Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

In this paper, the robust H∞ filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the H∞ performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed H∞ performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.

[1]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[2]  Lihua Xie,et al.  Optimal Full-Order and Reduced-Order Estimators for Discrete-Time Systems With Multiple Packet Dropouts , 2008, IEEE Transactions on Signal Processing.

[3]  Michael V. Basin,et al.  Optimal filtering for linear states over polynomial observations , 2007, 2007 46th IEEE Conference on Decision and Control.

[4]  A. Hermoso-Carazo,et al.  Signal estimation with nonlinear uncertain observations using covariance information , 2009 .

[5]  Zidong Wang,et al.  A delay-dependent approach to H ∞ filtering for stochastic delayed jumping systems with sensor non-linearities , 2007, Int. J. Control.

[6]  Qing-Long Han,et al.  Absolute stability of time-delay systems with sector-bounded nonlinearity , 2005, Autom..

[7]  Huijun Gao,et al.  Delay-Dependent Robust and - Filtering for a Class of Uncertain Nonlinear Time-Delay Systems , 2003 .

[8]  Sing Kiong Nguang,et al.  H∞ filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach , 2004, IEEE Trans. Signal Process..

[9]  Huijun Gao,et al.  $${\cal{H}}_{\infty}$$ and $${\cal{L}}_{\bf 2}/{\cal{L}}_{\infty}$$Model Reduction for System Input with Sector Nonlinearities , 2005 .

[10]  Guang-Ren Duan,et al.  H∞ filtering for multiple-time-delay measurements , 2006, IEEE Trans. Signal Process..

[11]  Chung-Shi Tseng,et al.  Robust Fuzzy Filter Design for a Class of Nonlinear Stochastic Systems , 2007, IEEE Transactions on Fuzzy Systems.

[12]  J. Lam,et al.  Fixed-Order Robust Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities , 2006 .

[13]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[14]  Z. Han,et al.  Robust H∞ filtering of fuzzy dynamic systems , 1999 .

[15]  E. Boukas,et al.  Mixed H 2 /H ∞ Nonlinear Filtering , 2007 .

[16]  Guang-Hong Yang,et al.  Robust H∞ filtering for continuous time-varying uncertain systems with adaptive mechanism , 2008, 2008 American Control Conference.

[17]  LiuXiaohui,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009 .

[18]  Michael V. Basin,et al.  Optimal Filtering for Linear System States over Polynomial Observations , 2006, First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06).

[19]  S. Nguang,et al.  H/sub /spl infin// filtering for fuzzy dynamical systems with D stability constraints , 2003 .

[20]  Guanrong Chen.  A simple treatment for suboptimal Kalman filtering in case of measurement data missing , 1990 .

[21]  G. Feng.  Robust H/sub /spl infin// filtering of fuzzy dynamic systems , 2005 .

[22]  Huijun Gao,et al.  Induced l2 and Generalized H2 Filtering for Systems With Repeated Scalar Nonlinearities , 2005 .

[23]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[24]  James Lam,et al.  Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities , 2006, IEEE Transactions on Signal Processing.

[25]  Fuwen Yang,et al.  Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty , 2003, Autom..

[26]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[27]  Seiichi Nakamori,et al.  Signal estimation based on covariance information from observations featuring correlated uncertainty and coming from multiple sensors , 2008, Signal Process..

[28]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

[29]  Donghua Zhou,et al.  Robust H ∞ filtering for networked systems with multiple state delays , 2007, Int. J. Control.

[30]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[31]  Zidong Wang,et al.  H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities , 2008, Autom..

[32]  Huijun Gao,et al.  Induced l/sub 2/ and generalized H/sub 2/ filtering for systems with repeated scalar nonlinearities , 2005, IEEE Transactions on Signal Processing.

[33]  X. Guan,et al.  State Feedback Controller Design of Networked Control Systems with Time Delay in the Plant , 2006, 2006 Chinese Control Conference.

[34]  James Lam,et al.  $H_{\bm \infty}$ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements , 2009, IEEE Transactions on Fuzzy Systems.

[35]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[36]  Huijun Gao,et al.  Delay-dependent robust H∞ and L2-L∞ filtering for a class of uncertain nonlinear time-delay systems , 2003, IEEE Trans. Autom. Control..

[37]  Daniel W. C. Ho,et al.  Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements , 2009, Autom..

[38]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Bor-Sen Chen,et al.  Robust H∞ filtering for nonlinear stochastic systems , 2005 .

[40]  Lihua Xie,et al.  Optimal linear estimation for systems with multiple packet dropouts , 2008, Autom..

[41]  M. Aliyu,et al.  Mixed ℋ︁2/ℋ︁∞ nonlinear filtering , 2009 .

[42]  Y. Hung,et al.  H/sub /spl infin// control for networked systems with random communication delays , 2006, IEEE Transactions on Automatic Control.