Target control and source estimation metrics for dynamical networks

Vosughi, Amirkhosro; Johnson, Charles A.; Xue, Mengran; Roy, Sandip; Warnick, Sean

doi:10.1016/j.automatica.2018.11.054

Cited by 23 publications

(19 citation statements)

References 10 publications

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“…Our focus here is to develop structural and graph-theoretic results on the Gramian of the network model, with the aim of giving insights into target control. Because a number of graph-theoretic results have already been developed for the binary question of target controllability [10][11][12], we will primarily focus on the target-control metrics.…”

Section: Resultsmentioning

confidence: 99%

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Controllability-Gramian Submatrices for a Network Consensus Model

Roy

Xue

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Principal submatrices of the controllability Gramian and their inverses are examined, for a networkconsensus model with inputs at a subset of network nodes. Specifically, several properties of the Gramian submatrices and their inverses -including dominant eigenvalues and eigenvectors, diagonal entries, and sign patterns -are characterized by exploiting the special doubly-nonnegative structure of the matrices.In addition, majorizations for these properties are obtained in terms of cutsets in the network's graph, based on the diffusive form of the model. The asymptotic (long time horizon) structure of the controllability Gramian is also analyzed. The results on the Gramian are used to study metrics for target control of the network-consensus model.

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Section: Resultsmentioning

confidence: 99%

“…Because of the relevance of Gramian matrices to network controllability as well as dual observability/estimation problems, some structural and graph-theoretic results on the full Gramian have been developed for canonical network-consensus models, as well as for other dynamical network processes [9,11,16,17,20].…”

mentioning

confidence: 99%

Controllability-Gramian Submatrices for a Network Consensus Model

Roy

Xue

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

Self Cite

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“…A nonnegative symmetric positive-definite matrix is sometimes referred to as being doubly nonnegative [42]. Such matrices arise in a variety of applications ranging from control systems and network analysis to estimation and optimization [2,24,25,37,43], and characterizations of their inverses have been long-studied [11,12,28].…”

Section: The Rga and Its Inversementioning

confidence: 99%

On Radically Expanding the Landscape of Potential Applications for Automated-Proof Methods

Uhlmann

Wang

2021

SN COMPUT. SCI.

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In this paper, we examine the potential of optimization-based computer-assisted proof methods to be applied much more widely than commonly recognized by engineers and computer scientists. More specifically, we contend that there are vast opportunities to derive valuable mathematical results and properties that may be narrow in scope, such as in highly specialized engineering control applications, that are presently overlooked, because they have characteristics atypical of those that are conventionally studied in the areas of pure and applied mathematics. As a concrete example, we demonstrate use of sumof-squares (SOS) optimization for certifying polynomial nonnegativity as a part of a proposed dimension-pinning strategy to prove that the inverse of the relative gain array (RGA) of a d-dimensional positive-definite matrix is doubly stochastic for d ≤ 4 . However, it is not specifically this result and solution method that are of principal interest in this paper but rather how they illustrate the relevance of optimization-based proof techniques to engineering system design more broadly. We believe that our paper is the first to explicitly emphasize the fundamental distinction between methods that can be applied to prove results/properties over a fixed number of dimensions versus those that hold generally. The latter class of problems is the conventional domain of mathematicians, but the former is what we propose to be a fertile and largely unrecognized class of problems that are amenable to automated-proof technologies, e.g., as we demonstrate using our novel dimensionpinning approach.

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“…Target controllability is an NP-hard problem 14 ; it means that this is at least, as hard as the hardest problems in NP-problem (Non-deterministic Polynomial-time) problem. and many algorithms have been developed to improve its outcomes 15 – 20 . In target controllability, the placement of the non-target nodes in the control signals' pathway can have some side effects on many applications.…”

Section: Introductionmentioning

confidence: 99%

Nodes with the highest control power play an important role at the final level of cooperation in directed networks

Ebrahimi

Yousefi

Shahbazi

et al. 2021

Sci Rep

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Controllability of complex networks aims to seek the lowest number of nodes (the driver nodes) that can control all the nodes by receiving the input signals. The concept of control centrality is used to determine the power of each node to control the network. The more a node controls the nodes through connections in the network, the more it has the power to control. Although the cooperative and free-rider strategies and the final level of cooperation in a population are considered and studied in the public goods game. However, it is yet to determine a solution to indicate the effectiveness of each member in changing the strategies of the other members. In a network, the choice of nodes effective in changing the other nodes’ strategies, as free-riders, will lead to lower cooperation and vice versa. This paper uses simulated and real networks to investigate that the nodes with the highest control power are more effective than the hubs, local, and random nodes in changing the strategies of the other nodes and the final level of cooperation. Results indicate that the nodes with the highest control power as free-riders, compared to the other sets being under consideration, can lead to a lower level of cooperation and are, therefore, more effective in changing the strategies of the other nodes. The obtained results can be considered in the treatment of cancer. So that, destroying the tumoral cells with the highest control power should be a priority as these cells have a higher capability to change the strategies of the other cells from cooperators to free-riders (healthy to tumoral).

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Target control and source estimation metrics for dynamical networks

Cited by 23 publications

References 10 publications

Controllability-Gramian Submatrices for a Network Consensus Model

Controllability-Gramian Submatrices for a Network Consensus Model

On Radically Expanding the Landscape of Potential Applications for Automated-Proof Methods

Nodes with the highest control power play an important role at the final level of cooperation in directed networks

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