Meng Zhan (502424), Shuai Liu (145969), Zhiwei He (502425) · Figshare · 2015
<p>Control of by adding one node (<i>m</i> = 10) and connecting it to any one node (lower part) and any two nodes (higher part) in an ER network, the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082161#pone-0082161-g001" target="_blank">Figs. 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082161#pone-0082161-g002" target="_blank">2</a>, in contrast to the uncontrolled value of (dashed line).</p>
Cited by 0Open access
Soumya Banerjee, Soumen Roy · arXiv (Cornell University) · 2012
Liu et al recently proposed a minimum number of driver nodes needed to obtain full structural controllability over a directed network. Driver nodes are unmatched nodes, from which there are directed paths to all matched nodes. Their most important assertion is that a system's controllability is to a great extent encoded by the underlying network's degree distribution, $P(k_{in}, k_{out})$. Is the controllability of a network decided almost completely by the immediate neighbourhood of a node, while, even slightly distant nodes play no role at all? Motivated by the above question, in this communication, we argue that an effective understanding of controllability in directed networks can be reached using distance based measures of closeness centrality and betweenness centrality and may not require the knowledge of local connectivity measures like in-degree and out-degree.
Cited by 9Open access
Zhe‐Ming Lu, Xinfeng Li · PLoS ONE · 2016
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.
Cited by 63Open access
Yassine El Gantouh, Saïd Hadd, Abdelaziz Rhandi · Evolution equations and control theory · 2020
<p style='text-indent:20px;'>In this paper, the rich feedback theory of regular linear systems in the Salamon-Weiss sense as well as some advanced tools in semigroup theory are used to formulate and solve control problems for network systems. In fact, we derive necessary and sufficient conditions for approximate controllability of such systems. These criteria, in some particular cases, are given by the well-known Kalman's controllability rank condition.
Cited by 5Open access
Stocker, Julia Elina · OSF Preprints (OSF Preprints) · 2023
Cited by 0Open access
Cassiano O. Becker, Sérgio Pequito, George J. Pappas et al. · 2017
In this paper, we address the constrained design of continuous-time linear dynamics to improve system control performance, which can be measured as a function of the controllability Gramian. In contrast with the problem of deployment of actuation capabilities to achieve a specified control performance, we seek to change the dynamics of linear systems while considering the deployed actuation mechanisms. Specifically, we consider spectral properties of the `infinite' controllability Gramian as control performance metrics, and apply constrained (i.e., bounded) perturbations in the system's parameters while respecting its structure. We show that two different (yet related) re-design problems for control enhancement can be cast as bilinear or linear matrix equality problems. Lastly, we propose different strategies to obtain the solution of these problems, and assess their performance in the context of multi-agent networks in the leader-follower setup.
Cited by 12
Cassiano O. Becker, Sérgio Pequito, George J. Pappas et al. · IEEE Transactions on Control of Network Systems · 2020
In this article, we consider the problem of tuning the edge weights of a networked system described by linear time-invariant dynamics. We assume that the topology of the underlying network is fixed, and that the set of feasible edge weights is a given polytope. In this setting, we first consider a feasibility problem consisting of tuning the edge weights such that certain controllability properties are satisfied. The particular controllability properties under consideration are 1) a lower bound on the smallest eigenvalue of the controllability Gramian and 2) an upper bound on the trace of the Gramian inverse. In both cases, the edge-tuning problem can be stated as a feasibility problem involving bilinear matrix equalities, which we approach using a sequence of convex relaxations. Furthermore, we also address a design problem consisting of finding edge weights able to satisfy the aforementioned controllability constraints while seeking to minimize a cost function of the edge weights, which we assume to be convex. Finally, we verify our results with numerical simulations over a number of random network realizations, as well as with an IEEE 14-bus power system topology.
Cited by 0Open access
Cunlai Pu, Wenjiang Pei, Andrew Michaelson · Physica A Statistical Mechanics and its Applications · 2012
Cited by 125
Shimaossadat Mousavi, ءMohammad Haeri, Mehran Mesbahi · Repository for Publications and Research Data (ETH Zurich) · 2019
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this direction, we introduce a new construct referred to as a perfect graph associated with a network with a given set of control nodes. The tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are then derived. Moreover, we obtain a characterization of critical edge-sets, the maximal set of edges whose any subset can be respectively added to, or removed from a network, while preserving strong structural controllability. In addition, procedures for combining networks to obtain strongly structurally controllable network-of-networks are proposed. Finally, controllability conditions are proposed for networks whose edge weights, as well as their structures, can vary over time.
Cited by 6Open access
Márton Pósfai, Yang‐Yu Liu, Jean-Jacques Slotine et al. · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · 2012
A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks.
Cited by 0Open access
Peng Gang Sun, Robert E. Kooij, Zhidong He et al. · 2019
In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes needed to fully control networks, where links are removed according to both random and targeted attacks. Our approximations rely on the concept of critical links. A link is called critical if its removal increases the required number of driver nodes. We validate our approximation on both realworld and synthetic networks. For random attacks, the approximation is always very good, as long as the fraction of removed links is smaller than the fraction of critical links. For some cases, the approximation is still accurate for larger fractions of removed links. The approximation for an attack, where first the critical links are removed, is also accurate, as long as the fraction of removed links is sufficiently small. Finally, we show that the critical link attack is the most effective among 4 considered attacks, as long as the fraction of removed links is smaller than the fraction of critical links.
