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

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
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• 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|EXTENSIONS AND APPLICATIONS OF CNSS WITH SWITCHING TOPOLOGIES

In the above sections, we have surveyed some recent developments in the analysis and synthesis of CNSs with switching topologies, mainly focusing on the synchronization and consensus behaviors and comparison to complex networks and MASs’ scenarios. The above survey is by no means complete. However, it depicts the whole general framework of coordination control for CNSs with dynamic communication networks and lays the fundamental basis for other exciting and yet critical issues concerning CNSs with switching topologies. These extensions still deserve further study, although a variety of efficient tools have been successfully developed to solve various challenging problems in those active research fields. Next, we elaborate on several state-of-the-art extensions and applications of CNSs with dynamic topologies.

Resilience analysis and control of complex cyber-physical networks. Most of the units in various network infrastructures are cyber-physical systems in the Internet of Things era. One of the essential and significant features of the cyber-physical system is integrating and interacting with its physical and cyber layers. As a new generation of CNS, the complex cyber-physical network has received drastic attention in recent years. Specifically, the CNSs’ paradigm provides an excellent way to model various large-scale crucial infrastructure systems, such as power grid systems, transportation systems, water supply networks, and many others [4]. These systems all capture the basic features that large numbers of interconnected individuals through wired or wireless communication links, and many essential functions of these large-scale infrastructure systems fall under the purview of coordination of CNSs. Disruption of these critical networked infrastructures could be a real-world effect across an entire country and even further, significantly impacting public health and safety and leading to massive economic losses. The alarming historical events urgently remind us to seek solutions for maintaining certain functionality of CNSs against malicious cyberattacks (i.e., resilience or cybersecurity). It is critically essential to exploit security threats during the initial design and development phase.

Noteworthily, any successful cyber or physical attack mentioned above on complex cyber-physical networks may introduce undesired switching dynamics (e.g., loss of links due to DoS attacks or human-made physical damages) to the operation of these networks [194]. Inspired by the pioneering work [194], [168] further investigated the distributed observer-based cyber-security control of complex dynamical networks. This work considered the scenario that the communication channels for controllers and observers might both subject to malicious cyber attacks, which aim to block the information exchanges and result in disconnected topologies of the communication networks. New security control strategies are proposed, and an algorithm to properly select the feedback gain matrices and coupling strengths has been given. The asynchronous attacks in these two communication channels were explored in [169], where the attacks can be launched independently and may occur at different time intervals. Recently, [69] studied the distributed cooperative control for DC cyber-physical microgrids under communication delays and slow switching topologies would destruct the system’s transient behaviors at the switching time instants. The average switching dwell-time-dependent control conditions were given to ensure the exponential stability of the considered cyber-physical systems. For the event-triggered communication scenario, [26] studied the distributed consensus for general linear MASs subjected to DoS attacks. By the switched and time-delay system approaches, one constraint was provided to illustrate the convergence rate of consensus errors and uniform lower bound of non-attacking intervals of DoS attacks.

## cs代写|复杂网络代写complex network代考|ALGEBRAIC GRAPH THEORY

Suppose a CNS consists of $N$ nodes (agents) which interact with each other through a communication or sensing network or a combination of both. It is natural to model the interactions among the $N$ nodes (agents) by undirected or directed graphs. Without loss generality, the $N$ nodes can be labeled as node $1, \ldots, N$. Let $\mathcal{V}={1, \cdots, N}$ be the set of nodes. Then the directed graph is described by $(\mathcal{V}, \mathcal{E})$, where the set of edges $\mathcal{E} \subseteq \mathcal{V} \times \mathcal{V}$ represent the interactions among the $N$ nodes. For notational simplicity, the graph $(\mathcal{V}, \mathcal{E})$ is denoted by $\mathcal{G}$. The edge $(j, i) \in \mathcal{E}$ if and only if node $i$ can receive the information from node $j$. When $(j, i) \in \mathcal{E}$, node $j$ is said to be a neighbor of node $i$. Denote by $\mathcal{N}{i}$ the set of neighbors of node $i$.

If there exists a sequence of distinct nodes $i{1}, \ldots, i_{m}$ such that $\left(i, i_{1}\right),\left(i_{1}, i_{2}\right), \ldots,\left(i_{m-1}, i_{m}\right),\left(i_{m}, k\right) \in \mathcal{E}$, then it is said that node $i$ has a directed path to node $k$, or node $k$ is reachable from node $i . \mathcal{G}$ is strongly connected if each node has at least one directed path to any other nodes. More generally, if there exists a node, called the root, which has at least one directed path to any other nodes, $\mathcal{G}$ is said to contain a directed spanning tree. Denote by $a_{i j}$ the weight of the edge $(j, i), i, j=1, \ldots, N$. It is assumed throughout this book that $a_{i j} \geq 0$, where $a_{i j}>0$ if and only if $(j, i) \in \mathcal{E}$, and $a_{i j}=0$, otherwise. In addition, it is assumed in this book that $a_{i i}=0$, that is, self-loop is forbidden. $\mathcal{G}$ is called an undirected graph if $(i, j) \in \mathcal{E}$ whenever $(j, i) \in \mathcal{E}$ and $a_{i j}=a_{j i}$. An undirected graph is connected if there exists at least one undirected path between each pair of distinct nodes. For undirected graphs, the existence of an undirected spanning tree is equivalent to being connected. However, for directed graphs, the existence of a directed spanning tree is a weaker condition than being strongly connected. Please see Figure $2.1$ for a directed graph which is not strongly connected but contains a directed spanning tree.

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## MATLAB代写

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