Research On Controllability And Controllable Robustness Of Complex Network

There are many complex systems in our life can be abstracted into complex networks composed with nodes and edges, previous work mainly concentrated on the complexity of network topologies and relationships between it and the network dynamics, researches have made great progress and achievements. However, the ultimate goal of complex network research is not only to understand the complexity of the mechanism and structure of the complex systems, but to control the state of the complex network systems. In order to realize the control of the complex network, the premise is that we need to judge whether the complex network system is controllable or not, the research of the network controllability is of great practical significance. Although the traditional control theory on the system control research has been very mature, but because of the complexity of the complex network system structure,traditional control theory and methods are not directly applicable to research on control of complex network systems. Lin gives the concept of "structure" and "controllability" of linear time invariant control system as early as 1976, and the necessary and sufficient conditions for the controllability of the structure are found through the research. The controllability of complex networks accompanied by Liu and Barabási in 2011, based on the structural controllability theory of the linear time invariant control system, real complex systems were studied and a model of structural controllability was built. And the complex network controllability has gradually become a hot issue in research of directed complex networks with it.Firstly, real complex networks are always suffered attacks from nature or human inevitably, and the network suffered attacks will be cascading failure, making the control difficulty of networks increased. Based on the theory of structural controllability, the analysis to network controllability when parts of the load edges suffered attacks and occur cascading failure is done in classical directed ER and directed BA networks. Considering the influence of cascading failure on the controllability and the establishment and control of networks bounded by the cost, the nonlinear model of load-capacity is introduced into the directed networks in this article, and multi-objective particle swarm optimization algorithm based on crowding distance sorting strategy(MOPSO-CD) is adopted to optimize capacity parameters.Compared with the linear model of load-capacity, the simulation finds the nonlinear model of load-capacity that the parameters are optimized can resist the cascading failure effectively,and the network controllable robustness is improved. The universal applicability and effectiveness of the parameter optimization model to improve the network controllable robustness is verified in practical transportation networks at last.Secondly, for the phenomenon of the directed complex network prefer to lose control even collapse when suffered intentional or random attacks. Based on the theory of structural controllability in this paper, the controllability of different topology networks and the changes of controllability under cascading failure while suffered attacks are analyzed. By defining two parameters S and ? that related to the network cost, the network controllable robustness measure ??? to deal with cascading failure and the joint costs measure ?T? of network construction and control are proposed, and the network controllable robustness is simulated in classical directed ER and BA networks. Taking the construction and control of networks are restricted by the cost into account, we explore the effectiveness of the control, the impact of the network edge capacity and control inputs to the network controllable robustness are studied intensively. Allocating different edge capacity and control inputs to different topology networks, the network controllable robustness can be improved as the cost reduced effectively.Finally, for this situation that the dependency modality is influence on the controllability of directed interdependent networks, based on the theory of exact controllability in this paper,the model of directed interdependent network controllability is built firstly. Then through the simulation and analysis of the random dependency modality on the directed interdependent network controllability, we put forward to three kinds dependency modalities of directed networks: the highest in degree and the highest out degree ?HI- HO? 、the highest in degree and the lowest out degree ?HI- LO? 、 the lowest in degree and the lowest out degree?LI- LO?. The directed interdependent network controllability is studied with different dependency modalities in DER-DER 、 DER-DSF and DSF-DSF networks in the end. Here results show that the controllability is the strongest based on the dependency modality of the lowest in degree and the lowest out degree, and the controllability is the worst based on dependency modality of the highest in degree and the highest out degree.The research provides a reference for the building of strong controllability of actual directed interdependent networks.