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RESEARCH ARTICLE

Fixed-time sliding mode control with disturbance observer and variable exponent coefficient for nonlinear systems

Zeeshan Anjum1† ,  Wen-Jer Chang2* ,  Muhammad Shamrooz Aslam3† ,  Rizwan Ullah1†
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1 School of Mechanical and Electrical Engineering, Quanzhou University of Information Engineering, Quanzhou, Fujian, China
2 Department of Marine Engineering, National Taiwan Ocean University, Keelung, Taiwan
3 Artificial Intelligence Research Institute, China University of Mining and Technology, Xuzhou, Jiangsu, China
†These authors contributed equally to this work.
IJOCTA, 025160085 https://doi.org/10.36922/IJOCTA025160085
Received: 19 April 2025 | Revised: 25 July 2025 | Accepted: 28 July 2025 | Published online: 20 August 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This article presents a novel control approach for robust fixed-time trajectory tracking in nonlinear dynamic systems affected by external disturbances and model uncertainties, utilizing a fixed-time disturbance observer. Initially, a new fast disturbance observer was designed to reliably estimate external disturbances and model uncertainties within a fixed timeframe, independent of initial conditions and without requiring strict assumptions about the nature of these disturbances and uncertainties. Based on the disturbance estimates, a new robust fixed-time trajectory tracking sliding mode control strategy was developed, incorporating a fixed-time sliding variable and a reaching law with a state-dependent exponent coefficient. Using Lyapunov-based analysis, it is proven that the tracking errors of the closed-loop system converge to a neighborhood of the origin within a fixed time, independent of the initial conditions. Finally, comprehensive simulations were conducted to validate the effectiveness of the proposed strategy, demonstrating its advantages in achieving fast convergence, avoiding singularities, reducing chattering, and compensating for model uncertainties and external disturbances.

Keywords
Fixed-time stability
Fixed-time disturbance observer
Sliding mode variable
Variable exponent coefficient
Funding
The authors would like to thank the Natural Science Funding of Fujian Province, China (Grant/Award Number: 2024J011561) for their support in this research.
Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of this article.
References
  1. Nikdel N, Badamchizadeh M, Azimirad V, Nazari M. Adaptive backstepping control for an n-degree of freedom robotic manipulator based on combined state augmentation. Rob Comput Integr Manuf. 2017;44:129-143. https://doi.org/10.1016/j.rcim.2016.08.007

 

  1. Aslam MS, Tiwari P, Pandey HM, Band SS, El Sayed H. A delayed Takagi–Sugeno fuzzy control approach with uncertain measurements using an extended sliding mode observer. Inf Sci (NY). 2023;643:119204. https://doi.org/10.1016/j.ins.2023.119204

 

  1. Aslam MS, Zhenhua M, Ullah R, Li Y, Sheng A, Majid A. Stability and admissibility analysis of T–S descriptive systems and its applications. Soft Comput. 2022;26(15):7159-7166. https://doi.org/10.1007/s00500-022-07323-1

 

  1. Purwar S, Kar IN, Jha AN. Adaptive output feed- back tracking control of robot manipulators using position measurements only. Expert Syst Appl. 2008;34(4):2789-2798. https://doi.org/10.1016/j.eswa.2007.05.030

 

  1. Shojaei K, Shahri AM, Tarakameh A. Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties. Rob Comput Integr Manuf. 2011;27(1):194-204. https://doi.org/10.1016/j.rcim.2010.07.007

 

  1. Kaveh A, Vahedi M, Gandomkar M. Improving the performance of a chaotic nonlinear system of fractional-order brushless direct current electric motor using fractional-order sliding mode control. Int J Optim Control: Theor Appl. 2025;15(3): 379-395. https://doi.org/10.36922/ijocta.8407

 

  1. Yavuz M, O¨ ztu¨rk M, Ya¸skıran B. Comparison of fractional order sliding mode controllers on robot manipulator. Int J Optim Control: Theor Appl. 2025;15(2):281-293. https://doi.org/10.36922/ijocta.1678

 

  1. Mohan Raja M, Vijayakumar V, Veluvolu KC, Shukla A, Nisar KS. Existence and optimal control results for Caputo fractional delay Clark’s sub differential inclusions of order r (1,2) with sectorial operators. Optim Control Appl Methods. 2024;45(4):1832-1850. https://doi.org/10.1002/oca.3125

 

  1. Raja MM, Vijayakumar V, Veluvolu KC. Improved order in Hilfer fractional differential systems: solvability and optimal control problem for hemivariational inequalities. Chaos Solitons Frac- tals. 2024;188:115558. https://doi.org/10.1016/j.chaos.2024.115558

 

  1. Shtessel Y, Edwards C, Fridman L, Levant A. Sliding Mode Control and Observation. Vol 10. Springer; 2014.

 

