Research On Complex Network Control Problem Based On Consistency And Rewiring Mechanism

Complex networks have found wide-ranging applications in various domains of social science,and controlling complex networks has become a critical research direction in network science.The primary objective of control research is to develop efficient control strategies that minimize the control costs while achieving network controllability.The current state of control research is based on the theoretical framework of network controllability and strict controllability,which analyzes the influence of distinct network topology features on system control performance.Network systems are impacted by more than just topology structure,and other factors such as practical constraints and control parameters need to be considered in control research.Therefore,studying network control problems requires taking into account several aspects,including control time,control path,control energy,and control strategies.In this study,the main focus is on exploring the impact of network topology structure and individual dynamic characteristics constraints on network control energy consumption for both continuous and discrete networks.The primary objective of this research is to attain network controllability and reach the target state while minimizing control energy consumption,while also proposing an energy-saving optimization strategy to prevent system failure.The significant contributions of this study are summarized as follows:The primary focus of this study is to examine the impact of behavioral consistency on the control energy of complex networks.Specifically,we investigate how non-zero initial states affect network control energy in cases where nodes exhibit either consistent or inconsistent behavior.Our findings demonstrate that different network topology structures result in distinct dynamic trends in node states from the initial to the consensus final states.Additionally,we observe that an increase in the initial state range of nodes leads to an increase in the control energy required to achieve consensus from non-zero initial states to the final state.Therefore,enhancing network controllability can be achieved by reducing the initial state differences among network nodes.When the average degree of the network is relatively high or the power-law index is low,nodes are more closely connected,and behavioral consistency can reduce the energy span required for nodes to reach the ideal state,thereby reducing the total energy consumption needed for the network to reach consensus.When a network is under external attack,its internal structural topology will change,thereby affecting the network’s demand for control energy.This thesis considers the impact of complex network topology on control energy and proposes a control energy optimization strategy based on rewiring edges to address the problem of control energy imbalance that may occur in directed networks when nodes fail.The strategy first defines the weight of edges based on the degree value of nodes and relies on a reasonable selection of affected nodes and similar edge weight nodes to achieve edge rewiring.The network topology under this mechanism can quickly adjust after node failure,maintain the stability of the network topology,and improve the network’s robustness,thereby optimizing network control energy.Compared to traditional rewiring algorithms,the proposed strategy exhibits better control energy optimization ability for both traditional network models and real-world networks,making networks more controllable after node failure.