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.

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Dynamical analysis and triple compound combination anti-synchronization of novel fractional chaotic system

Journal of Vibration and Control ◽

10.1177/1077546320987733 ◽

2021 ◽

pp. 107754632098773

Author(s):

Pushali Trikha ◽

Lone S Jahanzaib ◽

Nasreen ◽

Dumitru Baleanu

Keyword(s):

Chaotic System ◽

Secure Communication ◽

Sliding Mode ◽

Dynamical Analysis ◽

Phase Portraits ◽

Adaptive Sliding Mode Control ◽

The Novel ◽

Novel Technique ◽

Analysis Phase ◽

Fractional Chaotic System

This study introduces a novel 3-D fractional chaotic system with two quadratic terms and no equilibrium point. Thorough dynamical analysis of the introduced system is done studying Lyapunov dynamics with respect to fractional order and parameter value, Kaplan–Yorke dimension, bifurcation analysis, phase portraits, existence, and uniqueness of solution, dissipative and symmetric character, etc. The novel system is anti-synchronized using the novel technique ‘triple compound combination’ considering uncertainties and disturbances on a parallel system by two methods—nonlinear and adaptive sliding mode control. A proposed application of achieved synchronization in secure communication is presented. A comparative study of obtained results with published literature is also presented.

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Analysis, Control and FPGA Implementation of a Fractional-Order Modified Shinriki Circuit

Journal of Circuits System and Computers ◽

10.1142/s0218126619502323 ◽

2019 ◽

Vol 28 (14) ◽

pp. 1950232 ◽

Cited By ~ 1

Author(s):

Karthikeyan Rajagopal ◽

Fahimeh Nazarimehr ◽

Laarem Guessas ◽

Anitha Karthikeyan ◽

Ashokkumar Srinivasan ◽

...

Keyword(s):

Fractional Order ◽

Sliding Mode ◽

Dynamic Properties ◽

Fpga Implementation ◽

Pid Controllers ◽

Largest Lyapunov Exponent ◽

Unknown Parameters ◽

Integer Order ◽

Sliding Mode Controllers ◽

Fractional Orders

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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Modified Projective Synchronization of Chaotic Systems with Unknown Parameters

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.128-129.1182 ◽

2011 ◽

Vol 128-129 ◽

pp. 1182-1185

Author(s):

Min Xiu Yan ◽

Li Ping Fan

Keyword(s):

Lyapunov Stability ◽

Chaotic Systems ◽

Sliding Mode ◽

Lyapunov Stability Theory ◽

Projective Synchronization ◽

Adaptive Sliding Mode Control ◽

Unknown Parameters ◽

Response System ◽

Uncertain Chaotic Systems ◽

Modified Projective Synchronization

This paper proposes the modified projective synchronization of uncertain chaotic systems with unknown parameters via active adaptive sliding mode control (AASMC). The disturbances are considered both in the drive and the response system. The bounds of the disturbances are unknown. The adaptive updating laws are designed to tackle the unknown parameters. Moreover, the robustness and stability of the proposed AASMC is proved by the Lyapunov stability theory. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed scheme.

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Robust Adaptive Sliding Mode Control for Generalized Function Projective Synchronization of Different Chaotic Systems with Unknown Parameters

Mathematical Problems in Engineering ◽

10.1155/2013/407436 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9

Author(s):

Xiuchun Li ◽

Jianhua Gu ◽

Wei Xu

Keyword(s):

Sliding Mode ◽

Lyapunov Stability Theory ◽

Projective Synchronization ◽

Adaptive Sliding Mode Control ◽

Generalized Function ◽

Unknown Parameters ◽

Adaptive Sliding Mode ◽

Function Projective Synchronization ◽

Response Systems ◽

Generalized Function Projective Synchronization

When the parameters of both drive and response systems are all unknown, an adaptive sliding mode controller, strongly robust to exotic perturbations, is designed for realizing generalized function projective synchronization. Sliding mode surface is given and the controlled system is asymptotically stable on this surface with the passage of time. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding controller is designed to ensure the occurrence of the sliding motion. Finally, numerical simulations are presented to verify the effectiveness and robustness of the proposed method even when both drive and response systems are perturbed with external disturbances.

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Chaos Suppression Using Genetically Optimized PID Control of the 4-D Novel Hyperchaotic Vaidyanathan System

Engineering, Technology & Applied Science Research ◽

10.48084/etasr.2394 ◽

2018 ◽

Vol 8 (6) ◽

pp. 3619-3623

Author(s):

G. Laarem ◽

A. Merbouha

Keyword(s):

Genetic Algorithms ◽

Impact Factor ◽

Dynamical Analysis ◽

Pid Controllers ◽

Hyperchaotic System ◽

The Novel ◽

Proportional Integral ◽

Fast Speed ◽

Chaos Suppression ◽

The Impact

In this paper, a dynamical analysis of the novel hyperchaotic system with four parameters is presented. Genetically optimized proportional integral and derivative (PID) controllers were designed and applied for the chaos suppression of the 4-D novel hyperchaotic system, by varying the genetic algorithms (GA) options to view the impact factor on the optimized PID controllers. The use of the final optimized PID controllers ensures less time of convergence and fast speed chaos suppression. In this paper, a dynamical analysis of the novel hyperchaotic system with four parameters is presented. Genetically optimized proportional integral and derivative (PID) controllers were designed and applied for the chaos suppression of the 4-D novel hyperchaotic system, by varying the genetic algorithms (GA) options to view the impact factor on the optimized PID controllers. The use of the final optimized PID controllers ensures less time of convergence and fast speed chaos suppression.

