Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

ABSTRACT This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.

[1]  Peng Shi,et al.  Fault Estimation Observer Design for Discrete-Time Takagi–Sugeno Fuzzy Systems Based on Piecewise Lyapunov Functions , 2012, IEEE Transactions on Fuzzy Systems.

[2]  Wei Zhang,et al.  Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays , 2011, Int. J. Appl. Math. Comput. Sci..

[3]  Guang-Hong Yang,et al.  Fault detection filter design for stochastic time-delay systems with sensor faults , 2012, Int. J. Syst. Sci..

[4]  Ligang Wu,et al.  Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[5]  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.

[6]  Ke Zhang,et al.  Fast fault estimation and accommodation for dynamical systems , 2009 .

[7]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[8]  Bin Jiang,et al.  An improved adaptive fault estimation design for polytopic LPV systems with application to helicopter models , 2009, 2009 7th Asian Control Conference.

[9]  Rathinasamy Sakthivel,et al.  Fault-Distribution Dependent Reliable H∞ Control for Takagi-Sugeno Fuzzy Systems , 2014 .

[10]  Hamid Reza Karimi,et al.  Fault detection for continuous‐time switched systems under asynchronous switching , 2014 .

[11]  Pagavathigounder Balasubramaniam,et al.  Delay-interval-dependent robust stability results for uncertain stochastic systems with Markovian jumping parameters ☆ , 2011 .

[12]  Wen Chen,et al.  Fault Reconstruction and Fault-Tolerant Control via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays , 2015, IEEE Transactions on Industrial Electronics.

[13]  A. El Hajjaji,et al.  Adaptive fault tolerant control design for Takagi–Sugeno fuzzy systems with interval time-varying delay , 2014 .

[14]  Bin Jiang,et al.  A new criterion of fault estimation for neutral delay systems , 2009, International Conference on Modelling, Identification and Control.

[15]  Peng Shi,et al.  A New Approach to Observer-Based Fault-Tolerant Controller Design for Takagi-Sugeno Fuzzy Systems with State Delay , 2009, Circuits Syst. Signal Process..

[16]  Hamid Reza Karimi,et al.  Fault Detection, Isolation, andTolerant Control of Vehicles using Soft Computing Methods , 2014 .

[17]  Marcel Staroswiecki,et al.  Dynamic Output Feedback-Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Systems With Actuator Faults , 2010, IEEE Transactions on Fuzzy Systems.

[18]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[19]  Hamid Reza Karimi,et al.  A robust fault detection design for uncertain Takagi–Sugeno models with unknown inputs and time-varying delays , 2014 .

[20]  Ligang Wu,et al.  Induced l2 filtering of fuzzy stochastic systems with time-varying delays , 2013, IEEE Transactions on Cybernetics.

[21]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[22]  C. Lien,et al.  Stability criteria for uncertain neutral systems with interval time-varying delays , 2008 .

[23]  Xi-Qin He,et al.  New Results on $H_\infty$ Filter Design for Nonlinear Systems With Time Delay via T–S Fuzzy Models , 2011, IEEE Transactions on Fuzzy Systems.

[24]  H. Karimi,et al.  Discrete‐time H −  ∕ H ∞  sensor fault detection observer design for nonlinear systems with parameter uncertainty , 2015 .

[25]  Hamid Reza Karimi,et al.  Data-driven design of robust fault detection system for wind turbines , 2014 .

[26]  Jianhua Zhang,et al.  A new criterion of fault estimation for neutral delay systems , 2015, 2015 7th International Conference on Modelling, Identification and Control (ICMIC).

[27]  Jiang Bin,et al.  Analysis and design of adaptive fault estimation for time-varying delay systems , 2008, 2008 27th Chinese Control Conference.

[28]  Ahmed El Hajjaji,et al.  Observer-Based Robust $H_{\infty }$ Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay , 2010, IEEE Transactions on Fuzzy Systems.

[29]  Renfa Li,et al.  A delay-derivative-dependent approach to robust H∞ filter design for uncertain systems with time-varying distributed delays , 2011, J. Frankl. Inst..

[30]  Fuli Wang,et al.  Robust Fault Estimation for Takagi–Sugeno Nonlinear Systems with Time-Varying State Delay , 2015, Circuits Syst. Signal Process..

[31]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[32]  Ron J. Patton,et al.  Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults , 2013 .

[33]  Guang-Hong Yang,et al.  Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach , 2014, IEEE Transactions on Fuzzy Systems.

[34]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[35]  Tong Heng Lee,et al.  $H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach , 2008, IEEE Transactions on Fuzzy Systems.

[36]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[37]  Rongrong Wang,et al.  Robust fault-tolerant H ∞ control of active suspension systems with finite-frequency constraint , 2015 .

[38]  Jinliang Liu,et al.  H∞ filter design for nonlinear systems with time-delay through T-S fuzzy model approach , 2010, 2010 Chinese Control and Decision Conference.

[39]  Huaguang Zhang,et al.  A new fuzzy H∞ filter design for nonlinear continuous-time dynamic systems with time-varying delays , 2009, Fuzzy Sets Syst..

[40]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[41]  Wang Xiaofeng,et al.  H∞ control for linear systems with interval time-varying delay , 2013, Proceedings of the 32nd Chinese Control Conference.