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