Sliding Mode Control with Application to Fault-Tolerant Control: Assessment and Open Problems

This paper is prepared within a collaboration between the Instituto Politecnico Nacional, which is a Mexican research institute that manages research on sliding-mode control theory, and the ARIA research team of the Integration du Materiau au Systeme Lab., a French research group that engages research on model-based fault diagnosis and fault-tolerant control theories. The paper reviews the application of sliding mode control techniques to fault tolerant control and provides perspectives leading to posing some open problems. Operating principles, definitions of the basic concepts are recalled along with the control objectives and design procedures. The evolution of the sliding mode control technique through five generations (as classified by Fridman, Moreno and coworkers) is reviewed. Their respective design procedures, limitations, and robustness properties are also highlighted. The application of the five generations of sliding-mode controllers to fault-tolerant control is discussed. The focus is on some open problems that are judged to commonly be overlooked. Some applications in real-world systems are also presented.

[1]  Halim Alwi,et al.  Design and Analysis of an Integral Sliding Mode Fault-Tolerant Control Scheme , 2012, IEEE Transactions on Automatic Control.

[2]  Franck Plestan,et al.  Pneumatic actuator control: Solution based on adaptive twisting and experimentation , 2013 .

[3]  Michael I. Friswell,et al.  Fixed-Time Attitude Control for Rigid Spacecraft With Actuator Saturation and Faults , 2016, IEEE Transactions on Control Systems Technology.

[4]  Tang Pan,et al.  Observer based finite-time fault tolerant quadrotor attitude control with actuator faults , 2020 .

[5]  Xiaodong Zhang,et al.  Nonlinear Adaptive Fault-Tolerant Quadrotor Altitude and Attitude Tracking With Multiple Actuator Faults , 2018, IEEE Transactions on Control Systems Technology.

[6]  Huijun Gao,et al.  Reconfigurable Tolerant Control of Uncertain Mechanical Systems With Actuator Faults: A Sliding Mode Observer-Based Approach , 2018, IEEE Transactions on Control Systems Technology.

[7]  Antonella Ferrara,et al.  Sliding Mode Fault Diagnosis with Vision in the Loop for Robot Manipulators , 2020, New Trends in Robot Control.

[8]  Martin Horn,et al.  A novel saturated super-twisting algorithm , 2018, Syst. Control. Lett..

[9]  David Henry.  From fault diagnosis to recovery actions for aeronautic and aerospace missions: A model-based point of view , 2008 .

[10]  Denis Efimov,et al.  Supervisory fault‐tolerant control with mutual performance optimization , 2013 .

[11]  Hee-Jun Kang,et al.  Finite-Time Fault-Tolerant Control for a Robot Manipulator Based on Synchronous Terminal Sliding Mode Control , 2020 .

[12]  Arman Sargolzaei,et al.  A Survey on Active Fault-Tolerant Control Systems , 2020 .

[13]  Halim Alwi,et al.  Fault tolerant control using sliding modes with on-line control allocation , 2008, Autom..

[14]  Danwei Wang,et al.  Finite-time fault-tolerant attitude stabilization for spacecraft with actuator saturation , 2015, IEEE Transactions on Aerospace and Electronic Systems.

[15]  Halim Alwi,et al.  Development and evaluation of sliding mode schemes for the RECONFIGURE benchmark problem , 2016, 2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol).

[16]  Shuanghe Yu,et al.  Fixed-time output feedback sliding mode tracking control of marine surface vessels under actuator faults with disturbance cancellation , 2020 .

[17]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[18]  Okyay Kaynak,et al.  Sliding Mode Observer-Based FTC for Markovian Jump Systems With Actuator and Sensor Faults , 2017, IEEE Transactions on Automatic Control.

[19]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[20]  Halim Alwi,et al.  Application and evaluation of an LPV integral sliding mode fault tolerant control scheme on the RECONFIGURE benchmark , 2016, 2016 American Control Conference (ACC).

