Networked Systems Modeling And Consistency Analysis Of A Number Of Issues,

Systems that could be modeled by networks—networked systems—are ubiquitous in all domains of science and technology, and permeate many aspects of human lives. They offer researchers from various disciplines with a number of exciting challenges and opportunities. In particular, analyzing and designing the structure and function of networked systems is one of the most interesting and important tasks and the research along this line has found applications in various fields, such as distributed sensor fusion in sensor networks and distributed algorithms in control systems, to name just a couple. In this dissertation, by using linear system theory, nonlinear control theory, matrix analysis, graph theory, the modeling and consensus problems of networked systems are investigated systematically. The main work can be summarized as follows:(1) An evolving model with tunable degree distribution and clustering coefficient is proposed. The geometric properties and resilience of networks generated by this model are examined both analytically and numerically. The results show that arbitrary scaling exponent of power laws and clustering can be obtained by simply changing the control parameters. Moreover, the present model is found to have a good hierarchical structure. The present model helps in understanding the complex inherency for a wide variety of networked systems. Furthermore, a better description of these systems would benefit our recognition for other complex systems as well, for which so far less topological information is available.(2) The consensus problem with incomplete information, i.e., no individual gets complete pertinent information, and disconnected interaction topologies is considered. The necessary and sufficient conditions for the convergence of individuals' states to a common value are derived. In addition, some results which bridge the gaps between the properties of matrices and the characteristics of their associated digraphs are obtained. Especially, it is proved that the sum of the number of spanning components in the digraph of a weighted skew-Laplacian matrix and its rank equals the order of the matrix.(3) The consensus problem with discontinuous information transmission and time delays is considered, i.e., the process of receiving information by a node may be discontinuous due to unreliable information sources; information transmission is not instant, but has heterogeneous and time-varying delays. It is shown that even if no nodes have full knowledge of the objective, through cooperation they can achieve the objective asymptotically, demonstrating the essence and importance of cooperation in multi-agent networks and networked systems.(4) The consensus problem for a multi-agent system with general nonlinear coupling is investigated. It is demonstrated that, under suitable conditions on communication, all agents approach a prescribed value if a small fraction of them are controlled by simple feedback control. The stability analysis is based on a blend of graph-theoretic and system-theoretic tools where the contraction analysis and multiple Lyapunov functions play central roles.(5) The problems of characterizing and improving the consensus speed on random networks are investigated. The relation between the consensus speed and the parameters of random network models is established by purely algebraic argument. It is demonstrated that: for ER model, the more nodes and edges, the faster consensus; for WS model, the more edges and rewiring, and the less nodes, the faster consensus; while for BA model, the more edges, the faster consensus.