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Megastability; chaotic oscillator; contraction theory; backstepping controller; nonlinear active controller; synchronisation.

This paper reports a modified 2D periodically forced oscillator. Numerical simulation results using the phase portrait and Lyapunov exponents’ spectrum say that the proposed oscillator depicts megastability. Offset boosting in the new system is shown using the variable boostable phenomenon. Very limited research is available on such type of oscillator. Further, in this paper, a controller based on contraction theory is designed for the synchronisation between the two identical modified chaotic oscillators. The performances of the designed controller are compared with two widely used and well-known controllers for the chaotic systems. These controllers are (i) nonlinear active controller (NAC) and (ii) backstepping controller (BSC). It is found that the contraction theory-based controller performs better in terms of the less synchronisation time, negligible steady-state error and low control energy. Further, synchronisation between two identical Rossler chaotic systems is also presented to validate the effectiveness of the contraction theory. The simulation results validate the objectives of this paper.

J P SINGH¹ S JAFARI² A J M KHALAF³ V-T PHAM⁴ B K ROY⁵

1. Department of Electrical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440 010, India
2. Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran
3. Ministry of Higher Education and Scientific Research, Baghdad, Iraq
4. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam
5. Electrical Engineering Department, National Institute of Technology Silchar, Silchar 788 010, India

Published

28 August 2020

Manuscript received

16 December 2019

Manuscript revised

13 May 2020

Accepted

18 June 2020

Final version published online

28 August 2020