[21]  Halim Alwi,et al.  On the synthesis of an integrated active LPV FTC scheme using sliding modes , 2019, Autom..

[22]  Hee-Jun Kang,et al.  A Novel Fault-Tolerant Control Method for Robot Manipulators Based on Non-Singular Fast Terminal Sliding Mode Control and Disturbance Observer , 2020, IEEE Access.

[23]  Yuanqing Xia,et al.  Finite-time fault-tolerant control for rigid spacecraft with actuator saturations , 2013 .

[24]  Yongji Wang,et al.  Active fault-tolerant attitude tracking control with adaptive gain for spacecrafts , 2020 .

[25]  Halim Alwi,et al.  Flight evaluation of a sliding mode online control allocation scheme for fault tolerant control , 2020, Autom..

[26]  Xiaoping Liu,et al.  Finite‐time attitude‐tracking control for rigid spacecraft with actuator failures and saturation constraints , 2019, International Journal of Robust and Nonlinear Control.

[27]  Christopher Edwards,et al.  Fault tolerant flight control : a benchmark challenge , 2010 .

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

[29]  Sung Kyung Hong,et al.  Fault-tolerant Control of Quadcopter UAVs Using Robust Adaptive Sliding Mode Approach , 2018, Energies.

[30]  Jianglin Lan,et al.  A new strategy for integration of fault estimation within fault-tolerant control , 2016, Autom..

[31]  Raymond A. DeCarlo,et al.  Decentralized tracking for a class of interconnected nonlinear systems using variable structure control , 1988, Autom..

[32]  Martin Horn,et al.  Guaranteeing Disturbance Rejection and Control Signal Continuity for the Saturated Super-Twisting Algorithm , 2019, IEEE Control Systems Letters.

[33]  Peng Shi,et al.  Adaptive Dynamic Sliding Mode Control for Near Space Vehicles Under Actuator Faults , 2013, Circuits Syst. Signal Process..

[34]  Halim Alwi,et al.  An integral sliding mode fault tolerant control scheme for an octorotor using fixed control allocation , 2014, 2014 13th International Workshop on Variable Structure Systems (VSS).

[35]  Halim Alwi,et al.  Fault tolerant control of an octorotor using LPV based sliding mode control allocation , 2013, 2013 American Control Conference.

[36]  Jianglin Lan,et al.  A decoupling approach to integrated fault-tolerant control for linear systems with unmatched non-differentiable faults , 2018, Autom..

[37]  Xinghuo Yu,et al.  On nonsingular terminal sliding-mode control of nonlinear systems , 2013, Autom..

[38]  Jérôme Cieslak,et al.  Sensor fault diagnosis using a non-homogeneous high-order sliding mode observer with application to a transport aircraft , 2015 .

[39]  M. V. Iordache,et al.  Diagnosis and Fault-Tolerant Control , 2007, IEEE Transactions on Automatic Control.

[40]  Qun Zong,et al.  Adaptive disturbance observer‐based finite‐time continuous fault‐tolerant control for reentry RLV , 2017 .

[41]  Leonid M. Fridman,et al.  Super-Twisting Algorithm in presence of time and state dependent perturbations , 2018, Int. J. Control.

[42]  Yuri B. Shtessel,et al.  Super-twisting adaptive sliding mode control: A Lyapunov design , 2010, 49th IEEE Conference on Decision and Control (CDC).

[43]  Leonid M. Fridman,et al.  Saturated Super-Twisting Algorithm based on Perturbation Estimator , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[44]  Alfonso Baños,et al.  Nonlinear adaptive sliding mode control with fast non-overshooting responses and chattering avoidance , 2017, J. Frankl. Inst..

[45]  Qijia Yao,et al.  Adaptive finite-time sliding mode control design for finite-time fault-tolerant trajectory tracking of marine vehicles with input saturation , 2020, J. Frankl. Inst..

[46]  Ke Zhang,et al.  Spacecraft attitude control using nonsingular finite-time convergence Terminal Sliding Mode , 2016, 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC).

