scholarly journals An optimal nonlinear control for anti-synchronization of Rabinovich hyperchaotic system

2020 ◽  
Vol 19 (1) ◽  
pp. 380 ◽  
Author(s):  
Shaymaa Al-hayali ◽  
Saad Fawzi AL-Azzawi
Keyword(s):  
Nonlinear Control ◽  
Strategy Implementation ◽  
Hyperchaotic System ◽  
Analytical Results ◽  
Current Controller ◽  
Relevant Variables ◽  
Response Systems ◽  
Error Dynamics ◽  
Hyperchaotic Systems ◽  
Lyapunov Second Method

This work derives new results for the anti-synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems.  In comparison with previous strategies, the current controller (Nonlinear control) focused on the minimum possible limits for relevant variables. The better performance is realizing the anti- synchronization by designing a control with low terms. After obtaining analytical results of the proposed controller, numircal simulation is carried out using Matlab. The graphical results prove validity and applicability of proposed control without know any parameter.The proposed control has certain significance for reducing the time and complexity for strategy implementation.

scholarly journals Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Rehan ◽  
Keum-Shik Hong
Keyword(s):  
Electrical Stimulation ◽  
Nonlinear Control ◽  
Control Law ◽  
Input Control ◽  
Control Schemes ◽  
Multiple Input ◽  
Cognitive Diseases ◽  
Single Input ◽  
Error Dynamics ◽  
Nonlinear Control Law

Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and theL2gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides theL2bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

scholarly journals Novel nonlinear control structure for vector control of SPIM drive using BS PCH

2020 ◽  
Vol 11 (2) ◽  
pp. 1099
Author(s):  
Ngoc Thuy Pham
Keyword(s):  
Nonlinear Control ◽  
Vector Control ◽  
Closed Loop ◽  
System Structure ◽  
Current Loop ◽  
Equation Resolution ◽  
Damping Matrix ◽  
Current Controller ◽  
Novel Structure ◽  
The Difference

This paper presents a novel structure combining the port-controlled Hamiltonian (PCH) and Backstepping (BS) nonlinear control for the vector control of the six-phase induction motor (SPIM). In this new scheme, to improve the outer loop’s robustness, the BS technique using the integral tracking errors action is proposed in the speed and flux controllers design. The advantage of this proposed control law is not to increase the complexity of differential equation resolution due to being not increased system states numbers. To enhance more the performance of SPIM drives (SPIMD), port-controlled Hamiltonian (PCH) scheme is used in the inner current loop controllers. In this proposed PCH current controller, the stabilization of controller is achieved via system passivity. In that, the interconnection and damping matrix functions of PCH system are shaped so that the physical (Hamiltonian) system structure is preserved at the closed loop level and the closed loop energy function is equal to the difference between the physical energy of the system and the energy supplied by the controller. The proposed control design is based on combination PCH and BS techniques improve significantly performance and robustness. The proposed speed control scheme is validated by Matlab-Simulink software.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

2017 ◽  
Vol 6 (4) ◽  
pp. 1-16 ◽  
Author(s):  
A. Almatroud Othman ◽  
M.S.M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350113 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Drive System ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Response System ◽  
Opposite Situation ◽  
The One ◽  
Hyperchaotic Systems

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

A Symmetric Image Encryption Scheme Base on Hyperchaotic System

2015 ◽  
Vol 719-720 ◽  
pp. 1030-1037
Author(s):  
Tao Song
Keyword(s):  
Image Encryption ◽  
Security Analysis ◽  
Image Transmission ◽  
Hyperchaotic System ◽  
Dynamical Behaviors ◽  
Key Space ◽  
Increasing Demand ◽  
Low Dimensional ◽  
System Variables ◽  
Hyperchaotic Systems

In recent years, chaos-based image encryption technologies have been widely studied to meet the increasing demand for real-time secure image transmission applications. To overcome the drawbacks of small key space and weak security in many existing schemes based on low-dimensional chaotic maps, this paper suggests a security improved scheme with a permutation-diffusion architecture. In the permutation stage, baker map is employed to shuffle the pixel positions. In the diffusion stage, the value of each pixel is altered by using a key stream derived from hyperchaotic system. Compared with ordinary chaotic systems, hyperchaotic systems, with more complex dynamical behaviors and number of system variables, offer greater potential for secure cryptosystem construction. Extensive security analysis has been performed on the proposed scheme, including the most important ones like key space analysis, statistical analysis and key sensitivity, which has demonstrated the satisfactory security of the proposed scheme.

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

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.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

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