Controllability Of Complex Networks Research Articles

Dynamic Periodic Event-Triggered Synchronization of Complex Networks: The Discrete-Time Scenario.

This article reports the synchronization control of discrete-time complex networks using an event-triggered method. The main contributions are twofold: 1) a discrete-time scenario of the dynamic periodic event-triggered mechanism is developed to schedule the transmissions of measurements. The proposed mechanism monitors the synchronization error in a periodic manner, which is beneficial to reduce the calculation resources of sensors. Simultaneously, the proposed mechanism increases the triggering threshold so that it contributes to enlarging the average interevent interval and 2) a new Lyapunov functional is developed to deal with the periodic samplings. On the one hand, the proposed functional involves a delay-dependent term, which is convenient to formulate the synchronization criterion by the delay analysis technique. On the other hand, the functional takes the sawtooth constraint of periodic samplings into consideration by introducing a piecewise functional. Finally, a succinct criterion is derived such that the considered networks are synchronized with a predetermined error level. A simulation example is provided to show our advantages in comparison with the existing approaches.

Focus on Monitoring and Control of Complex Supply Systems

Abstract The ongoing rapid transformation of our energy supply challenges the operation and stability of electric power grids and other supply networks. This focus issue comprises new ideas and concepts in the monitoring and control of complex networks to address these challenges.

Coupling Dependence on Chaos Synchronization Process in a Network of Rulkov Neurons

This paper investigates the impact of network conformation on chaos synchronization in driven complex networks in a master-slave setting. We analyze the control and prediction of complex networks under perturbations. Although chaotic dynamics suppression is well understood in low-dimensional systems, it is not well described in more complex ones. To assess a network’s ability to amplify or suppress disturbances, we track ensembles of possible trajectories in the driven subsystem which give insights into nonlocal convergence properties in a master-slave setting. We demonstrate how the stability of forced networks of Rulkov neurons is dependent on network coupling architecture and how the duration of chaotic transients depends on initial conditions. Furthermore, we find that each network generator algorithm has specific sets of parameters that can lead to stable or nonstable states. Our results indicate that network types are more critical than isolated connections for suppressing chaotic dynamics in driven networks. Finally, we identify that under certain circumstances, the transient period before synchronization correlates with high convergence rates for certain initial conditions. This suggests nonuniform convergence rates in the phase space of driven neural networks.

Fault‐tolerant secure H∞$$ H\infty $$ synchronization for complex networks with semi‐Markov jump topology

SummaryThe article mainly studies the fault‐tolerant control of complex networks with semi‐Markov jump topology under hybrid attacks. First, the semi‐Markov process is imported to the topology change of sampled‐data complex networks. Second, by designing a strategy to resist mixed attacks, the system can remain stable even under mixed attacks. Then, some sufficient conditions have been established to guarantee performance through fault‐tolerant control mechanism even if it suffers from actuator failure. Finally, a numerical example and a practical example are used to prove the feasibility of the theory.

Target control of complex networks: How to save control energy.

Controlling complex networks has received much attention in the past two decades. In order to control complex networks in practice, recent progress is mainly focused on the control energy required to drive the associated system from an initial state to any final state within finite time. However, one of the major challenges when controlling complex networks is that the amount of control energy is usually prohibitively expensive. Previous explorations on reducing the control energy often rely on adding more driver nodes to be controlled directly by external control inputs, or reducing the number of target nodes required to be controlled. Here we show that the required control energy can be reduced exponentially by appropriately setting the initial states of uncontrollable nodes for achieving the target control of complex networks. We further present the energy-optimal initial states and theoretically prove their existence for any structure of network. Moreover, we demonstrate that the control energy could be saved by reducing the distance between the energy-optimal states set and the initial states of uncontrollable nodes. Finally, we propose a strategy to determine the optimal time to inject the control inputs, which may reduce the control energy exponentially. Our conclusions are all verified numerically, and shed light on saving control energy in practical control.

