### cs代写|复杂网络代写complex network代考|CS7280

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• Statistical Computing 统计计算
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• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## cs代写|复杂网络代写complex network代考|SYNCHRONIZATION OF COMPLEX NETWORKS

In the field of complex networks’ synchronization with switching topologies, a wide range of research has been recently focused on dealing with issues related to the switchings and their effects on synchronization.

There has been increasing recognition that each topology candidate’s properties and the switching strategy for topologies play essential roles in achieving synchronization for complex networks with switching topologies. The analytical approaches for synchronization of continuous- and discrete-time complex networks with switching topologies are generally different. Mathematically, the continuous-time complex network with switching topologies is a special kind of those with time-varying topology. However, it is preliminarily assumed in some existing works on synchronization of continuous-time network systems with time-varying topology that the connection links evolve continuously over time with a known bound for the changing rate [103] or with a time-varying Laplacian matrix being simultaneously diagonalizable [11]. Thus, the techniques developed in these works to solve synchronization problem of complex networks with special time-varying topology are generally hard to apply to that with switching topologies, especially to the case with directed switching topologies.

Specifically, averaging-based approaches were developed to analyze synchronization of continuous-time complex networks with fast switching topologies $[7,140]$ while multiple Lyapunov functions (MLFs)-based approaches were developed to analyze synchronization of continuous-time complex networks with slowly switching topologies (especially for the case with directed switching topologies) [190]. Furthermore, MLFLs-based approaches were usually employed to analyze synchronization of continuous-time complex networks with switching topologies under delayed or sampled-data coupling [90, 187]. Common Lyapunov function (CLF)- and functional (CLFL)-based approaches are applicable only to some special continuous-time complex networks with switching topologies such as each possible topology candidate is undirected [222].

## cs代写|复杂网络代写complex network代考|CONSENSUS OF MASS WITH SWITCHING TOPOLOGIES

Since the pioneer works [65] in which heading consensus of the linearized Vicsek’s model was analyzed, consensus of MASs with switching topologies has attracted increasing attention from a wide range of scientific interests.

Consensus of first-order MASs with switching topologies: In the year of 2004, consensus problem of continuous time first-order (integrator-type) MASs with directed switching and balanced topology was formulated and studied in [116]. Due to the balanced property of each possible topology candidate, a common Lyapunov function was constructed in [116] for analyzing the convergence behaviors of disagreement vector. Consensus of both continuous- and discrete time first-order MASs with directed switching topologies was further studied in [128] where each possible topology candidate is not required to be balanced. By using graphical approaches, some interesting issues on consensus of a class of first-order MASs with switching topologies were further addressed in [13]. By employing a CLFL based approach, it was proven in [83] that average consensus in continuous time first-order MASs with time delayed protocol can be achieved if each topology candidate is strongly connected and balanced, and some linear matrix inequalities hold. Note that most of the aforementioned results are concerned with consensus of first-order MASs with deterministically switching topologies. However, considering the underlying topology may randomly switch among a set of topology candidates in some practical applications, there have been a number of results focusing on consensus of first-order MASs with randomly switching topologies $[54,155,156]$.

Consensus of second-order MASs with switching topologies: Based on the stability results for switched systems provided in [108], some dwell time (DT) based criteria for consensus of continuous time second-order MASs under directed switching topologies were established in [129] where it was revealed that consensus can be achieved if each topology candidate contains a directed spanning tree and the DT for switchings among different topology candidates is larger than a threshold value. When the graph describing the communication topology among followers is undirected, it was proven in [59] by constructing a CLF that leader-following consensus could be achieved if the topology jointly contains a directed spanning tree. Later, leader-following consensus problem of MASs with switching jointly reachable interconnection and transmission delays was solved in [234] by designing the switching laws among topology candidates, where the dynamics of the leader are described by first-order integrator.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。