Analysis and Synthesis of Networked Control Systems by Yuanqing Xia, Mengyin Fu, Guo-Ping Liu

By Yuanqing Xia, Mengyin Fu, Guo-Ping Liu

Analysis and Synthesis of Networked keep an eye on platforms specializes in crucial features of this box, together with quantization over networks, info fusion over networks, predictive keep an eye on over networks and fault detection over networks. The networked regulate platforms have ended in a whole new diversity of real-world functions. lately, the options of net of items are constructed quickly, the study of networked regulate platforms performs a key function in web of items. The ebook is self-contained, supplying enough mathematical foundations for realizing the contents of every bankruptcy. it is going to be of important curiosity to scientists and engineers engaged within the box of Networked keep an eye on Systems.

Dr. Yuanqing Xia, a professor at Beijing Institute of expertise, has been engaged on keep watch over idea and its functions for over ten years.

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1) is said to be stable, if lim x k→∞ constant M > 0 such that P (k) 2 < M. 4 2 Stability Analysis of Quantized Systems over Networks Stability Analysis In this section, a quantization control strategy is given based on quantization strategy presented in previous section and the stability of system is discussed. 20) −D ◦ Q(ˆ x(k|k))) + ω(k) = (A + BK)x(k) − BK(x(k) − xˆ(k|k)) − BKs(k) + ω(k) where s(k) = x ˆ(k|k) − D ◦ Q(ˆ x(k|k)). 19). The inequality s(k) 2 ≤ nL/2 can be obtained by the former quantization strategy.

55) Here, the quantizer is selected as qμ (xi (k)) = 3μ(k)sgn{xi (k)}, if |xi (k)| > 3μ(k), xi (k) + 12 μ(k) , if |xi (k)| ≤ 3μ(k). 56) where xi (k) is the ith component of x(k) and sgn{xi (k)} is a symbolic function. 5. 6660 < 1. Let initial state x(0) = [7 8 7]T and μ(k) = A k , it is obvious that x(0) is saturate, that is, |x(0)| > M μ(0). 19) can be shown as Fig. 4. 5 5 Fig. 4 The selection of k0 . (P ) In Fig. 19). Then based on “zoom” strategy, μ(k) can be shown as Fig. 5 according to k0 = 3 and τ = 1.

5 µ(k) in “zoom” strategy. 8 7 6 E{|x(k)|2} 5 4 3 2 1 0 0 10 20 k Fig. 6 The mean square of x(k). 13. Note that when u(k) = θ(k)Kqμ (ϕ(k)x(k)), the states of closedloop will be influenced by random variable θ(k), then the states trajectory will be random. Therefore, the k0 selected is random and μ(k) must be adjusted according to k0 . 14. If the initial state is selected as x(0) = [1 2 1]T , then based on Fig. 7, k0 is selected as 1 and the “zooming-out” strategy can be omitted. 5 5 Fig. 7 The selection of k0 .

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