Physical controllability of complex networks and control. Target control of complex networks cancer systems biology. Controllability of real networks n d n d n explore the controllability of several real networks. Controllability metrics, limitations and algorithms for. 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. Abstract controlling complex networks is of paramount importance in science and engineering. Optimization of controllability and robustness of complex. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems. A combined algorithm for analyzing structural controllability and observability of complex networks luis ubeda 1. In recent years, complex networks have gained increasing attention in different fields of science and engineering. Design of structural controllability for complex network architecture. Improving controllability of complex networks by rewiring. Controlling complex network is an essential problem in network science and engineering. Meaning of controllability of arbitrary complex directed networks.
Physical controllability of complex networks asu digital. Exact controllability of complex networks file exchange. There exist well developed theoretical frameworks of controllability for linear dynamical systems in the traditional. The problem of controlling these networks is an interesting and challenging problem to investigate. We start from the target controllability problem of linear systems with a minimum number of external control sources.
Exact controllability of complex networks europe pmc. 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 system. Overall we see no obvious trend in n d or n d across these networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on. Vulnerability and controllability of networks of networks. A few social networks display the smallest observed n d values. Complex networks are ubiquitous, they are found in natural, social and manmade systems, such as generegulatory networks and mobile sensor networks. Pdf controllability of deterministic networks with the. Pinning control and controllability of complex dynamical networks.
In this work, we studied the target controllability of complex networks. May 11, 2011 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 system. Chen pinning control and controllability of complex dynamical networks 3 3 controllability of directed networks the concept of complete state controllability was. Optimizing controllability of complex networks by minimum. The mathematical form of classical control theory is not suitable for current complex networks, which may contain thousands of biological nodes. Understanding controllability of complex networks from microcosmic to macrocosmic peng gang sun and xiaoke mastrong structural control centrality of a complex network chengyi turecent citations a passenger flow control method for subway network based on network controllability lu zeng et alcontrol principles of complex systems yangyu liu et al. Although they propose these tools or models for analyzing the controllability of complex networks, few people study that how to improve the controllability of complex networks6. Despite the recent development of structural controllability theory, we continue to lack a framework to control. Cort es uc san diego controllability and identi cation of complex networks october 23, 2015 15 40 gramianbased reachability metrics lower bound on minimum input energy justi es following reachability metrics. Physical controllability of complex networks and control of nonlinear dynamical networks yingcheng lai arizona state university collaborators. Control centrality and hierarchical structure in complex. Controllability of complex networks references 3 of 12 from liu et al1 networks are either unknown for example regulatory networks or are known only approximately and are time dependent for example internet traffic. Although control theory offers mathematical tools for steering.
Control principles for complex biological networks. Abstract network science is a highly interdisciplinary field ranging from natural science to engineering technology and it has been applied to model complex systems and used to. To design and maintain a networked system under control. Overall we see no obvious trend in n d or n d across those networks. Iv, where pinning control of scale free complex networks of chaotic oscillators is studied through numerical simulations. Dominating scale free networks with variable scaling exponent. This article is from nature communications, volume 4. Structural controllability only needs to know the structure of complex networks and can provide the upper bound of the minimum number of driver nodes efficiently. 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. Pinning control and controllability of complex networks guanrong ron chen city university of hong kong ias workshop on frontiers in systems and control cityu august 2425, 2017 acknowledgements. In this paper, a new algorithm is proposed to improve the controllability of complex networks by rewiring links regularly which transforms the network structure. In our work we apply the various tools developed to. In existing frameworks of structural or exact controllability, the ability to. On quantitatively measuring controllability of complex.
The effect of this index is analyzed mainly based on empirical studies on various classes of network topologies, such as random network, smallworld network, and scale free network. As a group, regulatory networks display very high n d. By mapping the structural controllability problem to a maximum matching problem14, we were able to identify a minimum set of driver nodes of size n d, suf. Controllability describes our ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs. Related content controllability and observability of cascading failure networks peng gang sun and xiaoke ma. Target control and expandable target control of complex. Create scripts with code, output, and formatted text in a single executable document. This paper deals with controllability of complex networks. Pinning control and controllability of complex networks guanrong ron chen city university of hong kong, china joint work with xiaofan wang, lin wang shanghai jiao tong university, china xiang li, baoyu hou fudan university, china 35th chinese control conference, chengdu, july 2729, 2016. Pdf complex networks download full pdf book download. An overview in recent years, synchronization of complex networks of. The complete structural controllability of a network and its robustness against unwanted link failures and perturbations.
