Sensor fault estimation and tolerant control for Itô stochastic systems with a descriptor sliding mode approach

This paper investigates the problem of fault estimation and fault-tolerant control against sensor failures for a class of nonlinear Ito stochastic systems with simultaneous input and output disturbances. By using a new descriptor sliding mode approach, an accurate estimation of the system states, fault vector and disturbances can be obtained simultaneously. Based on the state estimates, an integral-type sliding mode control scheme against faults and disturbances is proposed to stabilize the resulting fault system. It is shown that the reachabilities of the proposed sliding mode surfaces can be guaranteed in both the state estimate space and the estimation error space simultaneously under the designed control schemes. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed technique.

[1]  Leonid M. Fridman,et al.  Sliding Mode Identification and Control for Linear Uncertain Stochastic Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  Marcel Staroswiecki,et al.  Fault Accommodation for Nonlinear Dynamic Systems , 2006, IEEE Transactions on Automatic Control.

[3]  Michael V. Basin,et al.  Sliding-Mode Filter Design for Linear Systems With Unmeasured States , 2011, IEEE Trans. Ind. Electron..

[4]  Leonid M. Fridman,et al.  Robust output Nash strategies based on sliding mode observation in a two-player differential game , 2012, J. Frankl. Inst..

[5]  Yuanqing Xia,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, 2008 27th Chinese Control Conference.

[6]  Shengyuan Xu,et al.  Hinfinity output feedback control for uncertain stochastic systems with time-varying delays , 2004, Autom..

[7]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

[8]  Steven X. Ding,et al.  Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems , 2007, Autom..

[9]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[10]  Yugang Niu,et al.  Observer-based sliding mode control for nonlinear state-delayed systems , 2004, Int. J. Syst. Sci..

[11]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[12]  Michael V. Basin,et al.  On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term , 2007, Syst. Control. Lett..

[13]  Sing Kiong Nguang,et al.  Delay dependent fault estimation for uncertain time delay nonlinear systems: an LMI approach , 2006, 2006 American Control Conference.

[14]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[15]  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.

[16]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

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

[18]  Denis V. Efimov,et al.  Actuator fault detection and compensation under feedback control , 2011, Autom..

[19]  Jian Liu,et al.  An LMI approach to H_ index and mixed H_/Hinfinit fault detection observer design , 2007, Autom..

[20]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

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

[22]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[23]  Shengyuan Xu,et al.  H∞H∞ output feedback control for uncertain stochastic systems with time-varying delays☆ , 2004 .

[24]  Wilfrid Perruquetti,et al.  Observability and detectability analysis of singular linear systems with unknown inputs , 2011, IEEE Conference on Decision and Control and European Control Conference.

[25]  Xingyu Wang,et al.  Robust sliding mode design for uncertain stochastic systems based on H∞ control method , 2010 .

[26]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[27]  Christopher Edwards,et al.  Nonlinear robust fault reconstruction and estimation using a sliding mode observer , 2007, Autom..

[28]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[29]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[30]  Yugang Niu,et al.  Design of Sliding Mode Control Subject to Packet Losses , 2010, IEEE Transactions on Automatic Control.

[31]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[32]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[34]  Peng Shi,et al.  Fuzzy-Model-Based Fault-Tolerant Design for Nonlinear Stochastic Systems Against Simultaneous Sensor and Actuator Faults , 2013, IEEE Transactions on Fuzzy Systems.