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Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Complexity ◽

10.1155/2020/5859273 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16 ◽

Cited By ~ 16

Author(s):

Fei Yu ◽

Zinan Zhang ◽

Li Liu ◽

Hui Shen ◽

Yuanyuan Huang ◽

...

Keyword(s):

Secure Communication ◽

Sliding Mode ◽

Equilibrium Points ◽

Lyapunov Stability Theory ◽

Adaptive Controller ◽

Phase Portraits ◽

Hyperchaotic System ◽

Unknown Parameters ◽

Receiver System ◽

Communication Scheme

By introducing a flux-controlled memristor model with absolute value function, a 5D multistable four-wing memristive hyperchaotic system (FWMHS) with linear equilibrium points is proposed in this paper. The dynamic characteristics of the system are studied in terms of equilibrium point, perpetual point, bifurcation diagram, Lyapunov exponential spectrum, phase portraits, and spectral entropy. This system is of the group of systems that have coexisting attractors. In addition, the circuit implementation scheme is also proposed. Then, a secure communication scheme based on the proposed 5D multistable FWMHS with disturbance inputs is designed. Based on parametric modulation theory and Lyapunov stability theory, synchronization and secure communication between the transmitter and receiver are realized and two message signals are recovered by a convenient robust high-order sliding mode adaptive controller. Through the proposed adaptive controller, the unknown parameters can be identified accurately, the gain of the receiver system can be adjusted continuously, and the disturbance inputs of the transmitter and receiver can be suppressed effectively. Thereafter, the convergence of the proposed scheme is proven by means of an appropriate Lyapunov functional and the effectiveness of the theoretical results is testified via numerical simulations.

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A direct yaw moment controller for a four in-wheel motor drive electric vehicle using adaptive sliding mode control

Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics ◽

10.1177/1464419318807700 ◽

2019 ◽

Vol 233 (3) ◽

pp. 549-567 ◽

Cited By ~ 3

Author(s):

Aria Noori Asiabar ◽

Reza Kazemi

Keyword(s):

Sliding Mode Control ◽

Control Algorithm ◽

Sliding Mode ◽

Adaptive Sliding Mode Control ◽

Regenerative Braking ◽

Lane Change ◽

Unknown Parameters ◽

Vehicle Handling ◽

Adaptive Sliding Mode ◽

Yaw Moment

In this paper, a direct yaw moment control algorithm is designed such that the corrective yaw moment is generated through direct control of driving and braking torques of four in-wheel brushless direct current motors located at the empty space of vehicle wheels. The proposed control system consists of a higher-level controller and a lower-level controller. In the upper level of proposed controller, a PID controller is designed to keep longitudinal velocity constant in manoeuvres. In addition, due to probable modelling error and parametric uncertainties as well as adaptation of unknown parameters in control law, an adaptive sliding mode control through adaptation of unknown parameters is presented to yield the corrective yaw moment such that the yaw rate tracks the desired value and the vehicle sideslip angle maintains limited so as to improve vehicle handling stability. The lower-level controller allocates the achieved control efforts (i.e. total longitudinal force and corrective yaw moment) to driving or regenerative braking torques of four in-wheel motors so as to generate the desired tyre longitudinal forces. The additional yaw moment applied by upper-lever controller may saturate the tyre forces. To this end, a novel longitudinal slip ratio controller which is designed based on fuzzy logic is included in the lower-level controller. A tyre dynamic weight transfer-based torque distribution algorithm is employed to distribute the motor driving torque or regenerative braking torque of each in-wheel motor for vehicle stability enhancement. A seven degree-of-freedom non-linear vehicle model with Magic Formula tyre model as well as the proposed control algorithm are simulated in Matlab/Simulink software. Three steering inputs including lane change, double lane change and step-steer manoeuvres in different roads are investigated in simulation environment. The simulation results show that the proposed control algorithm is capable of improving vehicle handling stability and maintaining vehicle yaw stability.

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ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

International Journal of Modern Physics B ◽

10.1142/s021797921350197x ◽

2013 ◽

Vol 27 (32) ◽

pp. 1350197

Author(s):

XING-YUAN WANG ◽

SI-HUI JIANG ◽

CHAO LUO

Keyword(s):

Lyapunov Stability ◽

Lyapunov Stability Theory ◽

Adaptive Controller ◽

Chaotic Synchronization ◽

Adaptive Synchronization ◽

Hyperchaotic System ◽

Unknown Parameters ◽

Chen System ◽

Synchronization Scheme ◽

Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

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Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Complexity ◽

10.1155/2017/4962739 ◽

2017 ◽

Vol 2017 ◽

pp. 1-23 ◽

Cited By ~ 5

Author(s):

Li Xiong ◽

Zhenlai Liu ◽

Xinguo Zhang

Keyword(s):

Secure Communication ◽

Control Method ◽

Dynamical Behavior ◽

Control Level ◽

Lyapunov Stability Theory ◽

Dynamical Analysis ◽

Linear Feedback ◽

Hyperchaotic System ◽

Error System ◽

New Hyperchaotic System

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

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