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Research Papers

Control Analysis of Rucklidge Chaotic System

[+] Author and Article Information
Muhammad Marwan

Department of Applied Mathematics
and Statistics,
Institute of Space Technology,
Islamabd 44000, Pakistan
e-mail: marwan78642@gmail.com

Salman Ahmad

Department of Applied Mathematics
and Statistics,
Institute of Space Technology,
Islamabd 44000, Pakistan
e-mail: salmanbzm@gmail.com

Muhammad Aqeel

Department of Applied Mathematics
and Statistics,
Institute of Space Technology,
Islamabd 44000, Pakistan
e-mail: medraqeel@gmail.com

Muhammad Sabir

Department of Applied Mathematics
and Statistics,
Institute of Space Technology,
Islamabd 44000, Pakistan
e-mail: ghssabir86@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 23, 2018; final manuscript received November 12, 2018; published online December 19, 2018. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 141(4), 041010 (Dec 19, 2018) (7 pages) Paper No: DS-18-1249; doi: 10.1115/1.4042030 History: Received May 23, 2018; Revised November 12, 2018

In this paper, we designed multiple control inputs for Rucklidge oscillator through sliding, adaptive, and backstepping control techniques. Dynamical stability through Lyapunov theory is discussed to check whether the above‐mentioned nonlinear dynamical system is stable or not for defined controller. Based on error dynamics, adaptive and sliding control techniques are used such that solution approaches to its stable state with time. Furthermore, simulation results of nonlinear Rucklidge system are included in this paper to confirm controlled results and to analyze applied techniques. A brief analysis of these techniques for considered dynamical system is an integral part of the paper.

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Figures

Grahic Jump Location
Fig. 1

Phase portrait of chaotic Rucklidge oscillator

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Fig. 2

Time history map of chaotic Rucklidge oscillator

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Fig. 3

Phase portrait of Rucklidge oscillator (sliding control technique)

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Fig. 4

Time history of Rucklidge oscillator (sliding control technique)

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Fig. 5

Phase portrait of Rucklidge oscillator (adaptive control technique)

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Fig. 6

Time history of Rucklidge oscillator (adaptive control technique)

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Fig. 7

Phase portrait of Rucklidge oscillator (backstepping control technique)

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Fig. 8

Time history of Rucklidge oscillator (backstepping control technique)

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Fig. 9

State variable x for controlled Rucklidge oscillator

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Fig. 10

State variable y for controlled Rucklidge oscillator

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Fig. 11

State variable z for controlled Rucklidge oscillator

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