[47]  Zhifeng Gao,et al.  Active fault tolerant control scheme for satellite attitude system subject to actuator time-varying faults , 2018 .

[48]  Kaibiao Sun,et al.  Attitude Tracking Control of A Quad‐Rotor with Partial Loss of Rotation Effectiveness , 2017 .

[49]  Peng Shi,et al.  Active fault tolerant control design for reusable launch vehicle using adaptive sliding mode technique , 2012, J. Frankl. Inst..

[50]  Chih-Chiang Chen,et al.  Study of Nonsingular Fast Terminal Sliding-Mode Fault-Tolerant Control , 2015, IEEE Transactions on Industrial Electronics.

[51]  Liang Zhang,et al.  Adaptive fault-tolerant control for a VTVL reusable launch vehicle , 2019 .

[52]  David Henry.  A Norm-based Point of View for Fault Diagnosis: Application to Aerospace Missions , 2010 .

[53]  Jianglin Lan,et al.  Integrated fault estimation and fault‐tolerant control for uncertain Lipschitz nonlinear systems , 2017 .

[54]  Asif Chalanga,et al.  Continuous Nested Algorithms : The Fifth Generation of Sliding Mode Controllers , 2015 .

[55]  S. T. Venkataraman,et al.  Control of Nonlinear Systems Using Terminal Sliding Modes , 1993 .

[56]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[57]  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.

[58]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

[59]  Halim Alwi,et al.  Development and evaluation of an integral sliding mode fault‐tolerant control scheme on the RECONFIGURE benchmark , 2019 .

[60]  Leonid M. Fridman,et al.  Variable Gain Super-Twisting Sliding Mode Control , 2012, IEEE Transactions on Automatic Control.

[61]  M. Basin,et al.  Multivariable continuous fixed-time second-order sliding mode control: design and convergence time estimation , 2017 .

[62]  G. Tao,et al.  FAULT ACCOMMODATION FOR NEAR SPACE HYPERSONIC VEHICLE WITH ACTUATOR FAULT , 2011 .

[63]  Bing Xiao,et al.  Fault-tolerant attitude control for flexible spacecraft subject to input and state constraint , 2020, Trans. Inst. Meas. Control.

[64]  Fayçal Ben Hmida,et al.  Robust Fault Tolerant Control Design for Nonlinear Systems not Satisfying Matching and Minimum Phase Conditions , 2020 .

[65]  Martin Horn,et al.  Necessary and sufficient stability criterion for the super-twisting algorithm , 2018, 2018 15th International Workshop on Variable Structure Systems (VSS).

[66]  Youmin Zhang,et al.  Adaptive Sliding Mode Fault-Tolerant Control for an Unmanned Aerial Vehicle , 2017, Unmanned Syst..

[67]  Chaomin Luo,et al.  Fault reconstruction using a terminal sliding mode observer for a class of second-order MIMO uncertain nonlinear systems. , 2020, ISA transactions.

[68]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[69]  Yuanqing Xia,et al.  Adaptive finite‐time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints , 2016 .

[70]  Wei Gong,et al.  Sliding mode based fault tolerant control for autonomous underwater vehicle , 2020, Ocean Engineering.

[71]  Arslan Ahmed Amin,et al.  A Review of Sliding Mode Control with the Perspective of Utilization in Fault Tolerant Control , 2021, Recent Advances in Electrical & Electronic Engineering (Formerly Recent Patents on Electrical & Electronic Engineering).

[72]  Paul M. Frank,et al.  Modelling for Fault Detection and Isolation versus Modelling for Control , 2000 .

[73]  Halim Alwi,et al.  Active Fault Tolerant Control of MuPAL-a Using Sliding Modes , 2018, 2018 Annual American Control Conference (ACC).

[74]  A. I. Bhatti,et al.  Air-to-fuel ratio control of gasoline engines using smooth sliding mode algorithm , 2017, 2017 13th International Conference on Emerging Technologies (ICET).

