Research On Some Key Problems In Controllability Of Complex Networks

Since the 21 st century,complex systems have brought a great improvement for the production and life of human beings.Meanwhile,the failure of complex systems can cause huge loss,such as the large-scale black out of power grids,traffic paralysis and the fast spread of rumours or infectious diseases.Hence complex systems should be controlled effectively.Then the benefits can be utilized effectively,and the unnecessary disaster can be avoided.Actually,most of the complex practical systems can be regarded as complex networks,though they are different greatly in the real world.Therefore the control of complex systems can be transformed to the control of complex networks.Before conducting the control of the complex networks,whether the controlled plant can be controlled effectively should be investigated.And that is to say we should be clear in whether the controlled plant has the controllability.If the controlled plant doesn't have the controllability,it should be adjusted until it possesses the controllability;and the control action can be performedonly after the condition that the controlled plant has the controllability is confirmed.So investigating the controllability is necessary for the control.Based on the previous work,several key problems of the controllability of complex networks are discussed in the dissertation.And the main contributions are as follows.1.For a network,the methods of local control are usually utilized to mainly control the key nodes that play more important roles in some aspects,when the whole topological structure is unknown.Thus,the prerequisite of controlling some key nodes is that we must be clear that which nodes are the key nodes.The contrast experiments indicate the index is effective and feasible and shows the key nodes of a network can be mined better according to the presented index,which provides a good guide and assistance in the strategy.2.When a network need be controlled accurately and totally,the corresponding maximum matching should be found firstly to fulfill the control of the unmatched nodes.Therefore how to find the maximum matching of the network is an issue we must deal with.The mining method for the maximum matching of complex networks is studied.Furthermore,we propose a method which uses elementary matrix transformations to recognize matching nodes for the maximum matching.And we find that the number of matching nodes is determined by the maximum geometric multiplicity of the network's matrix eigenvalues.Additionally,a heuristic method is proposed to mine the maximummatching,which can ensure the maximum matching fined is optimal.The result in various real networks and networks we construct show its effectiveness and feasibility.3.When a network has a relatively large-scale,it is hard to conduct the conventional maximum matching algorithm.So a coarse graining method is proposed from the view of granular computing that simulates the human thinking of solving the complicated problem.In the method,the large-scale network is decomposed to a number of small-scale sub-networks,and the corresponding maximum matching is computed.Furthermore,the range of application and the advantage of the method are verified in the experiments.And we find that the number of driving node will decrease if the network is granulated coarsely,and the influence of coarse granulating is relatively small for the network having a small number of the two kinds of structures.The proposed theories and methods on the controllability of complex networks have a good generalization performance,which has certain reference value for the control of varies complex systems.Meanwhile,it will help us to understand the relationship of network structures and controllability,and is expected to provide new thoughts and theoretical basis for the design of complex systems.