Lin wang and xiao fan wang, shanghai jiao tong university, china. This definition agrees well with our intuitive notion of control. We apply these tools to several real networks, finding that the number of driver nodes is. On quantitatively measuring controllability of complex networks. A new quantitative index using knowledge of control centrality and condition number is constructed to measure the controllability of given networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state. Controllability and directionality in complex networks. An index is chosen to quantitatively measure controllability of given network.
Controllability and identification of complex networks. Network controllability is concerned about the structural controllability of a network. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. Minimum driver node sets mdss play an important role in studying the structural controllability of complex networks. Although control theory offers mathematical tools for steering engineered and natural systems towards a. Understanding the controllability of complex networks from the microcosmic to the macrocosmic to cite this article. Controllability and modularity of complex networks. The remaining part of this letter is organized as follows. Pdf quantitative controllability index of complex networks. Controlling complex networks is of paramount importance in science and engineering. 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. Liu et al controllability of complex networks sandbox. We developed a new theoretical approach, the k walk theory, to identify the controllable subgraph that one node can control, and a ga to identify an approximately minimum set of driver nodes to control a specified target set of nodes.
May 11, 2011 controllability of complex networks controllability of complex networks liu, yangyu. The studies on the controllability of complex networks popularly existing in natural, social and manmade engineered systems have been a critical and attractive subject for both academic and practical communities. The effect of this index is analyzed mainly based on empirical studies on various classes of network topologies, such as random network, smallworld network, and scale free. Even if all weights are known, a bruteforce search requires us to compute the rank ofcfor 2n2 1 distinct combina. Previous studies have shown that an appropriate directional assignment can improve structural controllability. Although most of real systems exhibit nonlinear dynamics, studying their linearized dynamics is a prerequisite for studying those systems. The presented results help us better understand the controllability of complex networks and design an efficient attack strategy against network control. For complex networks with different controllable subspace dimensions, their controllability is mainly determined by the control centrality factor. Controllability of complex networks with unilateral inputs. Recent advances indicate that the controllability of complex network is dependent on the network s topology.
How to optimize structural controllability has also become a significant issue. Expandable target controllability of complex networks 2. A combined algorithm for analyzing structural controllability. In this paper, the controllability issue of complex network is discussed. Cort es uc san diego controllability and identi cation of complex networks october 23, 2015 15 40 gramianbased reachability metrics lower bound on minimum. Quantitative controllability index of complex networks. Target control of complex networks pubmed central pmc. Design of structural controllability for complex network. The controllability of general directed and weighted complex networks has.
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. On almost controllability of dynamical complex networks. Controllability of complex networks controllability of complex networks liu, yangyu. A challenging problem in network science is to control complex networks.
The concept of almost controllability is elaborated by both theoretical discussions and experimental verifications. In sum, we study the control centrality of single node in complex networks and find that it is related to the underlying hierarchical structure of networks. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. On almost controllability of dynamical complex networks with.
In this section, we analyze the correlation between controllability and modularity of complex networks on random networks with builtin gradually varied modularity as well as realworld networks such as the zachary network, the dolphin network and the coappearance network in the novel of les miserables 3. Pinning control and controllability of complex networks. A complex network, in context of network theory is a graph with nontrivial topological features. Therefore, past research has not been sufficient to arrive at a. This paper discusses the controllability problem of complex networks. 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. Recent research has shown that mdss tend to avoid highdegree nodes. If with suitable choice of inputs we can drive a system from its initial state to a desired final state within a finite time. In this paper, we look at the controllability problem focusing on. Understanding the controllability of complex networks from. Pinning control and controllability of complex dynamical. Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. Section 2 introduces the fundamental preliminaries about controllability of complex networks and describes the model concerned. Barabasi 1,2,5 the ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them.
On the role of network centrality in the controllability. In this section, we analyze the correlation between controllability and modularity of complex networks on random networks with builtin gradually varied modularity as well as realworld networks such as the zachary network, the dolphin network and the coappearance network in the novel of les miserables. Liu et al controllability of complex networks sandbox slides. Identifying the set of driver nodes, that can guide the entire systems dynamics. Controllability metrics, limitations and algorithms for complex networks fabio pasqualetti, sandro zampieri, and francesco bullo abstractthis 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.
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