[75]  Youmin Zhang,et al.  Fault tolerant control of a quadrotor UAV using sliding mode control , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[76]  Isabelle Fantoni,et al.  Comparative study of self tuning, adaptive and multiplexing FTC strategies for successive failures in an Octorotor UAV , 2020, Robotics Auton. Syst..

[77]  Halim Alwi,et al.  Actuator faults and blow-down limit detection, and fault tolerant control for the RECONFIGURE benchmark problem , 2016, 2016 IEEE Conference on Control Applications (CCA).

[78]  Mostafa Abedi,et al.  An anti-unwinding finite time fault tolerant sliding mode control of a satellite based on accurate estimation of inertia moments. , 2020, ISA transactions.

[79]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.

[80]  Halim Alwi,et al.  Integral sliding mode fault‐tolerant control allocation for a class of affine nonlinear system , 2018, International Journal of Robust and Nonlinear Control.

[81]  Martin Horn,et al.  Stability proof for a well-established super-twisting parameter setting , 2017, Autom..

[82]  Michael I. Friswell,et al.  Fixed-time rendezvous control of spacecraft with a tumbling target under loss of actuator effectiveness , 2016, IEEE Transactions on Aerospace and Electronic Systems.

[83]  Peng Shi,et al.  Decentralized asymptotic fault tolerant control of near space vehicle with high order actuator dynamics , 2013, J. Frankl. Inst..

[84]  Xiang Yu,et al.  A survey of fault-tolerant controllers based on safety-related issues , 2015, Annu. Rev. Control..

[85]  Halim Alwi,et al.  Fault Tolerance — Background and Recent Trends , 2018 .

[86]  Chun Liu,et al.  Decentralized Output Sliding-Mode Fault-Tolerant Control for Heterogeneous Multiagent Systems , 2020, IEEE Transactions on Cybernetics.

[87]  Yuanli Cai,et al.  On SFTSM control with fixed-time convergence , 2017 .

[88]  Leonid M. Fridman,et al.  Fault tolerant control allocation via continuous integral sliding-modes: A HOSM-Observer approach , 2015, Autom..

[89]  Youmin Zhang,et al.  Passive and active nonlinear fault-tolerant control of a quadrotor unmanned aerial vehicle based on the sliding mode control technique , 2013, J. Syst. Control. Eng..

[90]  Hassan Noura,et al.  Active fault tolerant control of quadrotor UAV using Sliding Mode Control , 2014, 2014 International Conference on Unmanned Aircraft Systems (ICUAS).

[91]  Ge Guo,et al.  Quantized Sliding Mode Control of Unmanned Marine Vehicles: Various Thruster Faults Tolerated With a Unified Model , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[92]  Jérôme Cieslak,et al.  On the synthesis of a sliding-mode-observer-based adaptive fault-tolerant flight control scheme. , 2020, ISA transactions.

[93]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

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

[95]  George Vukovich,et al.  Adaptive fault‐tolerant spacecraft attitude control using a novel integral terminal sliding mode , 2017 .

[96]  Jérôme Cieslak,et al.  Disturbances Observer based Fault Tolerant Control for a Class of Additive Faults , 2019 .

[97]  Xinghuo Yu,et al.  Fast terminal sliding-mode control design for nonlinear dynamical systems , 2002 .

[98]  Arie Levant,et al.  Universal single-input-single-output (SISO) sliding-mode controllers with finite-time convergence , 2001, IEEE Trans. Autom. Control..

[99]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

[100]  Youmin Zhang,et al.  Bibliographical review on reconfigurable fault-tolerant control systems , 2003, Annu. Rev. Control..

[101]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[102]  Yan Yan,et al.  Fixed-time velocity-free sliding mode tracking control for marine surface vessels with uncertainties and unknown actuator faults , 2020 .

[103]  Eric Bornschlegl,et al.  Robust FDI for fault-tolerant thrust allocation with application to spacecraft rendezvous , 2015 .

