Page 186 - IJOCTA-15-4

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.4, pp.728-737 (2025)
https://doi.org/10.36922/IJOCTA025180091

RESEARCH ARTICLE

Model reference adaptive control based time delay estimation with
RBF neural network for robot manipulators

Saim Ahmed 1,2* , Ahmad Taher Azar 1,2 , and Ibraheem Kasim Ibraheem 3,4

1
College of Computer and Information Sciences, Prince Sultan University, Riyadh, Saudi Arabia
2
Automated Systems and Computing Lab (ASCL), Prince Sultan University, Riyadh, Saudi Arabia
3
Department of Electrical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq
4
Department of Electronics and Communication Engineering, College of Engineering, Uruk University,
Baghdad, Iraq
sahmed@psu.edu.sa, aazar@psu.edu.sa, ibraheemki@coeng.uobaghdad.edu.iq
ARTICLE INFO ABSTRACT
Article History:
Received: May 1, 2025 In this paper, model-reference adaptive control (MRAC) with neural network
(NN) and time delay estimation (TDE) is proposed for controlling a robotic
Revised: July 4, 2025
manipulator. With more than two degrees of freedom (DoF) of the robot,
Accepted: July 18, 2025
the formulation of a known regression matrix is tedious and also difficult to
Published Online: September 4, 2025
compute for the different robotic systems. Therefore, this work introduces
Keywords: MRAC based on TDE with NN (MRAC-NNTDE) to achieve high-control per-
Model reference adaptive control, formance without prior knowledge of the regression matrix and offers a model-
Time delay estimation free scheme. Firstly, MRAC is applied to adjust the control gains, then TDE
Neural network is implemented to estimate the unknown dynamical robotic system, and NN
Robotic manipulator is employed to deal with the TDE estimation error. The overall stability of
AMS Classification 2010: the robotic dynamics is investigated using the Lyapunov theorem. In the end,
93D05; 93C95; 93C10; 70E60 computer simulations are compared to validate the effectiveness of the pro-
posed scheme.

1. Introduction been designed to improve joint position tracking
performance. 10,11
One of the most well-known control techniques Numerous robotics technologies make use of
in the field of control science and engineering is control system analysis and design. 12–14 In which,
model reference adaptive control (MRAC). De- MRAC has been widely used in robotic and
pending on the current state of the closed-loop aviation applications throughout the past few
system, MRAC either estimates the unknown pa- decades. 15 Furthermore, in the presence of non-
rameters or updates the control gain. 1,2 Both lin- linearities and outside disturbances, it is uti-
ear and nonlinear systems have been widely con- lized to precisely track the joint position of
3
3
trolled using this control technique. The adaptive uncertain robotic manipulators. Because it re-
scheme has been employed with well-known ad- quires a known regression matrix to deal with
vanced control techniques, for instance, H ∞ con- the unknown dynamics of robotic systems, 16 it
trol, sliding mode control (SMC), proportional- is quite difficult to calculate this known matrix
integral-derivative control (PID), neural net- for robotic manipulators with high degrees of
work (NN), and fuzzy logic control schemes, freedom (DOF). To address this challenge, re-
etc. 4–9 In addition, various MRAC schemes have searchers have proposed diverse adaptive control
*Corresponding Author
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