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Mathematical Problems in Engineering
Volume 2017, Article ID 7307452, 14 pages
Research Article

Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control

1Centre for Nonlinear Dynamics, Defense University, Bishoftu, Ethiopia
2Department of Electronics, Faculty of Technology, Intelligent Systems Laboratory, Faculty of Engineering Sciences, Ferhat Abbas University, Setif, Algeria
3Research and Development Centre, Vel Tech University, Chennai, India
4Department of Electronics Engineering, Chennai Institute of Technology, Chennai, India

Correspondence should be addressed to Karthikeyan Rajagopal; moc.liamg@nayekeihtrakr

Received 29 September 2016; Revised 2 November 2016; Accepted 8 November 2016; Published 19 February 2017

Academic Editor: Chuangxia Huang

Copyright © 2017 Karthikeyan Rajagopal et al. This 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.


We announce a new 4D hyperchaotic system with four parameters. The dynamic properties of the proposed hyperchaotic system are studied in detail; the Lyapunov exponents, Kaplan-Yorke dimension, bifurcation, and bicoherence contours of the novel hyperchaotic system are derived. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems with unknown parameters using sliding mode controllers and genetically optimized PID controllers. The stabilities of the controllers and parameter update laws are proved using Lyapunov stability theory. Use of the optimized PID controllers ensures less time of convergence and fast synchronization speed. Finally the proposed novel hyperchaotic system is realized in FPGA.