Input Structure Design for Structural Controllability of Complex Networks

This paper addresses the problem of the input design of large-scale complex networks. Two types of network components, redundant inaccessible strongly connected component (RISCC) and intermittent inaccessible strongly connected component (IISCC) are defined, and a subnetwork called a driver network is developed. Based on these, an efficient method is proposed to find the minimum number of controlled nodes to achieve structural complete controllability of a network, in the case that each input can act on multiple state nodes. The range of the number of input nodes to achieve minimal control, and the configuration method (the connection between the input nodes and the controlled nodes) are presented. All possible input solutions can be obtained by this method. Moreover, we give an example and some experiments on real-world networks to illustrate the effectiveness of the method.

Closed-loop control of higher-order complex networks: Finite-time and pinning strategies

Increasing evidences have demonstrated the essentiality of many-body interactions in modeling various systems in physics, biology, and social sciences. Control strategies are useful tools to steer real-world complex systems to desired targets. Existing works focus on open-loop control, which relies on predefined control signals, and closed-loop control, which requires an infinite-time duration, on conventional networks expressed by graphs. This work designs closed-loop controllers for higher-order complex networks characterized by simplicial complexes. Protocols including the linear feedback controller and a switching controller, which is a combination of a linear controller and a finite-time controller, are first adapted to higher-order networks to realize successful control tasks, with the rigorous upper bound of the control time theoretically derived and compared. Extensive numerical simulations on benchmark and real-world higher-order complex networks demonstrate the effectiveness of the control protocols and further provide insights on pinning control strategy to higher-order networks. These results shed light on a comprehensive discovery of controlling higher-order complex networks and have also applied values.

An Effective Multi-Agent Ant Colony Optimization Algorithm for QoS-Aware Cloud Service Composition

In order to improve the efficiency of wireless network virtualization resource processing, this paper combines the dynamic resource allocation algorithm to construct a wireless network virtualization resource sharing model. This paper proposes a task-oriented resource management model and uses the task-oriented TRS model to describe resources and service processes, reducing the complexity of formulating resource allocation strategies. Moreover, this paper comprehensively considers factors such as centralized coordination control cost and limited domain topology visibility to improve the dynamic resource allocation algorithm. Through the abstraction and unified representation of network resources, resource sharing, and efficient reuse, the coexistence and integration of heterogeneous wireless networks can be realized. Wireless network virtualization can decouple complex and diverse network management and control functions from hardware and extract them to the upper layer for unified coordination and management, thereby reducing network management costs and improving network management and control efficiency

Control core of undirected complex networks

With the development of complex networks, many researchers have paid greater attention to studying the control of complex networks over the last decade. Although some theoretical breakthroughs allow us to identify all driver nodes, we still lack an efficient method to identify the driver nodes and understand the roles of individual nodes in contributing to the control of a large complex network. Here, we apply a leaf removal process (LRP) to find a substructure of an undirected network, which is considered as the control core of the original network. Based on a strict mathematical proof, the control core obtained by the LRP has the same controllability as the original network, and it contains at least one set of driver nodes. With this method, we systematically investigate the structural property of the control core with respect to different average degrees of the original networks ($\langle k \rangle$). We denote the node density ($n_\text{core}$) and link density ($l_\text{core}$) to characterize the control core when applying the LRP, and we study the impact of $\langle k \rangle$ on $n_\text{core}$ and $l_\text{core}$ in two artificial networks: undirected Erd\"os-R\'enyi (ER) random networks and undirected scale-free (SF) networks. We find that $n_\text{core}$ and $l_\text{core}$ both change nonmonotonously with increasing $\langle k \rangle$ in the two typical undirected networks. With the aid of core percolation theory, we can offer the theoretical predictions for both $n_\text{core}$ and $l_\text{core}$ as a function of $\langle k \rangle$. Then, we recognize that finding the driver nodes in the control core is much more efficient than in the original network by comparing $n_{\text{D}}$, the controllability of the original network, and $n_{\text{core}}$, regardless of how $\langle k \rangle$ increases.

