Optimizing Pinning Control Algorithms In Complex Dynamical Networks

In recent years,more and more scholars have paid attention to the complex network.How to control the network to synchronization efficiently is a very meaningful research topic.In this thesis,we studied the undirected network pinning control based on general complex network dynamics model.According to the principle of control synchronization,the synchronization of the network depends on the coupling strength of the network and the minimum eigenvalue of the grounded Laplacian matrix.It is the core of the problem of optimal selection of control nodes to get a large minimum eigenvalue of grounded Laplacian matrix by reasonably selecting the set of controlled nodes.In this thesis,some mathematical inequality related to the minimum eigenvalue of grounded Laplacian matrix is derived,and the corresponding algorithm of control nodes selection for undirected and unweighted network is proposed.In the research of pinning single node,the concept of node resistance distance is introduced,and the inequality between resistance distance and the minimum eigenvalue of grounded Laplacian matrix is derived.Based on this inequality,the algorithm of pinning single node based on resistance distance is proposed.We verified the node selection ability of the algorithm by the experimental simulations and we also researched the positive correlation between the resistance distance of nodes and the minimum eigenvalue of grounded Laplacian matrix and we discussed the possibility of resistance distance being an alternative of the minimum eigenvalue of grounded Laplacian matrix to reduce computation complexity.Finally,the application of resistance distance in block network pinning control is studied.In the research of pinning multiple nodes,two multi-nodes selection algorithms for different number of controlled nodes are proposed: first,this thesis deduces the minimum eigenvalue related inequality of Laplacian deleted matrix,and proposes a recursive iterative algorithm for pinning multiple nodes.We verified that the algorithm can effectively filter the nodes and node combinations with bad control effect,reducing the number of controlled node combinations to a smaller scale,reducing the calculation times of the minimum eigenvalue of the grounded Laplacian matrix,reducing the calculation of the nodes selection problem.In addition,this thesis also proposes a pinning nodes selection strategy based on the topological relationship between the controlled node and the uncontrolled node.Compared with other nodes selection strategies,this strategy can make the minimum eigenvalue of the deleted matrix of Laplacian reach 1 by controlling fewer nodes than other strategy,and when the number of controlled nodes is the same,the eigenvalues of the deleted Laplacian are greater than other strategies.Experiments show that this strategy is superior to other nodes selection strategies.