Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations

Abstract This paper is concerned with the joint state and fault estimation problem for a class of uncertain time-varying nonlinear stochastic systems with randomly occurring faults and sensor saturations. A random variable obeying the Bernoulli distribution is used to characterize the phenomenon of the randomly occurring faults and the signum function is employed to describe the sensor saturation due to physical limits on the measurement output. The aim of this paper is to design a locally optimal time-varying estimator to simultaneously estimate both the system states and the fault signals such that, at each sampling instant, the covariance of the estimation error has an upper bound that is minimized by properly designing the estimator gain. The explicit form of the estimator gain is characterized in terms of the solutions to two difference equations. It is shown that the developed estimation algorithm is of a recursive form that is suitable for online computations. In addition, the performance analysis of the proposed estimation algorithm is conducted and a sufficient condition is given to verify the exponential boundedness of the estimation error in the mean square sense. Finally, an illustrative example is provided to show the usefulness of the developed estimation scheme.

[1]  Fuad E. Alsaadi,et al.  Event-based filtering for time-varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities , 2017, Inf. Fusion.

[2]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[3]  Peng Shi,et al.  Fault-Tolerant Sliding-Mode-Observer Synthesis of Markovian Jump Systems Using Quantized Measurements , 2015, IEEE Transactions on Industrial Electronics.

[4]  Konrad Reif,et al.  Stochastic stability of the discrete-time extended Kalman filter , 1999, IEEE Trans. Autom. Control..

[5]  Rongrong Wang,et al.  Actuator and sensor faults estimation based on proportional integral observer for TS fuzzy model , 2017, J. Frankl. Inst..

[6]  Bin Wu,et al.  Aircraft electric system intermittent arc fault detection and location , 2015, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Raquel Caballero-Águila,et al.  Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements , 2015, Int. J. Gen. Syst..

[8]  Zidong Wang,et al.  Finite-Horizon $H_{\infty}$ Fault Estimation for Uncertain Linear Discrete Time-Varying Systems With Known Inputs , 2013, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Jun Hu,et al.  State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays , 2014, Int. J. Gen. Syst..

[10]  Yong Qi,et al.  Online Estimation of the Approximate Posterior Cramer-Rao Lower Bound for Discrete-Time Nonlinear Filtering , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[11]  Peng Shi,et al.  Non-weighted quasi-time-dependent H∞ filtering for switched linear systems with persistent dwell-time , 2015, Autom..

[12]  Damien Koenig,et al.  Filtering and fault estimation of descriptor switched systems , 2016, Autom..

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

[14]  Jun Hu,et al.  Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements , 2013, Int. J. Control.

[15]  Sebastian Engell,et al.  Gain-scheduling trajectory control of a continuous stirred tank reactor , 1998 .

[16]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.

[17]  Alexander G. Loukianov,et al.  Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems , 2013, Int. J. Syst. Sci..

[18]  Hamid Reza Karimi,et al.  A Robust Observer-Based Sensor Fault-Tolerant Control for PMSM in Electric Vehicles , 2016, IEEE Transactions on Industrial Electronics.

[19]  Peng Shi,et al.  Integrated Fault Estimation and Accommodation Design for Discrete-Time Takagi–Sugeno Fuzzy Systems With Actuator Faults , 2011, IEEE Transactions on Fuzzy Systems.

[20]  N. Langlois,et al.  Fuzzy fault-tolerant-predictive control for a class of nonlinear uncertain systems , 2016 .

[21]  Donghua Zhou,et al.  On Designing $H_{\infty}$ Fault Detection Filter for Linear Discrete Time-Varying Systems , 2010, IEEE Transactions on Automatic Control.

[22]  Okyay Kaynak,et al.  Improved PLS Focused on Key-Performance-Indicator-Related Fault Diagnosis , 2015, IEEE Transactions on Industrial Electronics.

[23]  Huijun Gao,et al.  Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems , 2014, Autom..

[24]  A. Farina,et al.  Tracking a ballistic target: comparison of several nonlinear filters , 2002 .

[25]  Zidong Wang,et al.  H∞ filtering with randomly occurring sensor saturations and missing measurements , 2012, Autom..

[26]  Huijun Gao,et al.  A new approach to quantized feedback control systems , 2008, Autom..

[27]  Huijun Gao,et al.  Fault Detection for Markovian Jump Systems With Sensor Saturations and Randomly Varying Nonlinearities , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Daniel W. C. Ho,et al.  State/noise estimator for descriptor systems with application to sensor fault diagnosis , 2006, IEEE Transactions on Signal Processing.

[29]  Seiichi Nakamori,et al.  Signal estimation with multiple delayed sensors using covariance information , 2010, Digit. Signal Process..

[30]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[31]  Hamid Reza Karimi,et al.  Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations , 2011 .

[32]  H. Karimi,et al.  Mean-Square Filtering for Polynomial System States Confused with Poisson Noises over Polynomial Observations , 2011 .

[33]  Yugang Niu,et al.  Filtering For Discrete Fuzzy Stochastic Systems With Sensor Nonlinearities , 2010, IEEE Transactions on Fuzzy Systems.

[34]  Giuseppe Carlo Calafiore,et al.  Reliable localization using set-valued nonlinear filters , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[35]  Boulaid Boulkroune,et al.  ℋ −/ℋ ∞ fault detection filter for a class of nonlinear descriptor systems , 2013, Int. J. Control.

[36]  Peng Shi,et al.  Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Yuanqing Xia,et al.  A new continuous-discrete particle filter for continuous-discrete nonlinear systems , 2013, Inf. Sci..

[38]  Garry A. Einicke,et al.  Iterative filtering and smoothing of measurements possessing poisson noise , 2015, IEEE Transactions on Aerospace and Electronic Systems.