Structural controllability and observability of complex network with output feedback

Structural controllability and observability of complex network with output feedback

Adaptive event‐triggered pinning synchronization control for complex networks with random saturation subject to hybrid cyber‐attacks

SummaryThis research is concerned with the problem of pinning based output synchronization control for a complex networks with random saturation vulnerable to hybrid cyber‐attacks via an adaptive event‐triggered scheme (AETS). The output synchronization error systems are subject to suffer from deception attacks, replay attacks, and denial‐of‐service attacks. A novel hybrid cyber‐attack model is first constructed to integrate the three kinds of attacks into a synchronization of complex network. AETSs based on output synchronization errors with the consideration of hybrid cyber‐attacks, have been proposed to reduce the burden of communication. A pinning control strategy is used to decrease the control signal's input. By constructing a Lyapunov functional and using the linear matrix inequality technique, sufficient conditions are provided to ensure the output synchronization error system. Finally, a numerical simulation results are developed to illustrate the efficacy of the proposed theoretical methodology.

A cloud model-based method for passenger flow control at subway stations: A real-world case study

In the condition of large passenger flow, subway station managers take measures of passenger flow control organization for reducing high safety operation risks at subway stations. The volume of passenger flow in urban railway network operation continues to increase and the Congestion of passenger flow is very high. Passenger flow control measures can greatly give birth to the pressure of transportation and ensure an urban rail transit system’s safe operation. In this paper, we develop a cloud model-based method for passenger flow control, which extends the four-level risk-control grade of a large passenger flow at facilities by considering its fuzzy and stochastic characteristics. Then, an efficient passenger flow control strategy for subway stations is made, where the control time and locations are simultaneously determined. Finally, a station in the Beijing subway is studied to test the validity of the proposed approach. The results show that the time of maximum queuing length is much shorter and the density of passenger flow is lower than existing methods in practice. With the in-depth study of complex network controllability, many studies have applied to control judgment and real network optimization. This paper analyzes the cloud-model-based method for passenger flow control at subway stations and therefore a new method can be incorporated for developing and optimizing control strategies. A few researchers have attempted to find the solution to the problem of crowding risk classification and the passenger flow control strategy. The focus of some studies simultaneously solves the passenger flow control with multiple stations.

Complex Network Evolution Model Based on Turing Pattern Dynamics

Complex network models are helpful to explain the evolution rules of network structures, and also are the foundations of understanding and controlling complex networks. The existing studies (e.g., scale-free model, small-world model) are insufficient to uncover the internal mechanisms of the emergence and evolution of communities in networks. To overcome the above limitation, in consideration of the fact that a network can be regarded as a pattern composed of communities, we introduce Turing pattern dynamic as theory support to construct the network evolution model. Specifically, we develop a Reaction-Diffusion model according to Q-Learning technology (RDQL), in which each node regarded as an intelligent agent makes a behavior choice to update its relationships, based on the utility and behavioral strategy at every time step. Extensive experiments indicate that our model not only reveals how communities form and evolve, but also can generate networks with the properties of scale-free, small-world and assortativity. The effectiveness of the RDQL model has also been verified by its application in real networks. Furthermore, the depth analysis of the RDQL model provides a conclusion that the proportion of exploration and exploitation behaviors of nodes is the only factor affecting the formation of communities. The proposed RDQL model has potential to be the basic theoretical tool for studying network stability and dynamics.

Input node placement restricting the longest control chain in controllability of complex networks

The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is an inherent trade-off between minimizing the number of inputs and control energy. To better understand this trade-off, we study the problem of identifying a minimum set of input nodes such that controllabililty is ensured while restricting the length of the longest control chain. The longest control chain is the maximum distance from input nodes to any network node, and recent work found that reducing its length significantly reduces control energy. We map the longest control chain-constraint minimum input problem to finding a joint maximum matching and minimum dominating set. We show that this graph combinatorial problem is NP-complete, and we introduce and validate a heuristic approximation. Applying this algorithm to a collection of real and model networks, we investigate how network structure affects the minimum number of inputs, revealing, for example, that for many real networks reducing the longest control chain requires only few or no additional inputs, only the rearrangement of the input nodes.

