Control Energy Of Complex Networks

Related research on complex systems is a current research hot spot.In order to save energy as much as possible and improve energy utilization,the control energy problem of complex networks has gradually become an important direction in this field.This problem focuses on the energy consumed by controlling complex network systems and various strategies to reduce the control energy.This paper uses graph theory,matrix theory,and controllability theory and other related theoretical tools to specifically study several important issues of control energy of complex network.The main research contents and conclusions studied in this paper can be summarized as follows:Firstly,the problem of calculating the control energy of a directed network is studied,a simplified control energy algorithm for a directed network is proposed,and the relationship between control energy and control time when the system is controllable is clarified.We simplify the calculation of the control energy of directed network by substituting the Jordan transform.Then,the relationship between control energy and control time was found by deriving the control time.Last,through the study of the Price network,the effects of network heterogeneity and network size on control energy were discovered.Secondly,the lower bound of the extreme value of control energy of the directed network is studied.For different cases of positive and negative definiteness of the adjacency matrix,the quantitative relationship between the average degree of the directed network nodes and the lower bound of the extreme value of control energy is given by strict mathematical proofs.Thirdly,aiming at a special kind of problem in network control,that is,only a single node in a network needs to be controlled,the node energy problem of a directed network is studied.We select directed chained network as the research object,propose a node energy simplified algorithm for directed chained network,and prove that the node energy has a negative correlation with the number of driven nodes for this kind of network.