Controllability Of Complex Networks Research Articles

An integral sliding mode approach to distributed control of coupled networks with measurement Quantization

This paper is concerned with the distributed sliding mode control problem of complex networks under quantization mechanism. The complex networked control system is considered with inner coupling, uncertainties and quantized measurements among the agents. The quantizer, which is adopted as a logarithmic one, is designed to be on the sensor unit to implement the digital communication. In order to avoid the discontinuity of the sliding mode control law, namely, the sliding surface, an adaptive filter is utilized. Based on the filtered signal, an integral sliding-mode manifold is designed for each agent. A series of dynamic sliding mode control laws are synthesized to achieve the exponential reaching onto the sliding surface within a finite time for the whole networked system. The resulting sliding motion is analyzed using the Lyapunov functional approach, and a finite-gain L2 stability criterion is established. Finally, the effectiveness of the designed distributed sliding mode control scheme is illustrated with some simulation results.

Topological geometry analysis for complex dynamic systems based on adaptive control method

Several models had been proposed for dynamic systems, and different criteria had been analyzed for such models such as Hamiltonian, synchronization, Lyapunov expansion, and stability. The geometry criteria play a significant part in analyzing dynamic systems and some study articles analyze the geometry of such topics. The synchronization and the complex-network control with specified topology; meanwhile, the exact topology may be unknown. In the present paper, and by making use of the adaptive control method, a proposed control method is developed to determine the actual topology. The basic idea in the proposed method is to receive evolution of the network-nodes

Pinning synchronization of fractional and impulsive complex networks via event-triggered strategy

In this paper, the pinning control of fractional complex networks with impulses and time-varying delays is studied and a class of more general network structure is considered which consists of an instantaneous communication topology and a delayed communication topology. Based on the linear matrix inequality technique, some sufficient conditions are obtained to ensure synchronization of the network under a designed pinning event-triggered strategy. And Zeno behaviors are excluded. In addition, a pinning scheme is designed, which shows that the nodes with delayed communication are good candidates for applying pinning controllers. Finally, a numerical simulation is given to verify the correctness of the main results.

Irrelevance of linear controllability to nonlinear dynamical networks

There has been tremendous development in linear controllability of complex networks. Real-world systems are fundamentally nonlinear. Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal “importance”. For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly the irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to Caenorhabditis elegans connectome is examined and discussed.

Restricted control of complex systems with prevention of instability propagation

One of the challenges for complex systems is the issue of limited number of sensors and actuators for controlling relatively abundant number of agents. The infeasibility of large distribution of sensors and actuators prevents many advanced algorithms from exercising their power. Pinning control provides a remarkable resolution to this difficult problem albeit suboptimal solutions are often sought. In this paper, however, a restricted control approach is proposed particularly targeting the problem of controlling complex networks using only one sensor and one actuator at only one node. Performance achievability for both discrete frequencies and over frequency bands are investigated; the important problem of broad band stability is analyzed, and important results are obtained with easy-to-verified conditions; prevention of instability propagation is also delineated using the concept of bounding the controlled agent’s norm. Numerical examples are provided for verification of the theoretical results.

On Almost Controllability of Dynamical Complex Networks with Noises

This paper discusses the controllability problem of complex networks. It is shown that almost any weighted complex network with noise on the strength of communication links is controllable in the sense of Kalman controllability. The concept of almost controllability is elaborated by both theoretical discussions and experimental verifications.

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.

An Overlapping Community Detection Algorithm with Label Propagation Control for Complex Networks

An Overlapping Community Detection Algorithm with Label Propagation Control for Complex Networks

Decentralized Gain Adaptation for Optimal Pinning Controllability of Complex Networks

Coordinating ensembles of dynamical systems in a decentralized manner is of central importance when controlling complex networks. Pinning control is a much used technique where only a small fraction of the network nodes is directly controlled, with control gains being typically selected uniformly across the control layer. In this letter, we tackle the problem of optimally selecting the control gains of a pinning control strategy. Indeed, in networks of nonlinear dynamical systems fulfilling the so-called QUAD assumption, pinning controllability improves as the smallest eigenvalue $\lambda _{1}$ of an extended Laplacian matrix increases. Based on this observation, we pose a constrained optimization problem on the network. Rather than solving it in a centralized fashion, we propose a fully decentralized multilayer approach. Specifically, one layer is used to evaluate the sensitivity of $\lambda _{1}$ to the variation of the gains, while the second layer uses such an estimate to dynamically tune the control gains. The effectiveness of the approach is demonstrated via a representative example.