  1. Aslam MS, Qaisar I, Majid A, Ramaraj P. Design of sliding mode controller for sensor/actuator fault with unknown input observer for satellite control system. Soft Comput. 2021;25(24):14993- 15003. https://doi.org/10.1007/s00500-021-06420-x

 

  1. Ren C, Li X, Yang X, Ma S. Extended state observer-based sliding mode control of an omni- directional mobile robot with friction compensation. IEEE Trans Ind Electron. 2019;66(12):9480- 9489. https://doi.org/10.1109/TIE.2019.2892678

 

  1. Venkataraman S, Gulati S. Control of Nonlinear Systems Using Terminal Sliding Modes. IEEE;

 

  1. Zuo Z. Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl. 2015;9(4):545-552. https://doi.org/10.1049/iet-cta.2014.0202

 

  1. Ahmed S, Azar AT. Predefined-time fractional-order terminal SMC for robot dynamics. Int J Optim Control: Theor Appl. 2025;15(3):426-434. https://doi.org/10.36922/IJOCTA025060020

 

  1. Feng Y, Yu X, Man Z. Non-singular terminal sliding mode control of rigid manipulators. 2002;38(12):2159-2167. https://doi.org/10.1016/S0005-1098(02)00147-4

 

  1. Yu S, Yu X, Shirinzadeh B, Man Z. Continuous finite-time control for robotic manipulators with terminal sliding mode. 2005;41(11):1957-1964. https://doi.org/10.1016/j.automatica.2005.07.001

 

  1. Wang L, Chai T, Zhai L. Neural-network-based terminal sliding-mode control of robotic manipulators including actuator dynamics. IEEE Trans Ind Electron. 2009;56(9):3296-3304. https://doi.org/10.1109/TIE.2008.2011350

 

  1. Bakouri M, Alqarni A, Alanazi S, et al. Robust dynamic control algorithm for uncertain powered wheelchairs based on sliding neural net- work approach. AIMS Math. 2023;8(11):26821- 26839. https://doi.org/10.3934/math.20231373

 

  1. Ghasemi M, Nersesov SG. Finite-time coordination in multiagent systems using sliding mode control approach. 2014;50(4):1209- 1216. https://doi.org/10.1016/j.automatica. 2014.02.019

 

  1. Feng Y, Yu X, Han F. On nonsingular terminal sliding-mode control of nonlinear systems. 2013;49(6):1715-1722. https://doi.org/10.1016/j.automatica.2013.01.051

 

  1. Polyakov A. Nonlinear feedback design for fixed- time stabilization of linear control systems. IEEE Trans Autom Control. 2011;57(8):2106- 2110. https://doi.org/10.1109/TAC.2011.2179869

 

  1. Wang C, Tnunay H, Zuo Z, Lennox B, Ding Z. Fixed-time formation control of multirobot systems: design and experiments. IEEE Trans Ind Electron. 2018;66(8):6292-6301. https://doi.org/10.1109/TIE.2018.2870409

 

  1. Du H, Wen G, Wu D, Cheng Y, Lu¨J. Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems. 2020;113:108797. https://doi.org/10.1016/j.automatica.2019.108797

 

  1. Pan Y, Du P, Xue H, Lam HK. Singularity- free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst. 2020;29(8):2388-2398. https://doi.org/10.1109/TFUZZ.2020.2999746

 

  1. Golestani M, Esmaeilzadeh SM, Mobayen S. Fixed-time control for high-precision attitude stabilization of flexible spacecraft. Eur J Control. 2021;57:222-231. https://doi.org/10.1016/j.ejcon.2020.05.006

 

  1. Zhang L, Wei C, Jing L, Cui N. Fixed-time sliding mode attitude tracking control for a submarine- launched missile with multiple disturbances. Non- linear Dyn. 2018;93:2543-2563. https://doi.org/10.1007/s11071-018-4341-8

 

  1. Ni J, Liu L, Liu C, Hu X, Li S. Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Exp Briefs. 2016;64(2):151-155. https://doi.org/10.1109/TCSII.2016.2551539

 

  1. Wang L, Du H, Zhang W, Wu D, Zhu W. Implementation of integral fixed-time sliding mode controller for speed regulation of PMSM servo system. Nonlinear Dyn. 2020;102:185-196. https://doi.org/10.1007/s11071-020-05938-3

 

  1. Zuo Z, Tie L. A new class of finite-time nonlinear consensus protocols for multi-agent systems. Int J Control. 2014;87(2):363-370. https://doi.org/10.1080/00207179.2013.834484

 

  1. Chen C, Li L, Peng H, et al. A new fixed-time stability theorem and its application to the fixed- time synchronization of neural networks. Neural Netw. 2020;123:412-419. https://doi.org/10.1016/j.neunet.2019.12.028

 

