Karthikeyan Rajagopal

Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control

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.

Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

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.

Hyperchaotic Chameleon: Fractional Order FPGA Implementation

There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA) implementations of the systems with their power and resource utilization are presented.

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

Abstract Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.

Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

We investigate the chaotic oscillations in a fractional order model of a portal frame with nonideal loading. The bifurcation of the fractional order portal frame system for parameters and fractional orders are investigated. Bicoherence analysis shows the existence of quadratic nonlinearities. Fractional order adaptive sliding mode controllers are designed to suppress the chaotic oscillations with uncertain parameters. Power efficiency analysis of the FPGA implemented control scheme shows the maximum power utilization in the fractional order showing the largest Lyapunov exponent.

LabVIEW implementation of chaotic masking with adaptively synchronised forced Van der Pol oscillators and its application in real-time image encryption

Chaotic oscillators find many applications in the field of cryptography and secure communication engineering. This paper first details one such approach of applying a forced Van der Pol chaotic oscillator and its synchronised slave model in chaotic masking and image encryption. This approach applies the chaotic masking to the secondary image and thus changing the image pixels and the masked image is used for encoding the original image. We have developed a real-time image encryption algorithm by capturing pictures through the NI IMAQdx tools. The proposed model is implemented in LabVIEW and experimentally verified for the efficiency of the encryption algorithm.

Chaos Suppression in Fractional Order Permanent Magnet Synchronous Motor and PI controlled Induction motor by Extended Back stepping Control

Abstract In this paper we investigate the control of three-dimensional non-autonomous fractional-order model of a permanent magnet synchronous motor (PMSM) and PI controlled fractional order Induction motor via recursive extended back stepping control technique. A robust generalized weighted controllers are derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results.

Hyperchaotic Memcapacitor Oscillator with Infinite Equilibria and Coexisting Attractors

A newly introduced charge-controlled memcapacitor-based hyperchaotic oscillator with coexisting chaotic attractors is investigated. Dynamic analysis of the oscillator shows that it has infinite number of equilibrium points and shows multistability. Its multistability analysis in the parameter space shows the existence of chaotic and hyperchaotic attractors. Fractional-order analysis of the hyperchaotic oscillator shows that the hyperchaos remains in the fractional order too. Field programmable gate arrays are used to realize the proposed oscillator.

Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization using Sliding Mode Control

Abstract Most of the Real systems shows chaotic behavior when they approach complex states. Especially in physical and chemical systems these behaviors define the character of the system. The control of these chaotic behaviors is of very high practical importance and hence mathematical models of these chaotic systems proves vital in deciding the control structures. One such model of chemical reactors is the Willamowski–Rössler system (WR). In this paper we derive a fractional order sliding mode control scheme where the states of the WR system are driven back to the defined equilibrium points. We have also synchronized master and slave fractional order WR system using sliding mode control. As the entire control law is defined in fractional order, we derived a new methodology to prove the stability of the controller. The numerical simulation and analysis are achieved with LabVIEW.