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Tytuł artykułu

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Autorzy
Vaidyanathan S.
Treść / Zawartość
Pełne teksty:
Vaidyanathan_a_new_ACS_3_2017.pdf
Identyfikatory
DOI
10.1515/acsc-2017-0026
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.
Słowa kluczowe
EN
Wydawca
Polish Academy of Sciences, Committee of Automatic Control and Robotics
Czasopismo
Archives of Control Sciences
Rocznik
2017
Tom
Vol. 27, no. 3
Strony
409--439
Opis fizyczny
Bibliogr. 146 poz., wykr., wzory
Twórcy
autor
Vaidyanathan S.
sundarvtu@gmail.com
  • Research and Development Centre, Vel Tech University, Avadi, Chennai-600062, Tamil Nadu, India
Bibliografia
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Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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