Synchronisation of Unified Chaotic Systems Using Modified Nonlinear Active Control: Circuit Design, Implementation, and Secure Communication

Abstract

This paper accounts synchronisation of unified chaotic systems using a modified nonlinear active control technique, its circuit analogue circuit implementation, and secure communication. The proposed nonlinear active control approach utilises appropriate states of the unified chaotic systems. The modified nonlinear active control leads to the coupled error dynamics and does not require the external forcing parameters or gains, which differs from the active control techniques reported in the literature. The designed control law ensures the asymptotic stability in large, and the necessary condition is derived using Lyapunov stability theory. Further, the performance of the designed nonlinear active controller is compared based on different time integral performance of the errors with active, adaptive, and sliding mode control techniques. Numerical and circuit simulations are performed in MATLAB and NI-Multisim environments, respectively. Circuit simulated results accord to MATLAB simulation results. Further, unified chaotic system, its synchronisation, and application to secure communication are validated with breadboard circuit/hardware implementation.

KEYWORDS:

• Active control
• Analogue circuits
• Chaos
• Chaotic communication
• Lyapunov methods
• Lyapunov stability theory
• Nonlinear control systems
• Nonlinear systems
• Synchronisation
• Unified chaotic system

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The TEQIP-III Minor Research Grant supports this research work at the, National Institute of Technology Meghalaya (Sanctioned Project Ref. No. NITMGH/TEQIP-III/MP/2019-20/269, dated 30/11/2019).

Notes on contributors

Anand Kumar

Anand Kumar received MTech degree from the Department of Electrical Engineering at the National Institute of Technology, Meghalaya, Shillong, India in 2018. Currently, he is pursuing PhD from Indian Institute of Science, Bangalore, India. His research interest includes control systems, analogue circuit design, nonlinear control systems, and power electronics. Email: [email protected]

Piyush P. Singh

Piyush P Singh has received PhD degree in specialisation control and industrial automation in the Electrical Engineering Department at NIT Silchar, Assam in 2016. Presently, he is assistant professor in Electrical Engineering Department, NIT Meghalaya, Shillong, India. He has research interest in control systems, chaos synchronisation, chaos and nonlinear dynamics, chaos behaviour in power systems, smart grid, biological system, and control of complex networks. He has published more than 45 research papers in reputed, SCI and Scopus indexed journals and conferences. He is a senior member of IEEE Society and a Life Member of the Institute of Engineers (IE).