Adaptive sliding mode fault tolerant control for interval Type-2 fuzzy singular fractional-order systems

This article proposes an integral sliding mode control scheme for a class of uncertain nonlinear singular fractional-order systems subject to actuator faults. The interval type-2 Takagi–Sugeno model is used to represent the singular fractional-order systems. First, a novel integral sliding surface is constructed. A sufficient condition is given in terms of linear matrix inequalities which guarantees the admissibility and the robustness of the singular fractional-order systems against actuator faults. Then, aiming at the fault information which is difficult to get in the practical application, an adaptive estimation of fault information is proposed to update the sliding mode controller. A sliding mode fault tolerant control law is designed to make the singular fractional-order systems reach the sliding surface in a finite time. At last, the applicability and effectiveness of the proposed method is illustrated by a numerical simulation example.

[1]  Bin Wang,et al.  Stabilization conditions for fuzzy control of uncertain fractional order non-linear systems with random disturbances , 2016 .

[2]  Zhenjiang Zhao,et al.  Robust stability of uncertain fractional order singular systems with neutral and time-varying delays , 2020, Neurocomputing.

[3]  Juntao Fei,et al.  Dynamic Terminal Sliding-Mode Control for Single-Phase Active Power Filter Using New Feedback Recurrent Neural Network , 2020, IEEE Transactions on Power Electronics.

[4]  Ligang Wu,et al.  Optimal Guaranteed Cost Sliding-Mode Control of Interval Type-2 Fuzzy Time-Delay Systems , 2018, IEEE Transactions on Fuzzy Systems.

[5]  Peng Shi,et al.  Admissibilization of Singular Interval-Valued Fuzzy Systems , 2017, IEEE Transactions on Fuzzy Systems.

[6]  Nooshin Bigdeli,et al.  Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems , 2017, J. Frankl. Inst..

[7]  Zhiwei Gao,et al.  Fault Estimation and Fault-Tolerant Control for Discrete-Time Dynamic Systems , 2015, IEEE Transactions on Industrial Electronics.

[8]  Driss Boutat,et al.  A Unified Framework of Stability Theorems for LTI Fractional Order Systems With 0 < α < 2 , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Ju H. Park,et al.  Fuzzy logic systems-based integral sliding mode fault-tolerant control for a class of uncertain non-linear systems , 2016 .

[10]  Mohamed Darouach,et al.  Robust $H_{\infty }$ Observer-Based Control of Fractional-Order Systems With Gain Parametrization , 2017, IEEE Transactions on Automatic Control.

[11]  Xuefeng Zhang,et al.  Adaptive Sliding Mode Observer Design for a Class of T–S Fuzzy Descriptor Fractional Order Systems , 2020, IEEE Transactions on Fuzzy Systems.

[12]  Mohammed Chadli,et al.  New admissibility conditions for singular linear continuous-time fractional-order systems , 2017, J. Frankl. Inst..

[13]  R. Wu,et al.  Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances , 2015 .

[14]  Choon Ki Ahn,et al.  Fault-Tolerant Resilient Control For Fuzzy Fractional Order Systems , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[15]  Qingling Zhang,et al.  Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm , 2017 .

[16]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[17]  Juntao Fei,et al.  Experimental Investigation of Recurrent Neural Network Fractional-Order Sliding Mode Control of Active Power Filter , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Shailaja Kurode,et al.  Observer-Based Sliding Mode Control for a Class of Noncommensurate Fractional-Order Systems , 2015, IEEE/ASME Transactions on Mechatronics.

[19]  Yi Shen,et al.  Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays , 2019, Inf. Sci..

[20]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[21]  Junmi Li,et al.  Observer-based non-PDC controller design for T–S fuzzy systems with the fractional-order α : 0 < α < 1 , 2018 .

[22]  Juntao Fei,et al.  Fuzzy Double Hidden Layer Recurrent Neural Terminal Sliding Mode Control of Single-Phase Active Power Filter , 2021, IEEE transactions on fuzzy systems.

[23]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[24]  Mohamed Darouach,et al.  Robust stabilization of uncertain descriptor fractional-order systems , 2013, Autom..

