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 A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

2016 ◽  
Vol 26 (1) ◽  
pp. 19-47 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Method ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Recursive Procedure ◽  
Quadratic Nonlinearities

This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic 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 two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1= 0.20572,L2= 0 and L3= −1.20824. 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 novel jerk chaotic system is derived as DKY= 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method 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 have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.

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.

Utilizing an Adaptive Controller (Azadi Controller) for Trajectory Planning of PUMA 560 Robot

2011 ◽  
Vol 403-408 ◽  
pp. 4880-4887
Author(s):  
Sassan Azadi
Keyword(s):  
Steady State ◽  
Trajectory Planning ◽  
Positive Feedback ◽  
Fuzzy Controller ◽  
Research Work ◽  
Adaptive Controller ◽  
The Novel ◽  
Transient Responses ◽  
Simulation Results ◽  
Good Substitute

This research work was devoted to present a novel adaptive controller which uses two negative stable feedbacks with a positive unstable positive feedback. The positive feedback causes the plant to do the break, therefore reaching the desired trajectory with tiny overshoots. However, the two other negative feedback gains controls the plant in two other sides of positive feedback, making the system to be stable, and controlling the steady-state, and transient responses. This controller was performed for PUMA-560 trajectory planning, and a comparison was made with a fuzzy controller. The fuzzy controller parameters were obtained according to the PSO technique. The simulation results shows that the novel adaptive controller, having just three parameters, can perform well, and can be a good substitute for many other controllers for complex systems such as robotic path planning.

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

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 Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Wang ◽  
Ling Liu ◽  
Chongxin Liu ◽  
Ziwei Zhu ◽  
Zhenquan Sun
Keyword(s):  
Fractional Order ◽  
Control Strategy ◽  
Reference Signal ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
Control Input ◽  
Fractional Order Systems ◽  
Adaptive Backstepping ◽  
Unknown Parameters ◽  
Adaptive Backstepping Control

In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance. Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated. And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters. The virtual control laws and parameter update laws are designed in each step. Thereafter, a novel fractional-order adaptive controller is designed in terms of the fractional Lyapunov stability theorem. The proposed control strategy requires only one control input and can force the output of the chaotic system to track the reference signal asymptotically. Finally, the proposed method is applied to a noncommensurate fractional-order ferroresonance system with multiple unknown parameters. Numerical simulation confirms the effectiveness of the proposed method. In addition, the proposed control strategy also applies to commensurate fractional-order systems with unknown parameters.

scholarly journals Adaptive Fuzzy Synchronization of Fractional-Order Chaotic (Hyperchaotic) Systems with Input Saturation and Unknown Parameters

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Heng Liu ◽  
Ye Chen ◽  
Guanjun Li ◽  
Wei Xiang ◽  
Guangkui Xu
Keyword(s):  
Fractional Order ◽  
Control Method ◽  
External Disturbance ◽  
Input Saturation ◽  
Adaptive Fuzzy Control ◽  
Adaptive Controller ◽  
Unknown Parameters ◽  
Fuzzy Logic Systems ◽  
Adaptive Fuzzy ◽  
Hyperchaotic Systems

We investigate the synchronization problem of fractional-order chaotic systems with input saturation and unknown external disturbance by means of adaptive fuzzy control. An adaptive controller, accompanied with fractional adaptation law, is established, fuzzy logic systems are used to approximate the unknown nonlinear functions, and the fractional Lyapunov stability theorem is used to analyze the stability. This control method can realize the synchronization of two fractional-order chaotic or hyperchaotic systems and the synchronization error tends to zero asymptotically. Finally, we show the effectiveness of the proposed method by two simulation examples.

scholarly journals Backstepping control based on L1 adaptive theory for large transport aircraft heavy load airdrop

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141774948
Author(s):  
Pengchao Zhang
Keyword(s):  
High Efficiency ◽  
Control Method ◽  
Uniform Boundedness ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
Heavy Load ◽  
Transport Aircraft ◽  
External Loop ◽  
Control Switch ◽  
The Stability

A study of the L1 adaptive controller is conducted based on the backstepping method for the model of large transport aircraft with drastic changes appearing in heavy load airdrop process. The system is divided into an attitude subsystem and a velocity subsystem. For the attitude subsystem, the backstepping control is used to design the virtual control of path angle and the pitch angle in external loop with the L1 adaptive controller designed in internal loop to estimate the uncertainties and disturbances in the subsystem and to compensate them. In the stability analysis, the uniform boundedness of all signals in the closed-loop system is proven. Simulation results show that the proposed control method preserves the quick dynamic torque response, high efficiency, and robustness in heavy load airdrop; to some extent it can alleviate the control switch lead or lag problem and ensure the safety of the transport aircraft to fulfill the complete airdrop mission.

scholarly journals Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities

2016 ◽  
Vol 26 (4) ◽  
pp. 471-495 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Adaptive Control ◽  
Lyapunov Exponents ◽  
Research Work ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
System Parameters ◽  
Quadratic Nonlinearities ◽  
Unknown System

AbstractThis research work announces an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. We describe the qualitative properties of the novel 4-D hyperchaotic system and illustrate their phase portraits. We show that the novel 4-D hyperchaotic system has two unstable equilibrium points. The novel 4-D hyperchaotic system has the Lyapunov exponents L1= 3.1575, L2= 0.3035, L3= 0 and L4= −33.4180. The Kaplan-Yorke dimension of this novel hyperchaotic system is found as DKY= 3.1026. Since the sum of the Lyapunov exponents of the novel hyperchaotic system is negative, we deduce that the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to stabilize the novel 4-D hyperchaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 4-D hyperchaotic systems with unknown system parameters. The adaptive control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this research work.

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