Research on minimum control energy of complex networks by the non-independent control strategy of single control input

In this paper, we develop a new framework to calculate control energy of controlling complex networks at the same time obtain the lower control energy bound to achieve control by using the non-independent control strategy of single control input. Article utilizes a variable-θ making a slight structural disturbance to control input, which we can find a suitable control input to control network. Our results promote the studying on the minimum control energy to control complex networks by the non-independent control strategy of multiple control inputs.

Topology Effects on Sparse Control of Complex Networks with Laplacian Dynamics

Ease of control of complex networks has been assessed extensively in terms of structural controllability and observability, and minimum control energy criteria. Here we adopt a sparsity-promoting feedback control framework for undirected networks with Laplacian dynamics and distinct topological features. The control objective considered is to minimize the effect of disturbance signals, magnitude of control signals and cost of feedback channels. We show that depending on the cost of feedback channels, different complex network structures become the least expensive option to control. Specifically, increased cost of feedback channels favors organized topological complexity such as modularity and centralization. Thus, although sparse and heterogeneous undirected networks may require larger numbers of actuators and sensors for structural controllability, networks with Laplacian dynamics are shown to be easier to control when accounting for the cost of feedback channels.

Block-based minimum input design for the structural controllability of complex networks

Traditional control system design to complex networks is generally implemented by integrated structural analysis aiming at a global network. However, such a global method may be inefficient, in particular, when a massive network with a huge number of nodes and associations is considered. In this paper, motivated by the idea of “dividing and dealing”, we propose a block-based approach to the issue of minimum input design for structural controllability (MIDSC) of complex networks that potentially incurs in higher efficiency. Specifically, we consider a large-scale networked system that consists of several local blocks. The main challenge for control configuration design of this class of systems is how to find the minimum inputs of global network according to the local block information while maintaining system’s structural controllability. To this end, two block-based graphical algorithms are developed to meet the conditions required for achieving structural controllability, and meanwhile determine an optimal solution for addressing the MIDSC problem. The complexity of the proposed method is analyzed, which is also compared with existing algorithms designed mainly based on monolithic model. In particular, we show that, under some mild conditions on blocking structure, the complexity of the proposed algorithm is strictly lower than that of existing algorithms to the MIDSC problem.

A Sparse Neural Network Based Control Structure Optimization Game under DoS Attacks for DES Frequency Regulation of Power Grid

With the rapid growth of distributed energy sources, power grid has become a flexible and complex networked control system. However, it increases the chances of being a denial-of-service attack, which degrades the performance of the power grid, even causing cascading failures. To mitigate negative effects from denial-of-service attack and enhance the reliability of the power grid, we propose a networked control system structure based optimization scheme that is derived from a Stackelberg game model for the frequency regulation of a power grid with distributed energy sources. In the proposed game model, both denial-of-service attacker and control system designer as a defender are considered without using any analytical model. For defenders, we propose a sparse neural network based DES control and system structure design scheme. The neural network is used to approximate the desired control output and reinforce signals for the improvements of short- and long-term performance. It also introduces the sparse regulation of column grouping in the neural network learning process to explore the structure of control system that involves the placement of sensor, distributed energy sources actuator, and communication topology. For denial-of-service attackers, the related attack constraints and attack rewards are established. The solution of game equilibrium is considered as an optimal solution for both denial-of-service attack strategy and control structure. An offline optimization algorithm is proposed to solve the game equilibrium. The effectiveness of proposed scheme is verified by two cases, which illustrate the optimal solutions of both control structure and denial-of-service attack strategy.

Optimizing Controllability of Complex Networks by Minimum Driver Nodes

Optimizing Controllability of Complex Networks by Minimum Driver Nodes

Energy cost for controlling complex networks with linear dynamics.

Examining the controllability of complex networks has received much attention recently. The focus of many studies is commonly trained on whether we can steer a system from an arbitrary initial state to any final state within finite time with admissible external inputs. In order to accomplish the control at the minimum cost, we must study how much control energy is needed to reach the desired state. At a given control distance between the initial and final states, existing results have offered the scaling behavior of lower bounds of the minimum energy in terms of the control time. However, to reach an arbitrary final state at a given control distance, the minimum energy is actually dominated by the upper bound, whose analytic expression still remains elusive. Here we theoretically show the scaling behavior of a precise upper bound of the minimum energy in terms of the time required to achieve control. Apart from validating the analytical results with numerical simulations, our findings are applicable to any number of nodes that receive inputs directly and any types of networks with linear dynamics. Moreover, more precise analytical results for the lower bound of the minimum energy are derived with the proposed method. Our results pave the way for implementing realistic control over various complex networks with the minimum control cost.

