Research Article
Optimization of the Parameters of RISE Feedback Controller
Using Genetic Algorithm
Fayiz Abu Khadra,
1
Jaber Abu Qudeiri,
2
and Mohammed Alkahtani
3
1
Faculty of Engineering, King Abdulaziz University, Rabigh 21911, Saudi Arabia
2
Princess Fatima Alnijiris’s Research Chair for Advanced Manufacturing Technology (FARCAMT), King Saud University,
Riyadh 11421, Saudi Arabia
3
Industrial Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia
Correspondence should be addressed to Jaber Abu Qudeiri; jqudeiri@ksu.edu.sa
Received 4 March 2016; Revised 22 May 2016; Accepted 7 June 2016
Academic Editor: Yan-Jun Liu
Copyright © 2016 Fayiz Abu Khadra et al. Tis is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
A control methodology based on a nonlinear control algorithm and optimization technique is presented in this paper. A controller
called “the robust integral of the sign of the error” (in short, RISE) is applied to control chaotic systems. Te optimum RISE
controller parameters are obtained via genetic algorithm optimization techniques. RISE control methodology is implemented on
two chaotic systems, namely, the Dufng-Holms and Van der Pol systems. Numerical simulations showed the good performance of
the optimized RISE controller in tracking task and its ability to ensure robustness with respect to bounded external disturbances.
1. Introduction
Chaos is the complex, unpredictable, and irregular behavior
of systems. Te response of a chaotic system is sensitive to a
change in its initial conditions. Chaos can be found in many
applications such as oscillators, biology, chemical reactions,
robotics, lasers, and many other applications. For example,
Kengne et al. [1] considered the dynamics and synchroniza-
tion of improved Colpitts oscillators designed to operate in
ultrahigh frequency range. Also, two-well Dufng oscillator
with nonlinear damping term proportional to the power of
velocity was considered in [2]. Novel swarm dynamics and
their applications in automated multiagent systems biology
were presented [3]. Also, application of chaos theory to the
molecular biology of aging was presented [4]. For chemical
reactions, Petrov et al. [5] applied map-based, proportional-
feedback algorithm to stabilize the behavior in the chaotic
regime of an oscillatory chemical system. Gaspard [6] showed
that, for diferent chemical reactions, the reaction rate can
be related to the characteristic quantities of chaos. In the
feld of robotics, Volos et al. [7] experimentally investigated
the coverage performance of a chaotic autonomous mobile
robot. A smart scheme for chaotic signal generation in a
semiconductor ring laser with optical feedback was proposed
in [8].
Many studies have been conducted to analyze and control
chaotic systems. Chaotic systems are utilized as a benchmark
for testing the performance of controller. Diferent control
techniques have been tried to control uncertain nonlinear
systems. Shi et al. [9] designed adaptive delay feedback
controllers to control and suppress chaos in ultrasonic motor
speed control system. In [10], a nonlinear feedback lineariza-
tion control method combined with a modifed adaptive
control strategy was designed to synchronize the two unidi-
rectional coupled neurons and stabilize the chaotic trajectory
of the slave system to desired periodic orbit of the master
system. Sundarapandian [11] proposed explicit state feedback
control laws to regulate the output of the Tigan system so as
to track constant reference signals. Furthermore, a new state
feedback control law to regulate the output of the Sprott-G
chaotic system was derived [12]. Also, Yu et al. [13] proposed
a fuzzy adaptive control approach based on a modular design
for uncertain chaotic Dufng oscillators. In [14], sliding mode
adaptive controllers were proposed for synchronization of
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2016, Article ID 3863147, 9 pages
http://dx.doi.org/10.1155/2016/3863147