Details

Title

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Journal title

Archives of Control Sciences

Yearbook

2016

Numer

No 3

Publication authors

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title> <jats:p>A hyperjerk system is a dynamical system, which is modelled by an <jats:italic>n</jats:italic>th order ordinary differential equation with <jats:italic>n</jats:italic> ≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of <jats:italic>n</jats:italic> first order ordinary differential equations with <jats:italic>n</jats:italic> ≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as <jats:italic>L</jats:italic><jats:sub>1</jats:sub> = 0.14219, <jats:italic>L</jats:italic><jats:sub>2</jats:sub> = 0.04605, <jats:italic>L</jats:italic><jats:sub>3</jats:sub> = 0 and <jats:italic>L</jats:italic><jats:sub>4</jats:sub> = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as <jats:italic>D<jats:sub>KY</jats:sub></jats:italic> = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.</jats:p>

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

ISSN 1230-2384

References

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DOI

10.1515/acsc-2016-0018

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