Cited by 12
Indika Rajapakse (317946), Mark Groudine (62412), Mehran Mesbahi (317948) · Figshare · 2015
<p>The process of cell differentiation as a dynamical system varies in degree of controllability, or receptivity to external signals at particular stages, where cells pass through an intermediate highly receptive and entropic state. S1 (state 1, stem/progenitor state), S2 (state 2, transition state), S3 (state 3, terminally differentiated state).</p>
Cited by 0Open access
Remy Ben Messaoud (20521877), Vincent Le Du (20521880), Camile Bousfiha (20521883) et al. · Figshare · 2025
<p>a) Toy network with <i>n</i> = 7 nodes. Its state <i>x</i> = [<i>x</i><sub>1</sub>,<i>x</i><sub>2</sub>,…,<i>x</i><sub><i>7</i></sub>] can be seen as a signal over a graph. By exploiting the Laplacian eigenvectors <i>V</i> = [<i>V</i><sub>1</sub>,<i>V</i><sub>2</sub>,…,<i>V</i><sub><i>7</i></sub>] of the network, the signal <i>x</i> can be embedded in a spectral space via the graph Fourier transform (<i>GFT</i>) . The resulting eigenstate measures how the signal is spatially distributed across different topological scales, from coarser () to finer-grained () ones. We can also define the inverse operation <i>iGFT </i> that is illustrated in this panel. b) Low-dimensional controllability in terms of linear-time invariant (LTI) network output control. Instead of focusing on the network state, the goal is to determine the input signal <i>u</i>(t) that steers a low-dimensional output given by the subset of the eigenstate , where the output matrix <i>C</i><sup><i>EIG</i></sup> <i>= H</i><sub><i>r</i></sub><i>V</i><sup><i>T</i></sup> is obtained by selecting and reordering a number <i>r</i> < <i>n</i> of spectral components via a filtering matrix <i>H</i><sub><i>r</i></sub>. In this example, the network has <i>n</i> = 7 nodes and the first <i>r</i> = 3 spectral components are selected and reordered arbitrarily. Here, the filtering matrix <i>H</i><sub><i>r</i></sub> is a 3×7 matrix whose elements are {<i>h</i><sub>1,2</sub>} = {<i>h</i><sub>2,1</sub>} = {<i>h</i><sub>3,7</sub>} = 1 and zero elsewhere.</p>
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Liam Chung, Derek Ruths, Justin Ruths · Scientific Reports · 2021
Cited by 3Open access
Márton Pósfai, Yang-Yu Liu, Jean-Jacques Slotine et al. · Scientific Reports · 2013
A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks.
Cited by 202Open access
Manikya Valli Srighakollapu, Rachel Kalpana Kalaimani, Ramkrishna Pasumarthy · Systems & Control Letters · 2021
Cited by 4
Philip Solimine · Understanding complex systems · 2021
Cited by 4
Yang‐Yu Liu, Márton Pósfai, Jean-Jacques Slotine et al. · DSpace@MIT (Massachusetts Institute of Technology) · 2012
A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but the symmetries of the underlying matching problem can produce linear, quadratic or no dependence on degree correlation coefficients, depending on the nature of the underlying correlations. The results are supported by numerical simulations and help narrow the observed gap between the predicted and the observed number of driver nodes in real networks.
Cited by 172Open access
R. B. Tyan, V. Ya. Potemkin, S. V. Saponchik · Journal of Mining Science · 1974
Cited by 0
Huili Sun, Takuya Toyonaga, Saloni Mehta et al. · bioRxiv (Cold Spring Harbor Laboratory) · 2025
White matter undergoes rapid changes during the fetal period that are foundational for future cognitive functions. However, how these changes contribute to the brain's capacity to support its dynamic activities-its <i>controllability</i> -remains largely unknown. Here, we apply network control theory (NCT) to investigate the developmental trajectory of controllability from the second trimester through the first postnatal month. We analyzed structural connectivity data from fetuses and infants as part of the developing Human Connectome Project. We identified a robust, nonlinear U-shaped developmental curve of whole-brain controllability across the perinatal period, with a minimum at approximately 35 weeks of gestation. Preterm birth disrupted these trajectories, leading to greater controllability and earlier minimums compared to age-matched fetuses. Using gene expression microarray data from 18 fetal post-mortem brains, we identified genes implicated in synaptic functions that co-develop with changes in controllability during the fetal period. We then used positron emission tomography in seven pregnant rhesus macaques to quantify changes in fetal synaptic density. Increased synaptic density in non-human primates (NHPs) co-occurred with periods of reduced controllability in humans. Finally, using longitudinal scans of a pregnant woman, we mapped the trajectory of changes in maternal controllability during pregnancy. This trajectory exhibited a U-shaped pattern that inversely correlated with the fetal trajectory, reaching a maximum around 36 weeks. Together, fetal controllability follows a nonlinear trajectory that co-develops with synaptic functions and synchronizes with maternal changes in controllability during pregnancy.
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