{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:19:39Z","timestamp":1760235579689,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T00:00:00Z","timestamp":1630540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673099"],"award-info":[{"award-number":["61673099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, the problem of observer-based adaptive sliding mode control is discussed for nonlinear systems with sensor and actuator faults. The time-varying actuator degradation factor and external disturbance are considered in the system simultaneously. In this study, the original system is described as a new normal system by combining the state vector, sensor faults, and external disturbance into a new state vector. For the augmented system, a new sliding mode observer is designed, where a discontinuous term is introduced such that the effects of sensor and actuator faults and external disturbance will be eliminated. In addition, based on a tricky design of the observer, the time-varying actuator degradation factor term is developed in the error system. On the basis of the state estimation, an integral-type adaptive fuzzy sliding mode controller is constructed to ensure the stability of the closed-loop system. Finally, the effectiveness of the proposed control methods can be illustrated with a numerical example.<\/jats:p>","DOI":"10.3390\/sym13091615","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T23:55:22Z","timestamp":1630972522000},"page":"1615","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Adaptive Fuzzy Fault-Tolerant Control against Time-Varying Faults via a New Sliding Mode Observer Method"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4211-1601","authenticated-orcid":false,"given":"Yi","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Science, Shenyang University of Technology, Shenyang 110870, China"}]},{"given":"Yingying","family":"Nie","sequence":"additional","affiliation":[{"name":"School of Science, Shenyang University of Technology, Shenyang 110870, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7501-7972","authenticated-orcid":false,"given":"Liheng","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Automation, Harbin Engineering University, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5541","DOI":"10.1109\/TSP.2007.900154","article-title":"State and Disturbance Estimator for Time-Delay Systems With Application to Fault Estimation and Signal Compensation","volume":"55","author":"Gao","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1109\/TFUZZ.2008.2010867","article-title":"Fuzzy filter design for It\u00f4 stochastic systems with application to sensor fault detection","volume":"17","author":"Wu","year":"2009","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5678","DOI":"10.1109\/TIE.2017.2677327","article-title":"Takagi-Sugeno Fuzzy Model Based Fault Estimation and Signal Compensation with Application to Wind Turbines","volume":"64","author":"Liu","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1002\/rnc.3982","article-title":"Integrated fault estimation and fault-tolerant control for stochastic systems with Brownian motions","volume":"28","author":"Liu","year":"2018","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5380","DOI":"10.1016\/j.jfranklin.2020.02.050","article-title":"Intermediate variable observer based fault estimation and fault-tolerant control for nonlinear stochastic system with exogenous disturbance","volume":"357","author":"Liu","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/TFUZZ.2009.2036005","article-title":"Dynamic output feedback-fault tolerant controller design for Takagi\u2013Sugeno fuzzy systems with actuator faults","volume":"18","author":"Zhang","year":"2010","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1109\/TCYB.2019.2901542","article-title":"Fault-Tolerant Consensus Tracking Control for Linear Multiagent Systems Under Switching Directed Network","volume":"50","author":"Wang","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1109\/TCYB.2017.2785801","article-title":"Observer-Based Adaptive Fuzzy Fault-Tolerant Optimal Control for SISO Nonlinear Systems","volume":"49","author":"Li","year":"2019","journal-title":"IEEE Trans. Cybern."},{"key":"ref_9","first-page":"4707","article-title":"Data-Driven Robust Fault Detection and Isolation of Three-Phase Induction Motor","volume":"66","author":"Tariq","year":"2019","journal-title":"Automatica"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.automatica.2019.01.013","article-title":"Distributed adaptive fault-tolerant control approach to cooperative output regulation for linear multi-agent systems","volume":"103","author":"Deng","year":"2019","journal-title":"Automatica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4733","DOI":"10.1109\/TAC.2019.2904435","article-title":"Reduced order sliding mode observer-based fault estimation for Markov jump systems","volume":"64","author":"Yang","year":"2019","journal-title":"IEEE Trans Autom. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/TFUZZ.2010.2095861","article-title":"Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults","volume":"19","author":"Jiang","year":"2011","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_13","first-page":"219","article-title":"Sensor fault detection and isolation for a class of uncertain nonlinear system using sliding mode observers","volume":"61","author":"Allahverdi","year":"2020","journal-title":"Automatica"},{"key":"ref_14","first-page":"5380","article-title":"Adaptive actuator fault compensation and disturbance rejection scheme for spacecraft","volume":"357","author":"Li","year":"2021","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1016\/j.automatica.2005.03.019","article-title":"A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: An LMI approach","volume":"41","author":"Casavola","year":"2005","journal-title":"Automatica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s12555-011-0408-8","article-title":"Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations","volume":"9","author":"Karimi","year":"2011","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1002\/asjc.1882","article-title":"Fuzzy Sliding Mode Control for Active Suspension System with Proportional Differential Sliding Mode Observer: Fuzzy SMC for active suspension system with PD sliding mode observer","volume":"21","author":"Lin","year":"2019","journal-title":"Asian J. Control"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Piltan, F., Prosvirin, A.E., Jeong, I., Im, K., and Kim, J.M. (2019). Rolling-element bearing fault diagnosis using advanced machine learning-based observer. Appl. Sci., 9.","DOI":"10.3390\/app9245404"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zheng, W., Xia, B., Wang, W., Lai, Y., Wang, M., and Wang, H. (2019). State of charge estimation for power lithium-Ion battery using a fuzzy logic sliding mode Observer. Energies, 12.","DOI":"10.3390\/en12132491"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1109\/TPEL.2020.3000785","article-title":"An improved adaptive sliding mode observer for middle- and high-speed rotor tracking","volume":"36","author":"Xu","year":"2009","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5913","DOI":"10.1109\/TIE.2019.2952824","article-title":"An improved delay-suppressed sliding mode observer for sensorless vector-controlled PMSM","volume":"67","author":"Gong","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.isatra.2019.02.028","article-title":"Disturbance suppression for quadrotor UAV using sliding-mode-observer-based equivalent-input-disturbance approach","volume":"92","author":"Cai","year":"2019","journal-title":"ISA Trans."