Controllability of real networks n d n d n explore the controllability of several real networks. This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact web. For anisotropic networks networks with a preferential direction it seems. The ability to control complex networks via external inputs is fundamental to guarantee reliable and efcient network operation. Optimizing controllability of complex networks by minimum. How to optimize structural controllability has also become a significant issue. The principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well. It could for instance enable improved efficiency in the functioning of a network or lead to that entirely new applicative possibilities emerge. Controllability and modularity of complex networks. Recent research has shown that mdss tend to avoid highdegree nodes.
However, there is no comprehensive and easytouse platform for analyzing controllability of biomolecular networks although various algorithms for analyzing complex network controllability have been proposed recently. Wang x f, chen g, pinning control of scalefree dynamical networks, physica a, 310. Complex networks in which inputs are naturally unilateral occur in many other domains, such as for instance in transportation, in trade, or in power networks, see table 1 for more motivating examples. The controllability of general directed and weighted complex networks has. At last, the related key problems in grcbased controllability of complex networks processing framework are discussed. Pinning controllability of complex networks with community.
Dec 24, 2016 the controllability of dynamical networks depends on both network structure and node dynamics. Universal framework for edge controllability of complex networks. Sorrentino f, di bernardo m, garofalo f, chen g, controllability of complex networks. One final goal of our efforts is to control the complex systems in our daily life. For networks of linearly coupled linear dynamical systems the controllability of the network can be determined using the wellknown kalman rank criterion. They develop analytical tools to study the controllability of an arbitrary complex directed network using both model and real systems, ranging from regulatory, neural and metabolic pathways in. In our work we apply the various tools developed to.
On the controllability of networks with nonidentical linear. Functional target controllability of networks archive ouverte hal. To design and maintain a networked system under control. Pdf quantitative controllability index of complex networks. Structural controllability and controlling centrality of. Controllability of complex networks with unilateral. Input is an adjacency matrix directed or undirected. Especially, research on robustness and controllability of the network indicate the close correlation to the properties of complex networks such as scalefree, smallworld, etc. All relevant data are within the paper and its supporting information files. Control of multilayer biological networks and applied to. Aug 06, 20 this paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state. Cort es uc san diego controllability and identi cation of complex networks october 23, 2015 11 40 reachability gramian for bilinear control systems even though bilinear systems are not linear, analogous concept exist.
By means of simulations, we show that the degree descendi. With the evidence of ubiquity of temporal networks in our economy, nature and society, its urgent and significant to focus on its structural controllability as well as the corresponding characteristics, which nowadays is still an untouched topic. Illustration of edge orientation for optimal controllability. Analysis of the effect of degree correlation on the size. August 2429, 2014 recovering the controllability of complex networks jin ding, yongzai lu, fellow, ieee, jian chu state key laboratory of industrial control technology, institute of cybersystems and control, zhejiang university, 310027, hangzhou, p. May 11, 2011 controllability of complex networks controllability of complex networks liu, yangyu. Global pinning controllability of complex networks. Also controllability with constrained inputs has a long history, see chapter 5 of jacobson 14 for a survey focusing on driven control systems. On the pinning controllability of complex networks using. Pinning control and controllability of complex networks. Observability and controllability of nonlinear networks. Recently, controllability, which is a concept in control theory, has been applied to investigate the dynamics of complex networks.
This definition agrees well with our intuitive notion of control. Temporal networks are such networks where nodes and interactions may appear and disappear at various time scales. May 11, 2011 they develop analytical tools to study the controllability of an arbitrary complex directed network using both model and real systems, ranging from regulatory, neural and metabolic pathways in. For this problem i we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, ii we derive bounds based on the system dynamics network.
A combined algorithm for analyzing structural controllability. A frontier area of the research in network science and engineering is controlling complex networks, such as. The international conference on complex networks and their applications aims at bringing together researchers from different scientific communities working on areas related to complex networks. We apply these tools to several real networks, finding.
What links here related changes upload file special pages permanent link page. 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. Abstractcontrolling complex networks is of paramount importance in science and engineering. Introduction an observer model of a natural system has many. According to control theory, a system is controllable if the system can be. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with timedependent. Recovering the controllability of complex networks. Li x, wang x f, chen g, pinning a complex dynamical network to its equilibrium, ieee trans. To ultimately develop a framework to control complex and nonlinear networks, a necessary and fundamental step is to investigate the controllability of complex networks with linear dynamics. May 11, 2011 recent advances towards quantifying the topological characteristics of complex networks 12,14,15,16 have shed light on factor 1, prompting us to wonder whether some networks are easier to. Efficient target control of complex networks based on preferential matching.
