Controllability analysis of networks

Lombardi, Anna Maria; Hörnquist, Michael

doi:10.1103/physreve.75.056110

Cited by 125 publications

(90 citation statements)

References 6 publications

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“…In particular, Liu et al successfully adopted the classic structural controllability theory developed by Lin [141] to complex networks of various topologies [2], for which the traditional Kalman's rank condition [140] is difficult to be applied [145]. The ground breaking results show that, the structural controllability of a directed network can be assessed by using the maximum matching [150][151][152] algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…In the past a few years, great progress was made toward understanding the linear controllability of complex networks in terms of the fundamental issue of the minimum number of driver nodes required to steer the whole network system from an arbitrarily initial state to an arbitrarily final state in finite time [2,2,[145][146][147][148][149]. In particular, Liu et al successfully adopted the classic structural controllability theory developed by Lin [141] to complex networks of various topologies [2], for which the traditional Kalman's rank condition [140] is difficult to be applied [145].…”

Section: Introductionmentioning

confidence: 99%

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Predicting and Controlling Complex Networks

Lai¹

2015

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The research on the topology and dynamics of complex networks is one of the most focused area in complex system science. The goals are to structure our understanding of the real-world social, economical, technological, and biological systems in the aspect of networks consisting a large number of interacting units and to develop corresponding detection, prediction, and control strategies. In this highly interdisciplinary field, my research mainly concentrates on universal estimation schemes, physical controllability, as well as mechanisms behind extreme events and cascading failure for complex networked systems.Revealing the underlying structure and dynamics of complex networked systems from observed data without of any specific prior information is of fundamental importance to science, engineering, and society. We articulate a Markov network based model, the sparse dynamical Boltzmann machine (SDBM), as a universal network structural estimator and dynamics approximator based on techniques including compressive sensing and K-means algorithm. It recovers the network structure of the original system and predicts its short-term or even long-term dynamical behavior for a large variety of representative dynamical processes on model and real-world complex networks.One of the most challenging problems in complex dynamical systems is to control complex networks. Upon finding that the energy required to approach a target state with reasonable precision is often unbearably large, and the energy of controlling a set of networks with similar structural properties follows a fat-tail distribution, we identify fundamental structural "short boards" that play a dominant role in the enormous energy and offer a theoretical interpretation for the fat-tail distribution and simple strategies to significantly reduce the energy.Extreme events and cascading failure, a type of collective behavior in complex networked systems, often have catastrophic consequences. Utilizing transportation and evolutionary game dyi namics as prototypical settings, we investigate the emergence of extreme events in simplex complex networks, mobile ad-hoc networks and multi-layer interdependent networks. A striking resonancelike phenomenon and the emergence of global-scale cascading breakdown are discovered. We derive analytic theories to understand the mechanism of control at a quantitative level and articulate cost-effective control schemes to significantly suppress extreme events and the cascading process.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predicting and Controlling Complex Networks

Lai¹

2015

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“…The control of complex networks is of paramount importance in network science and engineering, which has received extensive attention in the past decade or so [1,2,3,4,5,6,7]. In control theory, the controllability property plays a pivotal role in many control problems.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is difficult to apply the traditional controllability theory directly to complex networks. Here, the first challenge faced is how to find the minimum set of driver nodes (i.e., drivers) needed to fully control the whole network [2], which is a computationally prohibitive task for large networks by the traditional Kalman's controllability rank condition [8,10]. In recent years, controllability has become a hot research topic in the field of complex networks [4,5,6,11,12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Analytical controllability of deterministic scale-free networks and Cayley trees

Wang

et al. 2015

Eur. Phys. J. B

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Abstract. According to the exact controllability theory, the controllability is investigated analytically for two typical types of self-similar bipartite networks, i.e., the classic deterministic scale-free networks and Cayley trees. Due to their self-similarity, the analytical results of the exact controllability are obtained, and the minimum sets of driver nodes (drivers) are also identified by elementary transformations on adjacency matrices. For these two types of undirected networks, no matter their links are unweighted or (nonzero) weighted, the controllability of networks and the configuration of drivers remain the same, showing a robustness to the link weights. These results have implications for the control of real networked systems with self-similarity.

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“…The concept of network controllability is well known in other fields such as biology [94] and structural design [95]. However, there are few controllability analyzes performed in power networks [96,97].…”

Section: Controllability Analysismentioning

confidence: 99%

Distribution system energy management through capacity constrained optimization

Uddin¹

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Due to the widespread installation of Distributed Energy Resources (DER) and Demand SideManagement resources (DSM) into Distribution Systems (DS), the usage pattern of the DS has changed remarkably in recent times. As a result, the DS has the potential to lead its network operational parameters, such as bus voltage profiles and line flows, outside of their allowable limits. Therefore, they increase the variability and range of variation of loads in the network. However, the DS generally are not designed for such conditions. Thus, it becomes necessary to reassess and redesign the network capacity. A standard strategy would be to increase the capacity of the network, however, this is costly. A cost-effective strategy could be to improve the management of such a system by improving the determination of its actual capacity. Recent advances in ICT equipment make it appear possible to manage the critical loading conditions instead of increasing capacity of the network. Thus, an energy management system is required to perform that function during critical loading. In this thesis, a framework for controlling a network-oriented autonomous energy management system on the distribution network using network capacity constrained is proposed.The framework is based on a State Estimation (SE) technique, which is able to determine the most probable system state of a network. Practically, the system's operational parameters may be unobservable due to measurement deficiency, loss of communication etc. In such a situation, the observability analysis needs to be performed on the available measurement data to investigate whether the operational parameters are observable or unobservable. Such an analysis is taken into account in this thesis.The proposed framework is akin to an Optimal Power Flow (OPF) problem, where SE gives a starting point to the simulation layer. The simulation layer supports the optimization under the network constraints. In this framework, the challenging task is to formulate the network constraints.To this end, a linearization based map is generated from the functional relationships between an arbitrary set of control variables and an extensive variety of constrainable operational parameters.This map permits the formulation of linear inequality constraints to build a flexible system to manage the network within existing capacity. The feasibility of the proposed constrained generation is demonstrated using an extensive variety of cost functions from a simple Linear Programming (LP) to non-linear functions like absolute value. The significant feature of this approach is that it is flexible both in terms of constrained parameters and control variables.Along with observability, controllability is another crucial factor regarding capacity constrained state optimization. The controllability analysis would allow the decision to be made of whether or not available control variables allow changing the value of operational parameters to specific values without other influences. With this in mind, a technique to a...

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Controllability analysis of networks

Cited by 125 publications

References 6 publications

Predicting and Controlling Complex Networks

Predicting and Controlling Complex Networks

Analytical controllability of deterministic scale-free networks and Cayley trees

Distribution system energy management through capacity constrained optimization

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