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By Alexey S. Matveev

ISBN-10: 0817644946

ISBN-13: 9780817644949

ISBN-10: 0817646078

ISBN-13: 9780817646073

This booklet provides a scientific idea of estimation and keep watch over over communique networks. It develops a thought that makes use of communications, keep an eye on, info and dynamical structures conception encouraged and utilized to complicated networking eventualities. The booklet establishes theoretically wealthy and virtually very important connections between sleek regulate thought, Shannon details conception, and entropy thought of dynamical platforms originated within the paintings of Kolmogorov.

This self-contained monograph covers the most recent achievements within the quarter. It comprises many real-world purposes and the presentation is accessible.

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Extra info for Estimation and Control over Communication Networks

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J [θ, e(θ)] ≤ t} . The main question to be considered is what is the minimum rate of the information exchange in the system for which stabilization is possible? In other words, we look for necessary and sufficient conditions for stabilizability expressed in terms of the channels transmission capacities c1 , . . , ck , along with the plant-sensors parameters A, B, Cj . Roughly speaking, such a capacity is the average number of bits transmitted over the channel during the sample period, despite the losses and delays.

A regime of the channel operation {τj (·)} compatible with these data is said to be possible. 3 For a given regime of the channel operation. 2. ) In this subsection, Nj denotes the size of the jth channel alphabet Ej . Noiseless instantaneous channel. The channel is constantly accessible; any transmission is successful and instantaneous. Then b− j (r) = ⌊(r + 1) · log2 Nj ⌋, b+ j (r) = ⌈(r + 1) · log2 Nj ⌉, cj = log2 Nj . 4. , ⌊a⌋ := max{k = 0, ±1, ±2, . . : k ≤ a}, ⌈a⌉ := min{k = 0, ±1, ±2, .

K. 2) Here x(t) ∈ Rn is the state; u(t) ∈ Rnu is the control; and yj (t) ∈ Rny,j is the output of the jth sensor. The system is unstable: There is an eigenvalue λ of the t→∞ matrix A with |λ| ≥ 1. The objective is to stabilize the plant: x(t) −−−→ 0. We consider a remote control setup. Each sensor is served by its own communication channel capable of transmitting signals from a finite alphabet Ej . Over this channel, the jth coder sends a message ej (t) ∈ Ej based on the prior measurements ej (t) = Ej [t, yj (0), .

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Estimation and Control over Communication Networks by Alexey S. Matveev


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