This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.
We announce a new 4D hyperchaotic system with four parameters. The dynamic properties of the proposed hyperchaotic system are studied in detail; the Lyapunov exponents, Kaplan-Yorke dimension, bifurcation, and bicoherence contours of the novel hyperchaotic system are derived. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems with unknown parameters using sliding mode controllers and genetically optimized PID controllers. The stabilities of the controllers and parameter update laws are proved using Lyapunov stability theory. Use of the optimized PID controllers ensures less time of convergence and fast synchronization speed. Finally the proposed novel hyperchaotic system is realized in FPGA.
In this paper, we investigate the control of 4-D nonautonomous fractional-order uncertain model of a PI speed-regulated current-driven induction motor (FOIM) using a fractional-order adaptive sliding mode controller (FOASMC). First, we derive a dimensionless fractional-order model of the induction motor from the well-known integer -model of the induction motor. Various dynamic properties of the fractional-order induction motor, such as stability of the equilibrium points, Lyapunov exponents, bifurcation, and bicoherence, are investigated. An adaptive controller is derived to suppress the chaotic oscillations of the fractional-order model of the induction motor. Numerical simulations of the adaptive chaos suppression methodology are depicted for the fractional-order uncertain model of the induction motor to validate the analytical results of this work. A genetically optimized fractional-order PID (FOPID) controller is also derived to stabilize the states of the FOIM system. FPGA implementation of the proposed FOASMC is also presented to show that the proposed controller is hardware realizable.
In this paper, we introduce a novel integer-order memristor-modified Shinriki circuit (MMSC). We investigate the dynamic properties of the MMSC system and the existence of chaos is proved with positive largest Lyapunov exponent. Bifurcation plots are derived to analyze the parameter dependence of the MMSC system. The fractional-order model of the MMSC system (FOMMSC) is derived and the bifurcation analysis of the FOMMSC system with the fractional orders is carried out. Fractional-order adaptive sliding-mode controllers (FOASMCs) and genetically optimized PID controllers are designed to synchronize identical FOMMSC systems with unknown parameters. Numerical simulations are conducted to validate the theoretical results. FPGA implementation of the FOASMC controllers is presented to show that the proposed control algorithm is hardware realizable. MMSC has trigonometric functions which make the system more complex and the optimization and synchronization of such systems in the integer order itself are harder, so the paper does the same in fractional order. The proposed system is a memristive circuit which can show special features such as multistability, hyperchaos, and multiscroll attractor. Such a system with these features is very rare in the literature.
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