Page 128 - IJOCTA-15-4

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.4, pp.670-685 (2025)
https://doi.org/10.36922//IJOCTA025160085

RESEARCH ARTICLE

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

2*
1†
3†
Zeeshan Anjum , Wen-Jer Chang , Muhammad Shamrooz Aslam , and Rizwan Ullah 1†
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
zeeshananjum139@outlook.com, wjchangntou@gmail.com, shamroz aslam@cumt.edu.cn, rizwan@qzuie.edu.cn

ARTICLE INFO ABSTRACT
Article History:
Received: April 19, 2025 This article presents a novel control approach for robust fixed-time trajectory
1st revised: July 9, 2025 tracking in nonlinear dynamic systems affected by external disturbances and
2 revised: July 25, 2025 model uncertainties, utilizing a fixed-time disturbance observer. Initially, a
Accepted: July 28, 2025 new fast disturbance observer was designed to reliably estimate external dis-
Published Online: August 20, 2025 turbances and model uncertainties within a fixed timeframe, independent of
Keywords: initial conditions and without requiring strict assumptions about the nature
Fixed-time stability of these disturbances and uncertainties. Based on the disturbance estimates,
Fixed-time disturbance observer a new robust fixed-time trajectory tracking sliding mode control strategy was
Sliding mode variable developed, incorporating a fixed-time sliding variable and a reaching law with
Variable exponent coefficient a state-dependent exponent coefficient. Using Lyapunov-based analysis, it is
proven that the tracking errors of the closed-loop system converge to a neigh-
AMS Classification:
borhood of the origin within a fixed time, independent of the initial conditions.
93C85, 93C41
Finally, comprehensive simulations were conducted to validate the effectiveness
of the proposed strategy, demonstrating its advantages in achieving fast conver-
gence, avoiding singularities, reducing chattering, and compensating for model
uncertainties and external disturbances.

1. Introduction Sliding mode control, a part of the variable
structure control family, is characterized by mod-
ifications in the control law structure as system
dynamics evolve over time. 10,11 It is well-known
Nonlinear dynamical systems often experience a for its effectiveness in mitigating system imperfec-
decline in performance due to uncertainties and tions. A recent work 12 proposed an SMC law that
external disturbances. Various nonlinear control guarantees asymptotic convergence of trajectory
1
methods, such as backstepping control, intelli- tracking errors. However, while linear SMC en-
gent control, 2,3 feedback linearization control, 4,5 sures asymptotic convergence of the system state,
sliding mode control (SMC), 6,7 and optimal it does not specify the convergence time. To ad-
control, 8,9 have been developed to optimize con- dress this limitation, the terminal SMC method
trol effectiveness in complex systems affected by was introduced in Venkataraman and Gulati, 13
model uncertainties and external disturbances.
†
These authors contributed equally to this work.
*Corresponding Author
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