[104]  Halim Alwi,et al.  Fault Tolerant Control Schemes Using Integral Sliding Modes , 2016 .

[105]  Halim Alwi,et al.  Mitigating total rotor failure in quadrotor using LPV based sliding mode control scheme , 2019, 2019 4th Conference on Control and Fault Tolerant Systems (SysTol).

[106]  Jorge Dávila,et al.  A fault tolerant controller based on quasi-continuous high-order sliding mode technique , 2016, 2016 American Control Conference (ACC).

[107]  Salah Laghrouche,et al.  Robust and adaptive Higher Order Sliding mode controllers , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[108]  Tzu-Chun Kuo,et al.  Adaptive Sliding-Mode Control for NonlinearSystems With Uncertain Parameters , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[109]  Shuzhi Sam Ge,et al.  Finite Time Fault Tolerant Control for Robot Manipulators Using Time Delay Estimation and Continuous Nonsingular Fast Terminal Sliding Mode Control , 2017, IEEE Transactions on Cybernetics.

[110]  Di Shi,et al.  Super-Twisting Extended State Observer and Sliding Mode Controller for Quadrotor UAV Attitude System in Presence of Wind Gust and Actuator Faults , 2018 .

[111]  Sung Kyung Hong,et al.  Active Fault-Tolerant Control of a Quadcopter against Time-Varying Actuator Faults and Saturations Using Sliding Mode Backstepping Approach , 2019, Applied Sciences.

[112]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[113]  Guangfu Ma,et al.  Observer-Based Fault-Tolerant Attitude Control for Rigid Spacecraft , 2017, IEEE Transactions on Aerospace and Electronic Systems.

[114]  Asif Chalanga,et al.  Continuous integral sliding mode control: A chattering free approach , 2013, 2013 IEEE International Symposium on Industrial Electronics.

[115]  Leonid M. Fridman,et al.  Output tracking of systems subjected to perturbations and a class of actuator faults based on HOSM observation and identification , 2015, Autom..

[116]  Asif Chalanga,et al.  Multivariable continuous integral sliding mode control , 2015, 2015 International Workshop on Recent Advances in Sliding Modes (RASM).

[117]  Danwei Wang,et al.  Integral-Type Sliding Mode Fault-Tolerant Control for Attitude Stabilization of Spacecraft , 2015, IEEE Transactions on Control Systems Technology.

[118]  Dariusz Ceglarek,et al.  Robust fault tolerant control of robot manipulators with global fixed-time convergence , 2020, J. Frankl. Inst..

[119]  Hongguang Xu,et al.  Adaptive Nonsingular Terminal Sliding Mode Control for Attitude Tracking of Spacecraft With Actuator Faults , 2019, IEEE Access.

[120]  Jaime A. Moreno,et al.  A linear framework for the robust stability analysis of a Generalized Super-Twisting Algorithm , 2009, 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE).

[121]  Sarah K. Spurgeon,et al.  Sliding mode observers for fault detection and isolation , 2000, Autom..

[122]  Eric Rogers,et al.  Design and Experimental Validation of an Adaptive Sliding Mode Observer-Based Fault-Tolerant Control for Underwater Vehicles , 2019, IEEE Transactions on Control Systems Technology.

[123]  Li Tieshan,et al.  Sliding mode fault-tolerant control for unmanned marine vehicles with signal quantization and time-delay , 2020, Ocean Engineering.

[124]  Hassan Noura,et al.  Design of passive fault-tolerant controllers of a quadrotor based on sliding mode theory , 2015, Int. J. Appl. Math. Comput. Sci..

[125]  Bo Li,et al.  Continuous finite-time extended state observer based fault tolerant control for attitude stabilization , 2019, Aerospace Science and Technology.

[126]  Jun Zhou,et al.  Analysis and design of second-order sliding-mode algorithms for quadrotor roll and pitch estimation. , 2017, ISA transactions.