If you access for the first time, click on register. Proceedings of the 19th world congress the international federation of automatic control cape town, south africa. In this paper, we study the controllability of networks with different numbers of communities and various strengths of community structure. Although control theory offers mathematical tools for steering. In the past few decades, the controllability of singlelayer networks with linear 15 and nonlinear 69 dynamics have been widely studied in a variety of biomedical systems. Our research progress wang x f, chen g, pinning control of scalefree dynamical networks, physica a, 310. Controllability of complex networks controllability of complex networks liu, yangyu. In the past decades, plenty of attentions 1,2,3,4,5 have been paid into the study of the structures and dynamics of complex networked systems, especially biological systems. Once the manuscript is ready, generate the pdf file named abstractnumber. We fix the number of nodes and the number of links in the networks of fig. Controllability and identification of complex networks.
Efficient target control of complex networks based on preferential. Recent advances towards quantifying the topological characteristics of complex networks 12,14,15,16 have shed light on factor 1, prompting us to wonder whether some networks are easier to. Cort es uc san diego controllability and identi cation of complex networks october 23, 2015 7 40 reachability metrics for bilinear control systems how easydi cult to control is a given bilinear control system. Quantitative controllability index of complex networks article pdf available in advances in mathematical physics 20183. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver. Biological physics, complex systems, nonlinear dynamics i. There exist well developed theoretical frameworks of controllability for linear dynamical systems in the traditional. Xiethis research is supported by the national natural science foundation of china grant no. Exact controllability of complex networks file exchange. Furthermore, apart from the controllability issue, the developed techniques provide new ways of analyzing complex networks with degreedegree correlations. Studying the controllability of biomolecular networks can result in profound knowledge about molecular biological systems. Network controllability is concerned about the structural controllability of a network. In practice, realworld networks consist of a large number of vertices and one may only be able to perform a control on a fraction of them only. Dynamical processes occurring on the edges in complex networks are relevant to a variety of realworld situations.
Controlling a complex network towards a desired state is of great. A complex network, in context of network theory is a graph with nontrivial topological features. For this problem i we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, ii we derive bounds based on the system. A novel algorithm for finding optimal driver nodes to. Despite the recent development of structural controllability theory, we continue to lack a. You must upload the pdf file of your contribution together with the files used to generate it into the submission system at cn. May 12, 2011 we apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network s degree distribution. Barabasi 1,2,5 the ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with timedependent control that can guide the systems entire dynamics. The algorithm addresses the two fundamental properties to guarantee structural controllability of a system.
Comment on controllability of complex networks with nonlinear. Pdf controllability of complex networks researchgate. How to construct a network with a fixed number of nodes as well as a fixed number of links that is easier to control is more important for the. Despite important advances in control theory, several questions regarding the control of complex networks are largely unexplored, as, for instance, the relation between network topology and its controllability degree. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes.
Minimum driver node sets mdss play an important role in studying the structural controllability of complex networks. Zhengzhong yuan, chen zhao, zengru di, wenxu wang, yingcheng lai download pdf. On the controllability of networks with nonidentical. Controllability of complex networks via pinning francesco sorrentino,1, mario di bernardo,1 franco garofalo,1 and guanrong chen2 1university of naples federico ii, naples 80125, italy 2city university of hong kong, kowloon, hong kong, peoples republic of china received 8 august 2006. However, the attention was restricted to a very particular type of nonidentical nodes, ones where the dynamics of each node are described by an identical. For directed networks, some edges with inappropriate direction affect the controllability of networks, such as e ed. Complex networks are ubiquitous, they are found in natural, social and manmade systems, such as generegulatory networks and mobile sensor networks. Controllability of complex networks with unilateral inputs. There exist well developed theoretical frameworks of controllability for linear dynamical systems in the traditional field of engineering control 28, 29. This article is from nature communications, volume 4. Although control theory offers mathematical tools for steering engineered and natural systems. Recently, controllability of complex networks has attracted enormous attention in various fields of science and engineering. Asymmetric complex networks for asymmetric networks the situation is more complexfor isotropic networks networks with no preferential directions it seems that the situation is the same as for symmetric networks, namely they are dif.
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