[25]  Cagatay Basdogan,et al.  Stable Physical Human-Robot Interaction Using Fractional Order Admittance Control , 2018, IEEE Transactions on Haptics.

[26]  Ligang Wu,et al.  State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions , 2015, IEEE Transactions on Fuzzy Systems.

[27]  Shu Liang,et al.  Bounded real lemmas for fractional order systems , 2015, Int. J. Autom. Comput..

[28]  Yi Zhao,et al.  Fuzzy Fractional Quadratic Regulator Problem Under Granular Fuzzy Fractional Derivatives , 2018, IEEE Transactions on Fuzzy Systems.

[29]  Miao Yu,et al.  Research on early warning algorithm for economic management based on Lagrangian fractional calculus , 2019 .

[30]  Kehui Sun,et al.  Color Image Compression-Encryption Algorithm Based on Fractional-Order Memristor Chaotic Circuit , 2019, IEEE Access.

[31]  Zhixia Ding,et al.  Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller , 2016, Neural Networks.

[32]  Guang-Hong Yang,et al.  Prescribed Performance Fault-Tolerant Control of Uncertain Nonlinear Systems With Unknown Control Directions , 2017, IEEE Transactions on Automatic Control.

[33]  Guang-Hong Yang,et al.  Dynamic output feedback H∞ control for fractional-order linear uncertain systems with actuator faults , 2019, J. Frankl. Inst..

[34]  Shuzhi Sam Ge,et al.  An Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Robust Fault Tolerant Control of Robot Manipulators , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[35]  Juntao Fei,et al.  Fractional-Order Finite-Time Super-Twisting Sliding Mode Control of Micro Gyroscope Based on Double-Loop Fuzzy Neural Network , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[36]  Shaocheng Tong,et al.  Adaptive Fuzzy Robust Fault-Tolerant Optimal Control for Nonlinear Large-Scale Systems , 2018, IEEE Transactions on Fuzzy Systems.

[37]  D. Matignon.  Stability properties for generalized fractional differential systems , 1998 .

[38]  Michael G. Strintzis,et al.  Face Recognition , 2008, Encyclopedia of Multimedia.

[39]  S.G. Eltaweel.  Color image compression , 2011, 2011 Seventh International Computer Engineering Conference (ICENCO'2011).

[40]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach , 2009, IEEE Transactions on Automatic Control.

[41]  Qing-Guo Wang,et al.  Static output feedback stabilization for fractional-order systems in T-S fuzzy models , 2016, Neurocomputing.

[42]  Clark R. Dohrmann,et al.  Adaptive Sliding Mode Control , 2002 .

[43]  Y. Chen,et al.  Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: The 0 , 2017, ISA transactions.

[44]  Manfredi Maggiore,et al.  Output‐Feedback Control , 2002 .

[45]  Jing Wang,et al.  Fractional order sliding mode control via disturbance observer for a class of fractional order systems with mismatched disturbance, , 2018, Mechatronics.

[46]  Zhiyu Xi,et al.  A New Design of Robust ${\rm H}_{\infty}$ Sliding Mode Control for Uncertain Stochastic T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[47]  Yucheng Dong,et al.  A Unified Framework , 2018, Linguistic Decision Making.

[48]  Tianyu Liu,et al.  Sufficient and necessary conditions for stabilizing singular fractional order systems with partially measurable state , 2019, J. Frankl. Inst..

[49]  Ahmed Alsaedi,et al.  Composite learning adaptive sliding mode control of fractional-order nonlinear systems with actuator faults , 2019, J. Frankl. Inst..

[50]  Yong Wang,et al.  The output feedback control synthesis for a class of singular fractional order systems. , 2017, ISA transactions.

[51]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[52]  Bo Chen,et al.  Face recognition using nonnegative matrix factorization with fractional power inner product kernel , 2019, Neurocomputing.

[53]  Yuanqing Xia,et al.  Robust Adaptive Sliding-Mode Control for Fuzzy Systems With Mismatched Uncertainties , 2010, IEEE Transactions on Fuzzy Systems.

[54]  Jianbin Qiu,et al.  Adaptive Fuzzy Sliding Mode Control for Network-Based Nonlinear Systems With Actuator Failures , 2018, IEEE Transactions on Fuzzy Systems.