Citation: Maaruf, M.; Hamanah,
W.M.; Abido, M.A. Hybrid
Backstepping Control of a Quadrotor
Using a Radial Basis Function Neural
Network. Mathematics 2023, 11, 991.
https://doi.org/10.3390/
math11040991
Academic Editors: Krzysztof Ejsmont,
Aamer Bilal Asghar, Yong Wang and
Rodolfo Haber
Received: 4 January 2023
Revised: 6 February 2023
Accepted: 8 February 2023
Published: 15 February 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Hybrid Backstepping Control of a Quadrotor Using a Radial
Basis Function Neural Network
Muhammad Maaruf
1
, Waleed M. Hamanah
2,3
and Mohammad A. Abido
2,4,5,
*
1
Control and Instrumentation Engineering Department, Center for Smart Mobility and Logistics,
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2
Interdisciplinary Research Center of Renewable Energy and Power Systems (IRC-REPS),
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
3
Applied Research Center for Metrology, Standards and Testing (ARC-MST),
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4
Department of Electrical Engineering, College of Engineering and Physics,
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
5
K.A.CARE Energy Research & Innovation Center, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
* Correspondence: mabido@kfupm.edu.sa
Abstract:
This article presents a hybrid backstepping consisting of two robust controllers utilizing the
approximation property of a radial basis function neural network (RBFNN) for a quadrotor with time-
varying uncertainties. The quadrotor dynamic system is decoupled into two subsystems: the position
and the attitude subsystems. As part of the position subsystem, adaptive RBFNN backstepping
control (ANNBC) is developed to eliminate the effects of uncertainties, trace the quadrotor’s position,
and provide the desired roll and pitch angles commands for the attitude subsystem. Then, adaptive
RBFNN backstepping is integrated with integral fast terminal sliding mode control (ANNBIFTSMC)
to track the required Euler angles and improve robustness against external disturbances. The
proposed technique is advantageous because the quadrotor states trace the reference states in a short
period of time without requiring knowledge of dynamic uncertainties and external disturbances. In
addition, because the controller gains are based on the desired trajectories, adaptive algorithms are
used to update them online. The stability of a closed loop system is proved by Lyapunov theory.
Numerical simulations show acceptable attitude and position tracking performances.
Keywords:
quadrotor; radial basis function neural network; backstepping; adaptive control; integral
fast terminal sliding mode control
MSC: 93-10
1. Introduction
Quadrotors have a simple mechanical structure and lighter weight, which enable
them to perform aggressive operation, hovering, vertical take-up, and landing [
1
,
2
]. Many
remarkable applications are accomplished using quadrotor platforms, such as aerial cine-
matography, mapping, payload delivery, and rescue mission surveillance, to name just a
few [
3
–
5
]. A control system architecture for achieving the practical application of quadro-
tors is one of the key problems that must be discussed. Without a strong control system,
the quadrotors would be seriously limited in operation. Therefore, several studies on the
design of the quadrotor control system have been carried out.
In the early stages of quadrotor control research, linear control techniques such as
linear quadratic regulator (LQR) and proportional derivative integral (PID) control [6–11]
were adopted. Both PID and LQR are linear control strategies and were used to stabilize
the quadrotor attitude and position by linearizing the dynamics of the quadrotor near some
operating points. As a result, the performances of the quadrotor, such as the robustness
Mathematics 2023, 11, 991. https://doi.org/10.3390/math11040991 https://www.mdpi.com/journal/mathematics
