scholarly journals Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

2015 ◽  
Vol 25 (1) ◽  
pp. 135-158 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham ◽  
Kavitha Madhavan
Keyword(s):  
Chaotic System ◽  
Research Work ◽  
The Novel ◽  
Adaptive Backstepping ◽  
Qualitative Properties ◽  
Unknown Parameters ◽  
Circuit Realization ◽  
Backstepping Controller ◽  
Hyperjerk System ◽  
Adaptive Backstepping Controller

Abstract A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ⩾ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ⩾ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.1448, L2 = 0.0328, L3 = 0 and L4 = −1.1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY= 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

scholarly journals Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities

2014 ◽  
Vol 24 (3) ◽  
pp. 375-403 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham ◽  
Kavitha Madhavan ◽  
Babatunde A. Idowu
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Research Work ◽  
The Novel ◽  
Adaptive Backstepping ◽  
Unknown Parameters ◽  
Circuit Realization ◽  
Backstepping Controller ◽  
Jerk System ◽  
Adaptive Backstepping Controller

Abstract In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model

scholarly journals A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

2017 ◽  
Vol 27 (3) ◽  
pp. 409-439 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Backstepping Control ◽  
Phase Portraits ◽  
The Novel ◽  
Adaptive Backstepping ◽  
Unknown Parameters ◽  
Recursive Procedure ◽  
Backstepping Controller ◽  
Adaptive Backstepping Controller

AbstractThis paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1= 0:2974, L2= 0 and L3= −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY= 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

scholarly journals Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

2016 ◽  
Vol 26 (3) ◽  
pp. 311-338 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Control Method ◽  
Research Work ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
The Novel ◽  
Qualitative Properties ◽  
Unknown Parameters ◽  
A Chain ◽  
Control And Synchronization ◽  
Hyperjerk System

AbstractA hyperjerk system is a dynamical system, which is modelled by annth order ordinary differential equation withn≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system ofnfirst order ordinary differential equations withn≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained asL1= 0.14219,L2= 0.04605,L3= 0 andL4= −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained asDKY= 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

scholarly journals Composite adaptive backstepping controller design and the energy calculation for active suspension system

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110105
Author(s):  
Xiaoyu Su ◽  
Bin Lin ◽  
Shuai Liu
Keyword(s):  
Adaptive Algorithm ◽  
Power Calculation ◽  
Calculation Formula ◽  
Adaptive Backstepping ◽  
Adaptive Law ◽  
Car Suspension ◽  
Backstepping Controller ◽  
Suspension Model ◽  
Storage Characteristics ◽  
Adaptive Backstepping Controller

The half-car suspension has the coupling of pitch angle and front and rear suspension. Especially when the suspension model has a series of uncertainties, the traditional linear control method is difficult to be applied to the half-car suspension model. At present, there is no systematic method to solve the suspension power. According to the energy storage characteristics of the elastic components of the suspension, the power calculation formula is proposed in this paper. This paper proposes a composite adaptive backstepping control scheme for the half-car active suspension systems. In this method, the correlation information between the output error and the parameter estimation error is used to construct the adaptive law. According to the energy storage characteristics of the elastic components of the suspension, the power calculation formula is introduced. The compound adaptive law and the ordinary adaptive law have good disturbance suppression, both of which can solve the pitching angle problem of the semi-car suspension, but the algorithm of the compound adaptive law is superior in effect. In terms of vehicle comfort, the algorithm of the general adaptive law can achieve stability quickly, but compared with the composite adaptive law, its peak value and jitter are higher, while the algorithm of the composite adaptive law is relatively gentle and has better adaptability to human body. In terms of vehicle handling, both control algorithms can maintain driving safety under road excitation, and the compound adaptive algorithm appears to have more advantages. Compared with the traditional adaptive algorithm, the power consumption of the composite adaptive algorithm is relatively lower than that of the former in the whole process. The simulation results show that the ride comfort, operating stability and safety of the vehicle can be effectively improved by the composite adaptive backstepping controller, and the composite adaptive algorithm is more energy-saving than the conventional adaptive algorithm based on projection operator.

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