H∞ filtering with randomly occurring sensor saturations and missing measurements

In this paper, the H"~ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H"~ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H"~-norm requirement is satisfied. Note that the regional l"2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

[1]  M. Basin.  On Optimal Filtering for Polynomial System States , 2003 .

[2]  Ian R. Petersen,et al.  Nonlinear state estimation for uncertain systems with an integral constraint , 1998, IEEE Trans. Signal Process..

[3]  Yang Yang,et al.  Harnessing battery recovery effect in wireless sensor networks: Experiments and analysis , 2010, IEEE Journal on Selected Areas in Communications.

[4]  James Lam,et al.  $H_{\infty}$ Positive Filtering for Positive Linear Discrete-Time Systems: An Augmentation Approach , 2010, IEEE Transactions on Automatic Control.

[5]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures , 2007, IEEE Transactions on Signal Processing.

[6]  David G. Ward,et al.  #00 Anti-Windup Design for Linear Systems Subject to Input Saturation * , 2002 .

[7]  James Lam,et al.  Robust H ∞ filtering for uncertain differential linear repetitive processes , 2008 .

[8]  Ali H. Sayed,et al.  Diffusion Strategies for Distributed Kalman Filtering and Smoothing , 2010, IEEE Transactions on Automatic Control.

[9]  Konrad Reif,et al.  Stochastic Stability of the Extended Kalman Filter With Intermittent Observations , 2010, IEEE Transactions on Automatic Control.

[10]  Jinzhi Wang,et al.  Output feedback H controller design for linear discrete-time systems with sensor nonlinearities , 2005 .

[11]  Ian R. Petersen,et al.  A Discrete-Time Robust Extended Kalman Filter for Uncertain Systems With Sum Quadratic Constraints , 2009, IEEE Transactions on Automatic Control.

[12]  Daniel W. C. Ho,et al.  Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation , 2010, Autom..

[13]  Gang George Yin,et al.  Weak Convergence of Hybrid Filtering Problems Involving Nearly Completely Decomposable Hidden Markov Chains , 2002, SIAM J. Control. Optim..

[14]  Zongli Lin,et al.  An output feedback /spl Hscr//sub /spl infin// controller design for linear systems subject to sensor nonlinearities , 2003 .

[15]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[16]  David G. Ward,et al.  An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation , 2002, IEEE Trans. Autom. Control..

[17]  Fuwen Yang,et al.  Set-membership filtering for systems with sensor saturation , 2009, Autom..

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

[19]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[20]  James Lam,et al.  Title Fault detection for fuzzy systems with intermittentmeasurements , 2009 .

[21]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..

[22]  Lihua Xie,et al.  Robust Kalman filtering for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[23]  Edwin Engin Yaz,et al.  Robust minimum variance linear state estimators for multiple sensors with different failure rates , 2007, Autom..

[24]  Davide Spinello,et al.  Nonlinear Estimation With State-Dependent Gaussian Observation Noise , 2010, IEEE Transactions on Automatic Control.

[25]  James Lam,et al.  Robust ℋ︁∞ filtering for uncertain differential linear repetitive processes , 2008 .

[26]  Zongli Lin,et al.  Robust filtering for discrete-time systems with saturation and its application to transmultiplexers , 2004, IEEE Transactions on Signal Processing.

[27]  Huijun Gao,et al.  ${\cal H}_{\infty}$ Estimation for Uncertain Systems With Limited Communication Capacity , 2007, IEEE Transactions on Automatic Control.

[28]  Ian R. Petersen,et al.  Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty , 1998, Autom..

[29]  F. Chapeau-Blondeau,et al.  Stochastic resonance for nonlinear sensors with saturation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.