Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters

Volume 23, Issue 2, pp 124--135 http://dx.doi.org/10.22436/jmcs.023.02.05
Publication Date: October 22, 2020 Submission Date: March 13, 2020 Revision Date: June 03, 2020 Accteptance Date: August 17, 2020

Authors

Muhammad Haris - Center of Foundation Studies, University of Buraimi, Al Buraimi, Oman. - Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Kedah, Malaysia. Muhammad Shafiq - Department of Electrical and Computer Engineering, Sultan Qaboos University, Muscat, Oman. Adyda Ibrahim - Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Kedah, Malaysia. Masnita Misiran - Department of Mathematics and Statistics, School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Kedah, Malaysia.


Abstract

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.


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ISRP Style

Muhammad Haris, Muhammad Shafiq, Adyda Ibrahim, Masnita Misiran, Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters, Journal of Mathematics and Computer Science, 23 (2021), no. 2, 124--135

AMA Style

Haris Muhammad, Shafiq Muhammad, Ibrahim Adyda, Misiran Masnita, Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters. J Math Comput SCI-JM. (2021); 23(2):124--135

Chicago/Turabian Style

Haris, Muhammad, Shafiq, Muhammad, Ibrahim, Adyda, Misiran, Masnita. "Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters." Journal of Mathematics and Computer Science, 23, no. 2 (2021): 124--135


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