On the structural controllability of networks of linear systems

Blackhall, Lachlan; Hill, David J.

doi:10.3182/20100913-2-fr-4014.00079

Cited by 33 publications

(22 citation statements)

References 9 publications

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“…Previous studies based on the structural control theory shed some light on how to determine the upper bound of the minimum number of driver nodes for target controllability 35 36 . We can use the maximum matching method to find the minimum set of driver nodes ( N D nodes) for full control of the network ( Fig.…”

Section: Resultsmentioning

confidence: 99%

Target control of complex networks

et al. 2014

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Controlling large natural and technological networks is an outstanding challenge. It is typically neither feasible nor necessary to control the entire network, prompting us to explore target control: the efficient control of a preselected subset of nodes. We show that the structural controllability approach used for full control overestimates the minimum number of driver nodes needed for target control. Here we develop an alternate ‘k-walk’ theory for directed tree networks, and we rigorously prove that one node can control a set of target nodes if the path length to each target node is unique. For more general cases, we develop a greedy algorithm to approximate the minimum set of driver nodes sufficient for target control. We find that degree heterogeneous networks are target controllable with higher efficiency than homogeneous networks and that the structure of many real-world networks are suitable for efficient target control.

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Section: Resultsmentioning

confidence: 99%

Target control of complex networks

et al. 2014

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“…This theory, although thoroughly investigated since the 70’s, e.g. in the works of Kalman 76 , Lin 77 , Murota 78 , etc., has recently received a new boost of attention 23 , 25 , 79 , 80 , partly due to recent results on efficient algorithms for core research problems within this framework.…”

Section: Methodsmentioning

confidence: 99%

Controlling Directed Protein Interaction Networks in Cancer

Kanhaiya

Czeizler

Gratie

et al. 2017

Sci Rep

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Control theory is a well-established approach in network science, with applications in bio-medicine and cancer research. We build on recent results for structural controllability of directed networks, which identifies a set of driver nodes able to control an a-priori defined part of the network. We develop a novel and efficient approach for the (targeted) structural controllability of cancer networks and demonstrate it for the analysis of breast, pancreatic, and ovarian cancer. We build in each case a protein-protein interaction network and focus on the survivability-essential proteins specific to each cancer type. We show that these essential proteins are efficiently controllable from a relatively small computable set of driver nodes. Moreover, we adjust the method to find the driver nodes among FDA-approved drug-target nodes. We find that, while many of the drugs acting on the driver nodes are part of known cancer therapies, some of them are not used for the cancer types analyzed here; some drug-target driver nodes identified by our algorithms are not known to be used in any cancer therapy. Overall we show that a better understanding of the control dynamics of cancer through computational modelling can pave the way for new efficient therapeutic approaches and personalized medicine.

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“…. This observation incidentally shows that the condition of Theorem 12 in[43] is not necessary, because the nodes corresponding with the target set {x 3 , x 4 } do not belong to a cactus in the graph.…”

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confidence: 97%

Functional Target Controllability of Networks: Structural Properties and Efficient Algorithms

Commault

Woude

Frasca

2020

IEEE Trans. Netw. Sci. Eng.

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In this paper we consider the problem of controlling a limited number of target nodes of a network. Equivalently, we can see this problem as controlling the target variables of a structured system, where the state variables of the system are associated to the nodes of the network. We deal with this problem from a different point of view as compared to most recent literature. Indeed, instead of considering controllability in the Kalman sense, that is, as the ability to drive the target states to a desired value, we consider the stronger requirement of driving the target variables as time functions. The latter notion is called functional target controllability. We think that restricting the controllability requirement to a limited set of important variables justifies using a more accurate notion of controllability for these variables. Remarkably, the notion of functional controllability allows formulating very simple graphical conditions for target controllability in the spirit of the structural approach to controllability. The functional approach enables us, moreover, to determine the smallest set of steering nodes that need to be actuated to ensure target controllability, where these steering nodes are constrained to belong to a given set. We show that such a smallest set can be found in polynomial time. We are also able to classify the possible actuated variables in terms of their importance with respect to the functional target controllability problem.

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On the structural controllability of networks of linear systems

Cited by 33 publications

References 9 publications

Target control of complex networks

Target control of complex networks

Controlling Directed Protein Interaction Networks in Cancer

Functional Target Controllability of Networks: Structural Properties and Efficient Algorithms

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