Abstract
In this paper, we consider the H ∞ filtering problem for linear systems using quantized measurements. The communication channel we consider consists of two cases: the ideal one and the unreliable one. For the ideal channel, we designed a filter to mitigate the quantization effects, which ensured not only the asymptotical stability but also a prescribed H ∞ filtering performance. For the unreliable channel, we introduced the stochastic variable satisfying Bernoulli random binary distribution to model the lossy measurements. We also designed a filter to cope with the losses and mitigate quantization effects simultaneously which ensured not only stochastic stability, but also a prescribed H ∞ filtering performance. Furthermore, we derive sufficient conditions for the existence of the above filters. Finally, a numerical example is given to illustrate that the proposed approach is effective and feasible.
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References
D. Delchamps, Controlling the flow of information in feedback systems with quantized measurements, in Proc. IEEE Conf. Deris. Control, Tampa, USA (1989), pp. 2355–2360
D. Delchamps, Extracting state information from a quantized output record. Syst. Control Lett. 13, 365–372 (1989)
H. Dong, Z. Wang, H. Gao, H ∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links. Signal Process. 89(8), 1567–1575 (2009)
N. Elia, K. Mitter, Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)
M. Fu, C. de Souza, State estimation using quantized measurements, IFAC World Congress, Seoul, Korea (2008), 12492–12497
M. Fu, L. Xie, The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1698–1711 (2005)
H. Gao, T. Chen, A new approach to quantized feedback control systems. Automatica 44(2), 534–542 (2008)
X. Gao, Z. Wang, D. Luo, Controllability and observability of quantitative networked control systems. J. Lanzhou Univ. Technol. 34(7), 88–90 (2008)
H. Gao, Y. Zhao, J. Lam, K. Chen, H ∞ Fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Trans. Fuzzy Syst. 17(2), 291–300 (2009)
R. Gray, D. Neuhoff, Quantization. IEEE Trans. Inf. Theory 44(6), 2325–2383 (1998)
C. Han, H. Zhang, Linear optimal filtering for discrete-time systems with random jump delays. Signal Process. 89(6), 1121–1128 (2009)
J. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)
R. Kalman, Nonlinear aspects of sampled-data control systems, in Proc. Symp. Nonlinear Circ. Theory, 7, Brooklyn (1956)
J. Klamka, Controllability of Dynamical Systems (Kluwer Academic, Dordrecht, 1991)
D. Liberzon, J. Hespanha, Stabilization of nonlinear systems with limited information feedback. IEEE Trans. Autom. Control 50(6), 910–915 (2005)
R. Lu, H. Su, J. Su, S. Zhou, M. Fu, Reduced-order H ∞ filtering for discrete-time singular systems with lossy measurements. IET Control Theory Appl. 4(1), 151–163 (2010)
L. Meier, Estimation and control with quantized measurements. IEEE Trans. Autom. Control 16(5), 523–524 (1971)
R. Miller, A. Michel, J. Farrel, Quantizer effects on steady state error specifications of digital control systems. IEEE Trans. Autom. Control 34(6), 651–654 (1989)
L. Montestruque, P. Antsaklis, On the model-based control of networked systems. Automatica 39(10), 1837–1843 (2003)
A. Packard, J. Doyle, The complex structured singular value. Automatica 29(1), 71–109 (1993)
C. Peng, Y. Tian, Networked H ∞ control of linear systems with state quantization. Inf. Sci. 177(24), 5763–5774 (2007)
L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, S. Sastry, Foundations of control and estimation over lossy networks. Proc. IEEE 95(1), 163–187 (2007)
P. Seiler, R. Sengupta, Analysis of communication losses in vehicle control problems, in Proc. Am. Control Conf., Arlington, USA (2001), pp. 1491–1496
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan, S. Sastry, Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49(9), 1453–1464 (2004)
H. Song, L. Yu, W. Zhang, H ∞ filtering of network-based systems with random delay. Signal Process. 89, 615–622 (2009)
S. Sun, Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts. Signal Process. 89, 1457–1466 (2009)
E. Tian, D. Yue, C. Peng, Quantized output feedback control for networked control systems. Inf. Sci. 178, 2734–2749 (2008)
Z. Wang, F. Yang, W. Daniel, X. Liu, Robust H ∞ control for networked systems with random packet. IEEE Trans. Syst. Man Cybern. 37(4), 916–924 (2007)
B. Widrow, I. Kollar, M. Liu, Statistical theory of quantization. IEEE Trans. Autom. Control 45, 353–361 (1996)
L. Xie, Output feedback H ∞ control of systems with parameter uncertainty. Int. J. Control 63(4), 741–750 (1996)
F. Yang, Z. Wang, Y. Hung, M. Gani, H ∞ control for networked systems with random communication delays. IEEE Trans. Autom. Control 51(3), 511–518 (2006)
J. Zheng, M. Fu, A reset state estimator for linear systems to suppress sensor quantization effects, in IFAC World Congress, Seoul, Korea (2008), pp. 9254–9259
S. Zhou, G. Feng, H ∞ filtering for discrete-time systems with randomly varying sensor delays. Automatica 44, 1918–1922 (2008)
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Lu, R., Li, H., Xue, A. et al. Quantized H ∞ Filtering for Different Communication Channels. Circuits Syst Signal Process 31, 501–519 (2012). https://doi.org/10.1007/s00034-011-9323-8
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DOI: https://doi.org/10.1007/s00034-011-9323-8