基于不动点交互建模的信息物理融合系统时间度量和表示研究

This project is aimed at ensuring the consistency of temporal properties measurement and representation for system state and interaction behavior of Cyber-Physical System(CPS) that continuous physical systems coexist and interact with discrete computing systems among feedback control of computation process and physical process, to ensure existence and uniqueness of system behavior. While traditional method for modeling physical process and computation process lacks of mechanism for swithching discrete logic control to continuous time behavior, effective software modeling must be based on differential invariants computing that is interacted by fixedpoint theory to measure time, concurrency, and controlled complexity. The proposed project, which has four focus areas of research, will provide temporal properties measurement and representation paradigm for CPS system, based on fixedpoint interaction modeling. (a) Interaction behavior model. The focus here is on extensively describing interaction semantics of super-dense time domain that determines component timing causal combination mechanism. (b) Global signal function. Key to this effort is research in defining global time function to formalize signal causal properties and transfer component interaction by time poset function. (c)Timing metrics function. The deliverables from this project will be a set of timing metrics function, based on extended generalized ultrametrics space method and symbolic framework. System behavior will be mapped to a fixed point of function model. Based on fixed point theorem, strict convergence of timing signal function is proved to the only fixed point, and existence and uniqueness of system behavior is supported. (d)Signal timing combination calculus. This project will provide a fundamentally system-level signal timing combinnation calculus strategy, based on the improved timing Petri nets model, which derives signal timing and determines scheduling logic.

信息物理融合系统中连续物理系统和离散计算系统共存且相互作用。因此，信息物理融合系统建模更强调计算进程与物理进程交互行为抽象和刻画，保证系统状态和交互行为在时间度量和表示上的一致性。传统建模方式针对物理进程和计算进程分别建立连续模型和离散模型，不便于离散逻辑控制与连续时间行为的关联转换，而不动点求解方法通过计算微分不变式，更适应于解决计算进程逻辑时间与物理进程物理时间的一致性问题。本项目研究基于不动点求解的信息物理融合系统时间度量和表示,包括:1)扩展超稠密时间域，确定组件时序因果组合机理,设计时间信号联系的交互模型; 2)基于交互模型，定义全局时间信号函数，形式化描述信号为时间确定的偏序集函数；3)扩展广义超测度空间不动点理论，定义时序度量函数，证明严格收敛的时间信号函数存在唯一不动点，映射函数模型不动点对应系统实时交互行为，确认系统行为在时间上的存在性和唯一性；4)基于行为函数不动点，改进时序Petri网，确定信号时序组合演算。

计算进程与物理进程交互行为抽象和刻画是保证信息物理融合系统状态和交互行为在时间度量和表示上一致性的关键。项目围绕基于不动点求解的信息物理融合系统时间度量和表示方法关键技术进行研究和探讨，在以下几个方面取得了一些进展： 1.研究交互模型，分析信息物理融合系统状态，定义状态转移实时时空事件，设计空间标签，建立时空Petri网模型，扩展超致密时间模型，实现构件时序因果组合；2. 研究时间信号，定义全局时间信号函数，描述构件接口事件流因果依赖，确定节点接口信号时间关系，定义构件为时间模型偏序集函数；3. 研究时序度量，证明严格收敛的时间信号函数存在唯一不动点，映射函数模型不动点对应系统实时交互行为，扩展广义超测度空间不动点理论分析时间模型因果构件收敛性和系统响应的存在性和唯一性；4. 研究时序组合，提出了时序语义分离方法，改进时间Petri网、随机Petri网与层次着色Petri网，确定信号时序的组合运算；设计执行时间与截止期协同、能耗均衡的调度算法，确定信息物理融合系统的交互行为；5. 研究应用验证，提出了时间点不确定任务动态调度方法，构建了多种领域的信息物理融合系统无线传感器网络应用场景，研究了基于斯坦纳树和凸多边形的无线传感器网络分区双连通恢复方法，提出了无线传感器网络簇间数据传输方法，验证了多种领域场景下信息物理融合系统时间度量和表示策略。本项目对基于不动点求解的信息物理融合系统时间度量和表示一致性进行了探索，摸清了该研究问题的重点难点，取得了一定的进展，为进一步研究奠定了坚实的基础。

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