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lopac, N., Bulic, N., and Vrkic, N. (2019). Sliding mode observer-based load angle estimation for salient-pole wound rotor synchronous generators. Energies, 12.","DOI":"10.3390\/en12091609"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chen, S., Zhang, X., Wu, X., Tan, G., and Chen, X. (2019). Sensorless control for IPMSM based on adaptive super-twisting sliding-mode observer and improved phase-locked loop. Energies, 12.","DOI":"10.3390\/en12071225"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1109\/9.975511","article-title":"Sliding mode observer for nonlinear uncertain systems","volume":"46","author":"Xiong","year":"2001","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1109\/TAC.2019.2931462","article-title":"Global Sliding Mode Observers for Some Uncertain Mechanical Systems","volume":"65","author":"Moreno","year":"2020","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2048","DOI":"10.1109\/TFUZZ.2019.2930036","article-title":"Fuzzy Descriptor Sliding Mode Observer Design: A Canonical Form-Based Method","volume":"28","author":"Li","year":"2020","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Nguyen, N.P., and Hong, S.K. (2019). Fault diagnosis and fault-tolerant control scheme for quadcopter UAVs with a total loss of actuator. Energies, 12.","DOI":"10.3390\/en12061139"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TASE.2008.917009","article-title":"Fault detection, isolation, and accommodation control in robotic systems","volume":"5","author":"Huang","year":"2008","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1049\/iet-cta.2018.5469","article-title":"Event-triggered scheme for fault detection and isolation of non-linear system with time-varying delay","volume":"14","author":"Aslam","year":"2020","journal-title":"IET Control Theory Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1016\/j.automatica.2014.04.006","article-title":"Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach","volume":"50","author":"Li","year":"2014","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1016\/j.automatica.2013.01.030","article-title":"Sensor fault estimation and tolerant control for It\u00f4 stochastic systems with a descriptor sliding mode approach","volume":"49","author":"Liu","year":"2013","journal-title":"Automatica"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jin, Z., Wang, Z., and Li, J. (2021). Input-to-state stability of the nonlinear fuzzy systems via small-gain theorem and decentralized sliding mode control. IEEE Trans. Fuzzy Syst.","DOI":"10.1109\/TFUZZ.2021.3099036"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Jin, Z., and Zhang, Q. (2021). Impulse elimination of the Takagi-Sugeno fuzzy singular system via sliding mode control. IEEE Trans. Fuzzy Syst.","DOI":"10.1109\/TFUZZ.2021.3053325"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"5647","DOI":"10.1109\/TIE.2019.2931517","article-title":"Finite-time continuous terminal sliding mode control of servo motor systems","volume":"67","author":"Hou","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_36","unstructured":"Hou, H., Yu, X., and Fu, Z. (2020). Sliding-mode control of uncertain time-varying systems with state delays: A non-negative constraints approach. IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1109\/TMECH.2019.2928642","article-title":"Discrete-time terminal sliding-mode tracking control with alleviated chattering","volume":"24","author":"Hou","year":"2019","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1002\/oca.2557","article-title":"Integrated fault tolerant attitude control approach for satellite attitude system with sensor faults","volume":"41","author":"Qian","year":"2020","journal-title":"Optim. Control Appl. Methods"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1080\/00207179.2018.1484173","article-title":"A fault tolerant tracking control for a quadrotor UAV subject to simultaneous actuator faults and exogenous disturbances","volume":"99","author":"Mallavalli","year":"2020","journal-title":"Int. J. Control"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/TCYB.2013.2262935","article-title":"Fuzzy Neural Network-Based Adaptive Control for a Class of Uncertain Nonlinear Stochastic Systems","volume":"44","author":"Chen","year":"2014","journal-title":"IEEE Trans. Cybern."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.jfranklin.2019.09.020","article-title":"Fault estimation based on sliding mode observer for Takagi-Sugeno fuzzy systems with digital communication constraints","volume":"357","author":"Feng","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"115858","DOI":"10.1016\/j.jsv.2020.115858","article-title":"Active control of linear vibrating systems for antiresonance assignment with regional pole placement","volume":"494","author":"Richiedei","year":"2021","journal-title":"J. Sound Vib."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00207170801942188","article-title":"Robust state-derivative pole placement LMI-based designs for linear systems","volume":"82","author":"Faria","year":"2009","journal-title":"Int. J. Control"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"126171","DOI":"10.1016\/j.amc.2021.126171","article-title":"Input-to-state stability of the nonlinear singular systems via small-gain theorem","volume":"402","author":"Jin","year":"2020","journal-title":"Appl. Mathe. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1109\/TAC.2015.2396645","article-title":"A small-gain approach to robust event-triggered control of nonlinear systems","volume":"60","author":"Liu","year":"2015","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1615\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:55:01Z","timestamp":1760165701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/9\/1615"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,2]]},"references-count":45,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["sym13091615"],"URL":"https:\/\/doi.org\/10.3390\/sym13091615","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,9,2]]}}}