Controllability Of Complex Networks Research Articles

Understanding the controllability of complex networks from the microcosmic to the macrocosmic

From a microcosmic perspective, nodes as meta-structures (or ‘smallest units’) for the constitution of a graph are of great importance for understanding complex network-based systems. In this paper, we develop a new framework, which first of all defines the meta-structures of a graph in different levels and tries to depict a graph from a low to a high level of abstraction. Further, based on this framework we study the meta-structure-driven control model and try to understand the controllability of complex networks from a microcosmic to a macrocosmic perspective. Finally, we analyze the impact of the community strength of networks on meta-structure-driven control. The results for artificial networks and real-world networks indicate that for meta-structure-driven control, the number of driver nodes is dependent on the networks’ degree distribution, and the dependence weakens as the level of the meta-structures increases. In addition, the networks are easier to control as the community strength increases, while this monotonicity is not preserved as the level of the meta-structures increases. We also find that it is harder to control sparse and inhomogeneous networks as the level of the meta-structures increases.

Input Selection for Performance and Controllability of Structured Linear Descriptor Systems

A common approach to controlling complex networks is to directly control a subset of input nodes, which then controls the remaining nodes via network interactions. Current approaches for selecting input nodes assume that either all system matrix entries are known and fixed, or are independent free parameters, and focus either on performance or controllability. In this paper, we make two contributions towards input selection in networked systems. First, we propose polynomial-time algorithms for input selection in structured linear descriptor systems, which are systems with dependencies between free parameters due to physical laws or design constraints. Second, we develop a framework for input selection based on joint consideration of controllability and performance. We make both contributions by mapping input selection to a submodular optimization problem under two matroid constraints, which enables development of polynomial-time algorithms with provable optimality guarantees. We provide improved optimalit...

Pinning control and controllability of complex dynamical networks

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.

Robustness of network controllability in cascading failure

It is demonstrated that controlling complex networks in practice needs more inputs than that predicted by the structural controllability framework. Besides, considering the networks usually faces to the external or internal failure, we define parameters to evaluate the control cost and the variation of controllability after cascades, exploring the effect of number of control inputs on the controllability for random networks and scale-free networks in the process of cascading failure. For different topological networks, the results show that the robustness of controllability will be stronger through allocating different control inputs and edge capacity.

Identifying Topologies of Complex Dynamical Networks With Stochastic Perturbations

Systems taking the form of networks abound in the world and attract extensive attention from the multidisciplinary nonlinear science community. As is known, network topology plays an important role in determining a network's intrinsic dynamics and function. In the past decade, many researchers have investigated the geometric features, control, and synchronization of complex networks with given or known topological structures. However, in many practical situations, the exact structure of a network is usually unknown. Therefore, inferring the intrinsic topology of complex networks is a prerequisite to understanding and explaining the evolutionary mechanisms and functional behaviors of systems built upon those networks. Furthermore, noise is ubiquitous in nature and in man-made networks. The goal of this paper is to present a simple and efficient technique to recover the underlying topologies of noise-contaminated complex dynamical networks with or without information transmission delay. The effectiveness of the approach is illustrated with a complex network composed of FHN systems. In addition, the impact of some network parameters on identification performance is further probed into.

Energy-Efficient Service Multiplexing on Profile-Based TWDM Access Systems

Both the variety of communication devices and their options in connecting to the Internet are continuously increasing due to the advances in numerous attractive network applications. These trends make designing the network much more complex. Legacy network design only had to consider predefined applications using common end-point devices such as plain old telephone system. On the other hand, the current and future network, especially in the access part, is expected to be universal so as to cover not only residential users, but also mobile users, and the huge number Internet of Things devices for the sake of cost efficiency. The key issue is the difficulty of designing a complex network that is also extremely energy efficient, particularly the future access system. Although many studies have attempted to improve the bandwidth utilization or energy efficiency in multiple-wavelength systems, little is known about how it will be impacted by the divergence among these multiple concrete services. In order to solve this energy issue, we propose a service multiplexing method with a profile-based network architecture, where each device declares its traffic profile. Our concept provides the feasible and practical control of complex network. It differs markedly from the methods that control the traffic at the packet or session level as it is easy to apply in actual networks.

Input graph: the hidden geometry in controlling complex networks.

The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder: what is the underlying relationship of all possible input nodes? Here we introduce input graph, a simple geometry that reveals the complex relationship between all control schemes and input nodes. We prove that the node adjacent to an input node in the input graph will appear in another control scheme, and the connected nodes in input graph have the same type in control, which they are either all possible input nodes or not. Furthermore, we find that the giant components emerge in the input graphs of many real networks, which provides a clear topological explanation of bifurcation phenomenon emerging in dense networks and promotes us to design an efficient method to alter the node type in control. The findings provide an insight into control principles of complex networks and offer a general mechanism to design a suitable control scheme for different purposes.