Effect of the interdependence between subnets on the structural controllability of complex networks

AbstractControllability is a hot issue in complex networks. In this paper, without changing the number and the positions of the controllers, the effect of interdependence (viz., inter‐coupling relations) between two directed subnets that are controllable or uncontrollable on the structural controllability of complex networks is investigated. According to the Kalman rank criterion and PBH rank criterion, some sufficient conditions and necessary conditions for the structural controllability or uncontrollability of interdependent networks are presented. The results show that (1) if the uncontrollable and controllable nodes in one subnet are inter‐coupled with the controllable and uncontrollable nodes in the other subnet, respectively, and the directions are from controllable nodes to the uncontrollable nodes, then the interdependent network may be controllable; (2) the interdependent network can be obtained structurally controllable if there are simply directed paths covering all the uncontrollable nodes of the two subnets, separately; and (3) the interdependent networks are structurally controllable no matter what kind of inter‐couplings between two controllable subnets. All of these results are adaptive to undirected subnets. The final example verifies the effectiveness and correctness of the results provided in this paper.

Estimating the Region of Attraction on Controlled Complex Networks With Time-Varying Delay

The importance of estimating the region of attraction (ROA) on complex networks has drawn attention very recently. However, challenging problems arise when applying the existing theory to networks with delay. In this article, we estimate the ROA on controlled complex networks with time-varying delay. A delay-independent ROA estimation method is derived at first. This method can deal with general delay and is convenient to use due to its independence of the delay. Accordingly, it may cause conservativeness. To further reduce the conservativeness, delay-dependent ROA estimation is established for networks with small delay by developing a new technique of dealing with the delay. Numerical simulations are provided to verify the theoretical results.

Synchronous Control of Complex Networks with Fuzzy Connections

Synchronous Control of Complex Networks with Fuzzy Connections

Investigating the effect of edge modifications on networked control systems: Stability analysis

This paper investigates the impact of addition/removal/reweighting of edges in a complex networked linear control system. For networks of positive edge weights, we show that when adding edges leads to the creation of new cycles, these in turn may lead to instabilities. Dynamically, these cycles correspond to positive feedback loops. Conditions are provided under which the modified network is guaranteed to be stable. These conditions are related to the steady state value of the transfer function matrix of the newly created positive feedbacks. The tools we develop in the paper can be used to investigate the fragility of a network, i.e., its robustness to structured perturbations.

Control energy scaling for target control of complex networks

To control complex networks in practice, recent work has focused on the control energy required to drive the associated system from an initial state to any final state within finite time when it is fully controllable. However, beyond the prohibitively high cost for controlling all nodes of a network, it is usually adequate to control some target nodes of most natural and technological networks. In other words, what we usually need is to implement target control frequently. Yet, understanding the control energy for target control remains an outstanding challenge so far. Here we theoretically present an efficient method to calculate the minimum control energy required for implementing target control of complex networks, which bypasses the sophisticated calculation of the traditional Gramian matrix of the original system. Surprisingly, we uncover that the scaling behavior is only determined by the controllable part of the network. Furthermore, for the upper and lower bounds of the minimum control energy, we systematically derive the exact scaling behavior in terms of the control time. In addition, for controlling temporal networks composed of a sequence of uncontrollable snapshots, we demonstrate that our method offers a more efficient and effective way for analyzing the associated control energy. Our theoretical results are all verified numerically, which paves the way for implementing realistic target control over much broader applications.

Analysis of cut vertex in the control of complex networks

The control of complex networks is affected by their structural characteristic. As a type of key nodes in a network structure, cut vertexes are essential for network connectivity because their removal will disconnect the network. Despite their fundamental importance, the influence of the cut vertexes on network control is still uncertain. Here, we reveal the relationship between the cut vertexes and the driver nodes, and find that the driver nodes tend to avoid the cut vertexes. However, driving cut vertexes reduce the energy required for controlling complex networks, since cut vertexes are located near the middle of the control chains. By employing three different node failure strategies, we investigate the impact of cut vertexes failure on the energy required. The results show that cut vertex failures markedly increase the control energy because the cut vertexes are larger-degree nodes. Our results deepen the understanding of the structural characteristic in network control.