Research On Structural Controllability And Observability Of Complex Network Systems

Complex networks are composed of dynamic units and their interactions,and are closely related to various natural,social and technological systems.In general,our understanding of complex networks is reflected in our ability to control them,that is,to drive the system from any initial state to any final state in a finite time.Therefore,how to control the complex network system is the frontier issue of network science,and it is also the focus of complex network system research.However,as a dual concept of controllability,the research and application of observability of complex networks cannot be ignored.Complex networks are observable when all state variables inside the complex network can be reflected by the output.Precise control and measurement of complex networked systems is usually not feasible or practical,so structural controllability and observability have been proposed.In this thesis,the structural controllability and observability of complex network node dynamic systems with output feedback,the robustness of edge dynamic systems based on structural controllability and observability,and related issues are proposed.The main research contents of the thesis include:The closed-loop control of the system is usually realized by using the output as the feedback quantity,so as to achieve the expected system performance index.We establish a theoretical framework of output feedback for complex network node dynamic systems,and study its structural controllability and observability.By proposing new concepts such as feedback-stem,feedback-bud,and feedback-cactus,the necessary and sufficient conditions for the controllable and observable structure of complex network node dynamic systems are proposed from the perspective of graph theory.Based on the maximum matching method,a minimum input and output theory is proposed to calculate the minimum number of driver nodes(or sensor nodes)required for a fully controllable(or observable)network with output feedback.The theory is applied to model networks and real networks,and the role of nodes and edges in the controllable and observable system structure is studied from the perspective of control and observation,and the corresponding theoretical formula is given.It is found that the driver node(or sensor node)has a greater probability of being a divergent node(or a convergent node).Some nodes are both driver nodes and sensor nodes,having a dual role.The proportion of such nodes is higher in sparse and homogeneous networks and is mainly affected by the degree distribution.The statistical results show that the length of the feedback-stem generally exhibits a power-law distribution in model networks and real networks.Numerical simulations and theoretical analysis show that edge participation is high in sparse and homogeneous networks.Aiming at the edge dynamic system of complex network,considering the structural controllability and observability of the system comprehensively,a theoretical framework based on edge classification is proposed to study the robustness of edge dynamic in complex network.The theory is applied to model networks,the influence of the network topology on the robustness is studied,and the corresponding theoretical formula is given.Applying edge classification to model networks,it is found that the proportion of critical edges in the new classification method is about twice that in the traditional classification method.