By Yuanqing Xia, Mengyin Fu, Guo-Ping Liu
Analysis and Synthesis of Networked keep an eye on structures specializes in crucial features of this box, together with quantization over networks, information fusion over networks, predictive keep an eye on over networks and fault detection over networks. The networked keep an eye on platforms have ended in a whole new variety of real-world functions. lately, the ideas of net of items are constructed speedily, the study of networked keep an eye on platforms performs a key function in web of items. The ebook is self-contained, offering adequate mathematical foundations for realizing the contents of every bankruptcy. will probably 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 know-how, has been engaged on keep an eye on idea and its purposes for over ten years.
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Additional info for Analysis and Synthesis of Networked Control Systems
12). 16) where m ∈ Z. 17). 3. 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.
5 0 10 20 30 40 50 60 70 80 k Fig. 01. P (k), increases (see Fig. 15). While L = 1000, the norm of covariance of estimated error, P (k), increases remarkably (see Fig. 18). It is worth to say that even if L is very large, for example L = 1000, the states of system are bounded although the bound is very large. 01, the error induced by quantization is small, and it is helpful to decrease the bound of estimated state x ˆ(k|k) after quantizing. If L increases, however, the decoder performs is not so well.
15 Norm of estimated error covariance when L=1. 5 Numerical Example 33 8000 x1 with quantized control x1 with conventional control 6000 4000 2000 x 1 0 −2000 −4000 −6000 −8000 −10000 0 10 20 30 40 50 60 70 80 90 100 k Fig. 16 x1 with quantized control when L=1000. 5000 x with quantized control 2 x2 with conventional control 4000 3000 2000 x 2 1000 0 −1000 −2000 −3000 −4000 −5000 0 10 20 30 40 50 60 k Fig. 17 x2 with quantized control when L=1000. 70 80 90 100 34 2 Stability Analysis of Quantized Systems over Networks 6 7 x 10 Norm of Estimated Error Covariance 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 k Fig.
Analysis and Synthesis of Networked Control Systems by Yuanqing Xia, Mengyin Fu, Guo-Ping Liu