Controllable containment control of multi-agent systems based on hierarchical clustering

ABSTRACT In the practical application, such as military, logistics or drone control, in order to meet the mission needs, the scale of multi-agent systems is constantly expanding, and the number of leaders required to implement control is increasing. In containment control, it has some difficulties in forming convex hulls by traditional control methods to achieve ideal control purposes. We propose a method that is more suitable and effective for large-scale networks to achieve containment control here. In this paper, a controllable containment control algorithm based on hierarchical clustering for multi-agent systems is proposed by combining the topology optimisation theory and complex network controllability theory. First, the multi-agent network is divided into several communities according to the hierarchical clustering algorithm. Then the maximum matching algorithm of bipartite graph is used to determine the minimum leader set satisfying the network controllability. Second, the corresponding control protocols are designed for the agents, and a position adjustment control force is introduced to adjust the motion of individuals that are located outside the convex hull in the process of containment among the communities. Therefore, when achieving and maintaining the controllable containment control within the community, the controllable containment control among the communities can be achieved effectively through the proposed algorithm. Finally, some simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Controllability of Bandlimited Graph Processes Over Random Time Varying Graphs

Controllability of complex networks arises in many technological problems involving social, financial, road, communication, and smart grid networks. In many practical situations, the underlying topology might change randomly with time, due to link failures such as changing friendships, road blocks or sensor malfunctions. Thus, it leads to poorly controlled dynamics if randomness is not properly accounted for. We consider the problem of controlling the network state when the topology varies randomly with time. Our problem concerns target states that are bandlimited over the graph; these are states that have nonzero frequency content only on a specific graph frequency band. We thus leverage graph signal processing and exploit the bandlimited model to drive the network state from a fixed set of control nodes. When controlling the state from a few nodes, we observe that spurious, out-of-band frequency content is created. Therefore, we focus on controlling the network state over the desired frequency band, and then use a graph filter to get rid of the unwanted frequency content. To account for the topological randomness, we develop the concept of controllability in the mean, which consists of driving the expected network state towards the target state. A detailed mean squared error analysis is performed to quantify the statistical deviation between the final controlled state on a particular graph realization and the actual target state. Finally, we propose different control strategies and evaluate their effectiveness on synthetic network models and social networks.

Node Importance in Controlled Complex Networks

The problem of node importance in a general controlled complex network is investigated in this brief. An index, ControlRank index, to measure the node importance is presented. The index is relatively intuitive and helps unify various indexes that are effective only in the networks with some particular topology. If all nodes except one are pinned in a network, the importance of the unpinned node is sorted in descending order of degree; even if a node is the most significant node, it does not necessarily belong to the most efficient node set; it is very crucial to have an eye on the information balance as for information dissemination in a network; it is reasonable to rank node importance by sorting the node degrees in a scale-free network. The results and phenomena provide us with a broader and clearer perspective to view node importance in complex networks.

Controllability and maximum matchings of complex networks.

Previously, the controllability problem of a linear time-invariant dynamical system was mapped to the maximum matching (MM) problem on the bipartite representation of the underlying directed graph, and the sizes of MMs on random bipartite graphs were calculated analytically with the cavity method at zero temperature limit. Here we present an alternative theory to estimate MM sizes based on the core percolation theory and the perfect matching of cores. Our theory is much more simplified and easily interpreted, and can estimate MM sizes on random graphs with or without symmetry between out- and in-degree distributions. Our result helps to illuminate the fundamental connection between the controllability problem and the underlying structure of complex systems.

Controllability and Its Applications to Biological Networks

Biological elements usually exert their functions through interactions with others to form various types of biological networks. The ability of controlling the dynamics of biological networks is of enormous benefits to pharmaceutical and medical industry as well as scientific research. Though there are many mathematical methods for steering dynamic systems towards desired states, the methods are usually not feasible for applying to complex biological networks. The difficulties come from the lack of accurate model that can capture the dynamics of interactions between biological elements and the fact that many mathematical methods are computationally intractable for large-scale networks. Recently, a concept in control theory — controllability, has been applied to investigate the dynamics of complex networks. In this article, recent advances on the controllability of complex networks and applications to biological networks are reviewed. Developing dynamic models is the prior concern for analyzing dynamics of biological networks. First, we introduce a widely used dynamic model for investigating controllability of complex networks. Then recent studies of theorems and algorithms for having complex biological networks controllable in general or specific application scenarios are reviewed. Finally, applications to real biological networks manifest that investigating the controllability of biological networks can shed lights on many critical physiological or medical problems, such as revealing biological mechanisms and identifying drug targets, from a systematic perspective.