Exponential synchronization via pinning adaptive control for complex networks of networks with time delays

This paper is concerned with the pinning adaptive synchronization control problem for a class of complex networks of networks. The complex networks of networks under consideration are composed of both leaders' network and followers' networks (also called “subnetworks”), where the leaders' network and subnetworks are regarded as the nodes of the networks of networks, each subnetwork can receive the information from leaders' network, but not the reverse. In order to achieve the synchronization for the networks of networks, pinning control strategy is adopted, and adaptive controllers are designed for the controlled nodes. By utilizing the stability theory of dynamical systems and some analysis techniques such as the Barbalat lemma, several sufficient criteria are obtained to ensure global exponential synchronization for the controlled complex networks of networks. Finally, a numerical simulation example is given to verify the theoretical results.

Robustness of controlling edge dynamics in complex networks against node failure.

The robustness of controlling complex networks is significant in network science. In this paper, we focus on evaluating and analyzing the robustness of controlling edge dynamics in complex networks against node failure. Using three categories of all nodes to quantify the robustness, we find that the percentages of the three types of nodes are mainly related to the degree distribution of networks. The simulation results of model networks and analytic calculations show that the sparse inhomogeneous networks, which emerge in many real complex networks, have strong control robustness from the point of the number of ordinary nodes, but the strong positive correlation between in and out degrees reduces the control robustness. Evaluation of real-world networks indicates that most of them have few or no critical nodes, that is, they do not need to increase driver nodes to maintain control for most of node failures. Then an adding circuit-link strategy is proposed to optimize the robustness of edge controllability.

Distributed synchronization control of complex networks with communication constraints

This paper is concerned with the distributed synchronization control of complex networks with communication constraints. In this work, the controllers communicate with each other through the wireless network, acting as a controller network. Due to the constrained transmission power, techniques such as the packet size reduction and transmission rate reduction schemes are proposed which could help reduce communication load of the controller network. The packet dropout problem is also considered in the controller design since it is often encountered in networked control systems. We show that the closed-loop system can be modeled as a switched system with uncertainties and random variables. By resorting to the switched system approach and some stochastic system analysis method, a new sufficient condition is firstly proposed such that the exponential synchronization is guaranteed in the mean-square sense. The controller gains are determined by using the well-known cone complementarity linearization (CCL) algorithm. Finally, a simulation study is performed, which demonstrates the effectiveness of the proposed design algorithm.

Control principles of complex systems

A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

Attack Vulnerability of Network Controllability.

Controllability of complex networks has attracted much attention, and understanding the robustness of network controllability against potential attacks and failures is of practical significance. In this paper, we systematically investigate the attack vulnerability of network controllability for the canonical model networks as well as the real-world networks subject to attacks on nodes and edges. The attack strategies are selected based on degree and betweenness centralities calculated for either the initial network or the current network during the removal, among which random failure is as a comparison. It is found that the node-based strategies are often more harmful to the network controllability than the edge-based ones, and so are the recalculated strategies than their counterparts. The Barabási-Albert scale-free model, which has a highly biased structure, proves to be the most vulnerable of the tested model networks. In contrast, the Erdős-Rényi random model, which lacks structural bias, exhibits much better robustness to both node-based and edge-based attacks. We also survey the control robustness of 25 real-world networks, and the numerical results show that most real networks are control robust to random node failures, which has not been observed in the model networks. And the recalculated betweenness-based strategy is the most efficient way to harm the controllability of real-world networks. Besides, we find that the edge degree is not a good quantity to measure the importance of an edge in terms of network controllability.

Optimization of controllability and robustness of complex networks by edge directionality

Recently, controllability of complex networks has attracted enormous attention in various fields of science and engineering. How to optimize structural controllability has also become a significant issue. Previous studies have shown that an appropriate directional assignment can improve structural controllability; however, the evolution of the structural controllability of complex networks under attacks and cascading has always been ignored. To address this problem, this study proposes a new edge orientation method (NEOM) based on residual degree that changes the link direction while conserving topology and directionality. By comparing the results with those of previous methods in two random graph models and several realistic networks, our proposed approach is demonstrated to be an effective and competitive method for improving the structural controllability of complex networks. Moreover, numerical simulations show that our method is near-optimal in optimizing structural controllability. Strikingly, compared to the original network, our method maintains the structural controllability of the network under attacks and cascading, indicating that the NEOM can also enhance the robustness of controllability of networks. These results alter the view of the nature of controllability in complex networks, change the understanding of structural controllability and affect the design of network models to control such networks.

Optimal control of complex networks based on matrix differentiation

Finding the key node set to be connected to external control sources so as to minimize the energy for controlling a complex network, known as the minimum-energy control problem, is of critical importance but remains open. We address this critical problem where matrix differentiation is involved. To this end, the differentiation of energy/cost function with respect to the input matrix is obtained based on tensor analysis, and the Hessian matrix is compressed from a fourth-order tensor. Normalized projected gradient method (NPGM) normalized projected trust-region method (NPTM) are proposed with established convergence property. We show that NPGM is more computationally efficient than NPTM. Simulation results demonstrate satisfactory performance of the algorithms, and reveal important insights as well. Two interesting phenomena are observed. One is that the key node set tends to divide elementary paths equally. The other is that the low-degree nodes may be more important than hubs from a control point of view, indicating that controlling hub nodes does not help to lower the control energy. These results suggest a way of achieving optimal control of complex networks, and provide meaningful insights for future researches.

