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Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design

Pham Viet-Thanh, Vaidyanathan Sundarapandian, Volos Christos, Jafari Sajad, Alsaadi Fawaz E., Alsaadi Fuad E.

Archives of Control Sciences

2019

Vol. 29, No. 1

73--96

We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap system displays chaotic attractors, which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.

A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design

Vaidyanathan S., Jafari S., Pham V.-T., Azar A. T., Alsaadi F. E.

Archives of Control Sciences

2018

Vol. 28, No. 2

239--254

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor.