By Alexey S. Matveev
This publication provides a scientific conception of estimation and keep watch over over conversation networks. It develops a conception that makes use of communications, keep an eye on, info and dynamical platforms idea stimulated and utilized to complicated networking situations. The ebook establishes theoretically wealthy and essentially very important connections between smooth keep watch over idea, Shannon details concept, and entropy idea of dynamical platforms originated within the paintings of Kolmogorov. This self-contained monograph covers the most recent achievements within the sector. It includes many real-world purposes and the presentation is obtainable.
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Additional info for Estimation and Control over Communication Networks (Control Engineering)
K. If at least one finite (k, ǫ)−spanning set exists, then q(k, ǫ) denotes the least cardinality of any (k, ǫ)−spanning set. If a finite (k, ǫ)−spanning set does not exist, then q(k, ǫ) := ∞. 1). 3. 1). 4. Notice that the topological entropy may be equal to infinity. In the case of a system without uncertainty with continuous F (·, ·) and compact X, the topological entropy is always finite . 5. , p. 20 of ). In the case of a continuous system without uncertainty, both definitions are equivalent .
2. The concluding Sect. 9 comments on an important assumption adopted in this chapter. 2 Example We first illustrate the class of problems to be studied by an example. We consider a platoon composed of k vehicles moving along a line and enumerated from right to left. The dynamics of the platoon are uncoupled, and the vehicles are described by the equations x˙ i = vi , v˙ i = ui , i = 1, . . 1) where xi is the position of the ith vehicle, vi is its velocity, and ui is the control input. Each vehicle is equipped with a sensor giving the distance yi = xi − xi−1 from it to the preceding one for i ≥ 2 and the position y1 = x1 for i = 1.
7. 2. 1). We prove that H = H(A). First prove that if α > H(A), then H ≤ α. 3 with β = 0 immediately implies the existence of an (k, ǫ)−spanning set of cardinality N where k1 log2 (N ) ≤ α for any ǫ > 0 and all large enough k. 3 of the topological entropy implies that H ≤ α. Since α is any number that is greater than H(A), we have proved that H ≤ H(A). Now we prove by contradiction that H ≥ H(A). Indeed, assume that this is not true and H < H(A). This inequality can hold only for positive H(A).
Estimation and Control over Communication Networks (Control Engineering) by Alexey S. Matveev