State feedback control design for Boolean networks.

BackgroundDriving Boolean networks to desired states is of paramount significance toward our ultimate goal of controlling the progression of biological pathways and regulatory networks. Despite recent computational development of controllability of general complex networks and structural controllability of Boolean networks, there is still a lack of bridging the mathematical condition on controllability to real boolean operations in a network. Further, no realtime control strategy has been proposed to drive a Boolean network.ResultsIn this study, we applied semi-tensor product to represent boolean functions in a network and explored controllability of a boolean network based on the transition matrix and time transition diagram. We determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real boolean functions and structure property of a network. An efficient tool is offered to assess controllability of an arbitrary Boolean network and to determine all reachable and non-reachable states. We found six simplest forms of controllable 2-node Boolean networks and explored the consistency of transition matrices while extending these six forms to controllable networks with more nodes. Importantly, we proposed the first state feedback control strategy to drive the network based on the status of all nodes in the network. Finally, we applied our reachability condition to the major switch of P53 pathway to predict the progression of the pathway and validate the prediction with published experimental results.ConclusionsThis control strategy allowed us to apply realtime control to drive Boolean networks, which could not be achieved by the current control strategy for Boolean networks. Our results enabled a more comprehensive understanding of the evolution of Boolean networks and might be extended to output feedback control design.

Atopic dermatitis: allergic dermatitis or neuroimmune dermatitis?

Advances in knowledge of neurocellulars relations have provided new directions in the understanding and treatment of numerous conditions, including atopic dermatitis. It is known that emotional, physical, chemical or biological stimuli can generate more accentuated responses in atopic patients than in non-atopic individuals; however, the complex network of control covered by these influences, especially by neuropeptides and neurotrophins, and their genetic relations, still keep secrets to be revealed. Itching and airway hyperresponsiveness, the main aspects of atopy, are associated with disruption of the neurosensory network activity. Increased epidermal innervation and production of neurotrophins, neuropeptides, cytokines and proteases, in addition to their relations with the sensory receptors in an epidermis with poor lipid mantle, are the aspects currently covered for understanding atopic dermatitis.

Effects Of Symmetry On The Structural Controllability Of Neural Networks: A Perspective.

The controllability of a dynamical system or network describes whether a given set of control inputs can completely exert influence in order to drive the system towards a desired state. Structural controllability develops the canonical coupling structures in a network that lead to un-controllability, but does not account for the effects of explicit symmetries contained in a network. Recent work has made use of this framework to determine the minimum number and location of the optimal actuators necessary to completely control complex networks. In systems or networks with structural symmetries, group representation theory provides the mechanisms for how the symmetry contained in a network will influence its controllability, and thus affects the placement of these critical actuators, which is a topic of broad interest in science from ecological, biological and man-made networks to engineering systems and design.

Stability and Control of Fractional Chaotic Complex Networks with Mixed Interval Uncertainties

AbstractThis paper investigates the stability and control in fractional complex networks with inner and outer interval uncertainties. Each node is defined as a chaotic system. Stability theorems for fractional order 0 < α < 1 and 1 ≤ α < 2 are derived in the chaotic complex network. Instead of removing the nonlinear part directly, for a class of nonlinear function, we use an interval matrix to deal with this problem. By using the Kronecker product and LMI toolbox, stability conditions are provided in terms of linear matrix inequalities, and feasible feedback controllers are solved. In numerical simulations, two examples (real‐valued complex network and complex‐valued complex network) are provided to demonstrate the robustness and effectiveness of our methods.

Emergence of complexity in controlling simple regular networks

Quantifying the capacity of a given node or a bunch of nodes in maintaining a system's controllability is a crucial problem in complex networks and control theory. We give a systematic analysis of the ability of a single node or a pairs of nodes to control an undirected unweighted chain and ring. By combining algebraic theory and graph spectrum analysis, we derive analytic expressions for the control range of some given control inputs and find that complex phenomena emerge even from these simplest graph structures. Specifically, the control range is sensitive to the location of driver nodes and shows complex periodic behaviors. Our findings have implications for evaluating the control range and practically controlling complex networks.

On the pinning controllability of complex networks using perturbation theory of extreme singular values. application to synchronisation in power grids

Pinning control on complex dynamical networks has emerged as a very important topic in recent trends of control theory due to the extensive study of collective coupled behaviors and their role in physics, engineering and biology. In practice, real-world networks consist of a large number of vertices and one may only be able to perform a control on a fraction of them only. Controllability of such systems has been addressed in [ 17 ], where it was reformulated as a global asymptotic stability problem. The goal of this short note is to refine the analysis proposed in [ 17 ] using recent results in singular value perturbation theory.