2-D时变网络系统在事件驱动机制下的状态估计与牵制控制研究

针对网络化环境下通信带宽有限以及2-D系统由于受到物理设备限制或外加随机扰动而易出现的多种信息不完全现象，本项目将首先深入分析其发生及变化的规律，建立能够反映由网络化引起的不完全信息、非线性和随机性等特征的2-D时变网络系统模型。其次，结合图论、随机分析、矩阵理论、微分包含等工具对所建2-D网络系统进行动态分析，讨论网络系统的稳定性、鲁棒性和相关运行性能；并借鉴复杂网络中的牵制控制思想，确定2-D耦合网络在时变拓扑结构下的最优牵制控制策略。随后，针对2-D系统的随机非线性特性，提出能有效平衡2-D系统性能和网络资源利用率的事件驱动条件；在此基础上，研究2-D时变网络系统在网络化环境下基于事件驱动机制的状态估计问题。最后，利用正系统理论与所建的2-D网络系统相关结果对2-D基因网络进行动态分析，设计可实现的有生物意义的调控策略；将之前所有算法进一步完善，给出评价结果，综合为功能相容的软件包。

Due to the existence of variety of incomplete informations which have been caused by the limited bandwidth in the networked environment and the physical limitations of the devices in the 2-D systems as well as the external random perturbations, in this project, deep analysis will be firstly given for the patterns of their occurrences and the laws of their variations so as to establish the time-varying 2-D network models which can intrinsically characterize the networked-induced phenomena such as incomplete information, nonlinearity and randomness. Next, based on the graph theories, the matrix theories and the analysis tools such as differential inclusion and stochastic analysis, dynamical analyses are carried out for the constructed 2-D network systems including the stability, the robustness and the other related dynamic performances. Moreover, inspired by the pinning control ideas in the complex networks, optimal pinning control strategies are to be determined for the 2-D coupled networks with time-varying topological structures. After that, according to the nonlinear stochastic features of the 2-D systems, some event-triggered mechanisms are proposed to effectively balance the performances of the system and the utilization rate of the network resources. Then, the event-triggered state estimation problems are addressed for the time-varying 2-D networked systems. Finally, by resorting to the theories on positive systems and the results derived for the constructed 2-D networks, dynamical analyses are carried on for the 2-D genetic networks, and regulatory schemes with biological meaning are also to be designed. Meanwhile, the algorithms set up in this project are further improved, evaluations are summarized, and functionally compatible software packages are provided.