Analysis and Control of a Three-Dimensional Autonomous Chaotic System

Authors

Abdollah Gholizadeh, Department of Applied Mathematics, Hakim sabzevari University, Sabzevar, IranFollow
Hassan Saberi Nik, Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, IranFollow
Amin Jajarmi, Department of Electrical Engineering, University of Bojnord, Bojnord, IranFollow

Author Country (or Countries)

Iran

Abstract

In this paper, a novel three-dimensional (3D) autonomous chaotic system is investigated, which displays complicated dynamical behaviors. Basic dynamical properties are analyzed by means of phase portraits and equilibria. Also, an optimal control law is designed for the novel chaotic system, based on the Pontryagin minimum principle (PMP). Furthermore, an adaptive and feedback control law is introduced to stabilize the new chaotic system with unknown parameters. The adaptive control results are established using the Lyapunov stability theory. Numerical simulations are included to demonstrate the efficiency and high accuracy of the proposed method.

Recommended Citation

Gholizadeh, Abdollah; Saberi Nik, Hassan; and Jajarmi, Amin (2015) "Analysis and Control of a Three-Dimensional Autonomous Chaotic System," Applied Mathematics & Information Sciences: Vol. 09: Iss. 2, Article 22.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss2/22