Selection of optimal set of driver nodes based on networked sensitivity in complex networked systems

doi:10.1109/INDIANCC.2017.7846497

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Selection of optimal set of driver nodes based on networked sensitivity in complex networked systems

Proceedings Article•DOI•

Selection of optimal set of driver nodes based on networked sensitivity in complex networked systems

Ram Niwash Mahia¹, Deepak Fulwani¹•Institutions (1)

Indian Institute of Technology, Jodhpur¹

01 Jan 2017-pp 332-337

TL;DR: This paper develops an algorithm to select the optimal set of driver nodes corresponding to minimum networked sensitivity w.r.t. maximum DC-Gain and a range of frequency.

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Abstract: In this paper, we investigate the correlation between optimal set of driver nodes and networked sensitivity of Complex Networked Systems (CNS). Here, we study the networked sensitivity between a pair of control and output nodes for interconnected directed and undirected networks. We investigate the importance of the optimal driver nodes based on new index of the networked control system, which is networked sensitivity in the networked system. In this paper, we discuss to select the optimal set of driver nodes corresponding to minimum networked sensitivity w.r.t. (i) maximum DC-Gain and (ii) a range of frequency. In particular, we develop an algorithm to select the optimal set of driver nodes which has minimum networked sensitivity. Finally, we validate theoretical results with the help of network examples.

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Book•

Algebraic Graph Theory

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Chris Godsil, Gordon F. Royle

01 Jan 2009

TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.

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Abstract: Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.

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8,307 citations

"Selection of optimal set of driver ..." refers background in this paper

...In this section we review the basic concepts in algebraic graph theory [21], and describe the modeling of complex networked systems....
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Journal Article•DOI•

Controllability of complex networks

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Yang Liu¹, Jean-Jacques E. Slotine², Albert-László Barabási³, Albert-László Barabási⁴, Albert-László Barabási¹ - Show less +1 more•Institutions (4)

Northeastern University¹, Massachusetts Institute of Technology², Harvard University³, Brigham and Women's Hospital⁴

12 May 2011-Nature

TL;DR: In this article, the authors developed analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics.

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Abstract: The ultimate proof of our understanding of natural or technological systems is reflected in our ability to control them. Although control theory offers mathematical tools for steering engineered and natural systems towards a desired state, a framework to control complex self-organized systems is lacking. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but that dense and homogeneous networks can be controlled using a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the high-degree nodes.

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2,889 citations

Book•

Network analysis and feedback amplifier design

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H. W. Bode

01 Jan 1945

2,469 citations

Additional excerpts

...described the sensitivity transfer function in terms of the Bode Integral formula [12], Doyle et al....
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Journal Article•DOI•

Multivariable feedback design: Concepts for a classical/modern synthesis

[...]

John Doyle¹, Gunter Stein²•Institutions (2)

Honeywell¹, Massachusetts Institute of Technology²

01 Feb 1981-IEEE Transactions on Automatic Control

TL;DR: This paper presents a practical design perspective on multivariable feedback control problems and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases.

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Abstract: This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results.

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2,272 citations

"Selection of optimal set of driver ..." refers background in this paper

...The networked sensitivity transfer function of the networked system (1) is defined as Definition 1: The networked sensitivity transfer function (denoted by NS(s)) [13], [14] is the ratio of the percentage change in network output variable value N(s) to the percentage change in parameter variation of element D(s) (such as DC-Gain or feedback gain), then the networked sensitivity transfer function is expressed as...
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...explained the multivariable feedback systems with some practical applications [13] and later, Reinschke et al....
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Book•

Topics in Mathematical System Theory

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R. E. Kalman, P. L Falb, Michael A. Arbib

01 Jan 1969

1,203 citations

"Selection of optimal set of driver ..." refers background or methods in this paper

...When the open loop DC-Gain is large, then the closed loop DC-Gain is nearly equal to 1 [1]....
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...This implies that the networked sensitivity becomes small [1]....
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...Therefore, the problem to control the complex networked systems has been vastly studied using tools from the control theory [1] and the graph theory [2]....
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...So, we define the transfer function (TF) of the networked system as the ratio of the Laplace transform of the output observed from node o (or observable node o) to the Laplace transform of the input applied to node c (or control node c) under the assumption that the initial condition of the networked system is zero [1]....
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