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Probability-guaranteed \(H_\infty\) finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations. (English) Zbl 1250.93121

Summary: In this paper, the probability-guaranteed \(H_{\infty }\) finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed \(H_{\infty }\) performance requirement can be guaranteed with probability constraint. By using the Difference Linear Matrix Inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions of a set of DLMIs that can be recursively solved by using the semi-definite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed \(H_{\infty }\) finite-horizon filtering problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

MSC:

93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
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[1] Shi, P.; Boukas, E. K.; Agarwal, R. K., Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE Trans. Automat. Control, 44, 8, 1592-1597 (1999) · Zbl 0986.93066
[2] Kallapur, A. G.; Petersen, I. R.; Anavatti, S. G., A discrete-time robust extended Kalman filter for uncertain systems with sum quadratic constraints, IEEE Trans. Automat. Control, 54, 4, 850-854 (2009) · Zbl 1367.93648
[3] Yoon, M. G.; Ugrinovskii, V. A.; Petersen, I. R., Robust finite horizon minimax filtering for discrete-time stochastic uncertain systems, Systems Control Lett., 52, 2, 99-112 (2004) · Zbl 1157.93531
[4] Fridman, E.; Shaked, U., An improved delay-dependent \(H_\infty\) filtering of linear neutral systems, IEEE Trans. Signal Process., 52, 3, 668-673 (2004) · Zbl 1369.93623
[5] Nguang, S. K.; Shi, P., Delay-dependent \(H_\infty\) filtering for uncertain time delay nonlinear systems: an LMI approach, IET Control Theory Appl., 1, 1, 133-140 (2007)
[6] Wu, L.; Ho, D. W.C., Fuzzy filter design for Itô stochastic systems with application to sensor fault detection, IEEE Trans. Fuzzy Syst., 17, 1, 233-242 (2009)
[7] Yue, D.; Han, Q., Robust \(H_\infty\) filter design of uncertain descriptor systems with discrete and distributed delays, IEEE Trans. Signal Process., 52, 11, 3200-3212 (2004) · Zbl 1370.93111
[8] Bolzern, P.; Colaneri, P.; Nicolao, G. D., On discrete-time \(H_\infty\) fixed-lag smoothing, IEEE Trans. Signal Process., 52, 1, 132-141 (2004) · Zbl 1369.93677
[9] Ishihara, J. Y.; Terra, M. H.; Espinoza, B. M., \(H_\infty\) filtering for rectangular discrete-time descriptor systems, Automatica, 45, 7, 1743-1748 (2009) · Zbl 1184.93112
[10] Zhang, H.; Feng, G.; Duan, G.; Lu, X., \(H_\infty\) filtering for multiple-time-delay measurements, IEEE Trans. Signal Process., 54, 5, 1681-1688 (2006) · Zbl 1373.94749
[11] Cao, Y.; Lin, Z.; Chen, Ben M., An output feedback \(H_\infty\) controller design for linear systems subject to sensor nonlinearities, IEEE Trans. Circuits Systems I, 50, 7, 914-921 (2003) · Zbl 1368.93145
[12] Niu, Y.; Ho, D. W.C.; Li, C., Filtering for discrete fuzzy stochastic systems with sensor nonlinearities, IEEE Trans. Fuzzy Syst., 18, 5, 971-978 (2010)
[13] Yang, F.; Li, Y., Set-membership filtering for systems with sensor saturation, Automatica, 45, 8, 1896-1902 (2009) · Zbl 1185.93049
[14] Wang, Z.; Ho, D. W.C.; Dong, H.; Gao, H., Robust \(H_\infty\) finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations, IEEE Trans. Automat. Control, 55, 7, 1716-1722 (2010) · Zbl 1368.93668
[15] I. Yaesh, S. Boyarski, U. Shaked, Probability-guaranteed robust \(H_\infty \); I. Yaesh, S. Boyarski, U. Shaked, Probability-guaranteed robust \(H_\infty \) · Zbl 1157.93373
[16] Boyarski, S.; Shaked, U., Discrete-time \(H_\infty\) and \(H_2\) control with structured disturbances and probability-relaxed requirements, Internat. J. Control, 77, 14, 1243-1259 (2004) · Zbl 1073.93017
[17] Boyarski, S.; Shaked, U., Robust \(H_\infty\) control design for best mean performance over an uncertain-parameters box, Systems Control Lett., 54, 6, 585-595 (2005) · Zbl 1129.93369
[18] S. Boyarski, U. Shaked, Probability-guaranteed robust full-order and reduced-order \(H_\infty \); S. Boyarski, U. Shaked, Probability-guaranteed robust full-order and reduced-order \(H_\infty \) · Zbl 1073.93017
[19] Yaesh, I.; Boyarski, S.; Shaked, U., Probability-guaranteed robust \(H_\infty\) performance analysis and state-feedback design, Systems Control Lett., 48, 5, 351-364 (2003) · Zbl 1157.93373
[20] Gershon, E.; Shaked, U.; Yaesh, I., \(H_\infty\) Control and Estimation of State-Multiplicative Linear Systems (2005), Springer-Verlag London Limited · Zbl 1116.93003
[21] Shen, B.; Wang, Z.; Liu, X., Bounded \(H_\infty\) synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon, IEEE Trans. Neural Netw., 22, 1, 145-157 (2011)
[22] Khalil, H. K., (Nonlinear Systems (1996), Upper Saddle River, Prentice-Hall: Upper Saddle River, Prentice-Hall NJ)
[23] Yaz, E.; Skelton, R. E., Parametrization of all linear compensators for discrete-time stochastic parameter systems, Automatica, 30, 6, 945-955 (1994) · Zbl 0799.93039
[24] Xiao, Y.; Cao, Y.; Lin, Z., Robust filtering for discrete-time systems with saturation and its application to transmultiplexers, IEEE Trans. Signal Process., 52, 5, 1266-1277 (2004) · Zbl 1370.93291
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