  1. Zhao L, Jia Y. Decentralized adaptive attitude synchronization control for spacecraft formation using nonsingular fast terminal sliding mode. Nonlinear Dyn. 2014;78:2779-2794. https://doi.org/10.1007/s11071-014-1625-5

 

  1. Chen M, Wu QX, Cui RX. Terminal sliding mode tracking control for a class of SISO uncertain non- linear systems. ISA Trans. 2013;52(2):198-206. https://doi.org/10.1016/j.isatra.2012.09.009

 

  1. Yang J, Li S, Yu X. Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans Ind Electron. 2012;60(1):160-169. https://doi.org/10.1109/TIE.2012.2183841

 

  1. Hua C, Li J, Yang Y, Guan X. Extended-state- observer-based finite-time synchronization control design of teleoperation with experimental validation. Nonlinear Dyn. 2016;85:317-331. https://doi.org/10.1007/s11071-016-2687-3

 

  1. Li S, Sun H, Yang J, Yu X. Continuous finite- time output regulation for disturbed systems under mismatching condition. IEEE Trans Autom 2014;60(1):277-282. https://doi.org/10.1109/TAC.2014.2324212

 

  1. Chen WH, Yang J, Guo L, Li S. Disturbance- observer-based control  and  related methods—an overview. IEEE Trans Ind Electron. 2015;63(2):1083-1095. https://doi.org/10.1109/TIE.2015.2478397

 

  1. Zhang L, Wei C, Wu R, Cui N. Fixed-time ex- tended state observer based non-singular fast terminal sliding mode control for a VTVL reusable launch vehicle. Aerosp Sci Technol. 2018;82:70-79. https://doi.org/10.1016/j.ast.2018.08.028

 

  1. Ding B, Xu D, Jiang B, Shi P, Yang W. Disturbance-observer-based terminal sliding mode control for linear traction system with prescribed performance. IEEE Trans Transp Electrific. 2020;7(2):649-658. https://doi.org/10.1109/TTE.2020.3027367

 

  1. Zhang CH, Yang GH. Event-triggered global finite-time control for a class of uncertain non- linear systems. IEEE Trans Autom Control. 2019;65(3):1340-1347. https://doi.org/10.1109/TAC.2019.2928767

 

  1. Liu S, Niu B, Zong G, Zhao X, Xu N. Adaptive fixed-time hierarchical sliding mode control for switched under-actuated systems with dead- zone constraints via event-triggered strategy. Appl Math Comput. 2022;435:127441. https://doi.org/10.1016/j.amc.2022.127441

 

  1. Wu Y, Li G, Zuo Z, Liu X, Xu P. Practical fixed-time position tracking control of permanent magnet DC torque motor systems. IEEE/ASME Trans Mechatron. 2020;26(1):563-573. https://doi.org/10.1109/TMECH.2020.3042806

 

  1. Cao S, Sun L, Jiang J, Zuo Z. Reinforcement learning-based fixed-time trajectory tracking control for uncertain robotic manipulators with input saturation. IEEE Trans Neural Netw Learn Syst. 2021;34(8):4584-4595. https://doi.org/10.1109/TNNLS.2021.3116713

 

  1. Rezaei E, Bolandi H, Fathi M. Designing a fixed- time observer-based adaptive non-singular sliding mode controller for flexible spacecraft. ISA Trans. 2024;148:32-44. https://doi.org/10.1016/j.isatra.2024.03.025

 

  1. Yang C, Teng T, Xu B, Li Z, Na J, Su CY. Global adaptive tracking control of robot manipulators using neural networks with finite-time learning convergence. Int J Control Autom Syst. 2017;15(4):1916-1924. https://doi.org/10.1007/s12555-016-0515-7

 

  1. Li H, Cai Y. On SFTSM control with fixed- time convergence. IET Control Theory Appl. 2017;11(6):766-773. https://doi.org/10.1049/iet-cta.2016.1457

 

  1. Yang L, Yang J. Nonsingular fast terminal sliding- mode control for nonlinear dynamical systems. Int J Robust Nonlinear Control. 2011;21(16):1865- 1879. https://doi.org/10.1002/rnc.1666

 

  1. Moulay E, L´echapp´e V, Bernuau E, Plestan F. Robust fixed-time stability: Application to sliding-mode control. IEEE Trans Autom Control. 2021;67(2):1061-1066. https://doi.org/10.1109/TAC.2021.3069667

 

  1. Zhai J, Xu G. A novel non-singular terminal sliding mode trajectory tracking control for robotic manipulators. IEEE Trans Circuits Syst II Exp Briefs. 2020;68(1):391-395. https://doi.org/10.1109/TCSII.2020.2999937

 

  1. Boukattaya M, Mezghani N, Damak T. Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems. ISA Trans. 2018;77:1-19. https://doi.org/10.1016/j.isatra.2018.04.007
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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