By Marzieh Nabi-Abdolyousefi

This interdisciplinary thesis includes the layout and research of coordination algorithms on networks, id of dynamic networks and estimation on networks with random geometries with implications for networks that aid the operation of dynamic structures, e.g., formations of robot autos, allotted estimation through sensor networks. the implications have ramifications for fault detection and isolation of large-scale networked structures and optimization versions and algorithms for subsequent new release airplane strength structures. the writer reveals novel purposes of the technique in strength platforms, corresponding to residential and commercial clever power administration systems.

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Dm−1 = 1, dm = rm − m + 1 i =1 while i = 0 do if {d1 , d2 , . . , dr˜ } ≥ {L 1 , L 2 , . . , L r˜ } and 1 ≤ di ≤ n − 1, ∀i then output {d1 , d2 , . . , dm } end i =m−1 while dm − di < 2 do i =i −1 end if i = 0 then for j = m − 1 to i by -1 do d j = di + 1 end end dm = s − m−1 j=1 d j end Although the algorithm above leads to a possible degree sequence for the underlying graph—consistent with the identification procedure—we need an additional set of conditions for ensuring that the obtained sequence in fact corresponds to that of a graph.

The proposed identification process is facilitated by introducing “ports” for stimulating a subset of network vertices via an appropriately defined interface and observing the network’s response at another set of vertices. 1) where A(G) = −L w (G) ∈ Rn×n , B ∈ Rn×rI , and C ∈ RrO ×n . 1. Consider the network in Fig. 1; set I = {1, 2}, O = {1, 4}, and the corresponding weights equal to one on every edge. Then, ⎡ 1 ⎢ −1 ⎢ A(G) = − ⎢ ⎢ 0 ⎣ 0 0 −1 3 −1 −1 0 0 −1 3 −1 −1 0 −1 −1 3 −1 ⎡ ⎤ ⎤ 10 0 ⎢0 1⎥ 0 ⎥ ⎢ ⎥ ⎥ 10000 ⎥ ⎥ −1 ⎥ , B = ⎢ ⎢0 0⎥, C = 0 0 0 1 0 .

14), is the state transition matrix for the Markov chain associated with the consensus protocol [1] (Chap. 3). 3 Characterization of the Network Topology via Node Knockout (a) 27 (b) (c) Fig. 2 a Graph G , b grounding the consensus protocol, and c the graph considered for the example {1} {2} In the same manner φG (s) = φG (s). As we ground node 2, two disconnected components will be generated, and the input and output nodes must be chosen from {2} {3} these distinct components of the graph. We therefore determine φG (s) and φG (s) {2} {3} {2} as φG (s) = s 3 + 4s 2 + 4s + 1 and φG (s) = φG (s).

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