[127]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[128]  Aamer Iqbal Bhatti,et al.  Higher order sliding mode based control scheme for air path of diesel engine , 2016, 2016 International Conference on Emerging Technologies (ICET).

[129]  Halim Alwi,et al.  A fault tolerant integral sliding mode control allocation scheme for the RECONFIGURE benchmark problem , 2014, 2014 American Control Conference.

[130]  Sauro Longhi,et al.  Flight control of a quadrotor vehicle subsequent to a rotor failure , 2014 .

[131]  Halim Alwi,et al.  Evaluation of a Sliding Mode Fault Tolerant Controller on the MuPAL-$\alpha$ Research Aircraft , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).

[132]  Hassan Noura,et al.  Passive fault tolerant control of quadrotor UAV using regular and cascaded Sliding Mode Control , 2013, 2013 Conference on Control and Fault-Tolerant Systems (SysTol).

[133]  Souad Bezzaoucha,et al.  An LMI approach for the Integral Sliding Mode and H∞ State Feedback Control Problem , 2015 .

[134]  Youmin Zhang,et al.  Adaptive Sliding Mode Fault Tolerant Attitude Tracking Control for Flexible Spacecraft Under Actuator Saturation , 2012, IEEE Transactions on Control Systems Technology.

[135]  Arslan Ahmed Amin,et al.  A review of Fault Tolerant Control Systems: Advancements and applications , 2019, Measurement.

[136]  Laxman M. Waghmare,et al.  Robust maneuvering of autonomous underwater vehicle: an adaptive fuzzy PI sliding mode control , 2017, Intell. Serv. Robotics.

[137]  David W Ginsberg,et al.  Variable structure control systems , 1989 .

[138]  Jun Zhou,et al.  A Two-Step Approach for an Enhanced Quadrotor Attitude Estimation via IMU Data , 2018, IEEE Transactions on Control Systems Technology.

[139]  N. E. Wu,et al.  Concepts and methods in fault-tolerant control , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[140]  Halim Alwi,et al.  Scheduled Fault Tolerant Integral Sliding Mode Control for BWB Aircraft , 2020, 2020 European Control Conference (ECC).

[141]  Jorge Davila,et al.  Exact Tracking Using Backstepping Control Design and High-Order Sliding Modes , 2013, IEEE Transactions on Automatic Control.

[142]  Hee-Jun Kang,et al.  Implementation of Fault-Tolerant Control for a Robot Manipulator Based on Synchronous Sliding Mode Control , 2020 .

[143]  Denis Efimov,et al.  Transient management of a supervisory fault-tolerant control scheme based on dwell-time conditions , 2015 .

[144]  Christopher Edwards,et al.  Adaptive dual-layer super-twisting control and observation , 2016, Int. J. Control.

[145]  Shun-Feng Su,et al.  Finite-time fault-tolerant trajectory tracking control of an autonomous surface vehicle , 2020, J. Frankl. Inst..

[146]  Halim Alwi,et al.  Application of an LPV based Model Reference FTC Scheme on the RECONFIGURE benchmark model , 2018, 2018 Annual American Control Conference (ACC).

[147]  Zhifeng Gao,et al.  Integrated fault tolerant tracking control for rigid spacecraft using fractional order sliding mode technique , 2020, J. Frankl. Inst..

[148]  Christopher Edwards,et al.  Enhancement of adaptive observer robustness applying sliding mode techniques , 2016, Autom..

[149]  Leonid M. Fridman,et al.  Finite-time state observation for non-linear uncertain systems via higher-order sliding modes , 2009, Int. J. Control.

[150]  Leonid Fridman,et al.  Fault tolerant control based on continuous twisting algorithms of a 3-DoF helicopter prototype , 2020 .

[151]  D. Henry.  Fault Diagnosis of Microscope Satellite Thrusters Using H-infinity/H_ Filters , 2008 .

[152]  Mingjun Zhang,et al.  Adaptive terminal sliding mode based thruster fault tolerant control for underwater vehicle in time-varying ocean currents , 2015, J. Frankl. Inst..