some time (e.g. in most existence-of-the-solutions theorems, although it has been recognized as backwards induction in game theory).The task is now to make explicit and systematize the use of coinductive and coalgebraic methods, and to apply them in analysis and design of embedded hybrid systems.

该项目侧重于嵌入式混合系统（EHS）的数学基础和设计方法。这种系统的基本特征是软件组件不仅彼此交互，而且通过传感器和执行器与物理世界交互。因此，计算的离散动力学与物理系统的连续动力学相结合。混合系统试图在一个统一的框架中捕捉这种双重动力。为了限制这两种类型的动力系统的巨大复杂性的干扰，连续轨迹通常被封装成状态，在离散计算路径的静态点。然后将连续数学方法与离散数学方法简单地结合起来分析这种组合系统。计划研究的起点是一个信念，即协代数的新兴领域提供了方法和技术，将允许连续和离散对象和方面的统一表示和实现方法。代数方法允许指定和规划有限对象和归纳结构，如表达式或建立良好的树，而共代数方法允许指定和规划无限对象，作为共归纳结构：它们一方面包括自动机和各种状态机，另一方面包括迭代函数系统，解析函数和算子，以及实数。在实际意义上，协归纳渗透于分析，就像归纳渗透于算术一样。不同之处在于，后者很久以前就被认为是一个基本的逻辑原理，而前者直到最近才被承认，尽管它已经隐含地出现了一段时间（例如，在大多数解的存在定理中，尽管它在博弈论中被认为是逆向归纳法）。现在的任务是明确和系统地使用共归纳和共代数方法，并将其应用于嵌入式混合系统的分析和设计。