scholarly journals Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

2020 ◽  
Vol 25 (3) ◽  
pp. 51
Author(s):  
Jesus R. Pulido-Luna ◽  
Jorge A. López-Rentería ◽  
Nohe R. Cazarez-Castro
Keyword(s):  
Asymptotic Stability ◽  
Test Performance ◽  
State Feedback ◽  
Chaotic Systems ◽  
Reconfigurable Hardware ◽  
Lyapunov Theory ◽  
Control Law ◽  
Heterogeneous Dynamics ◽  
Two Systems ◽  
Error State

In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

SYNCHRONIZATION CONTROL FOR A CLASS OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2005 ◽  
Vol 15 (07) ◽  
pp. 2235-2246 ◽  
Author(s):  
HER-TERNG YAU ◽  
JUI-SHENG LIN ◽  
JUN-JUH YAN
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Sliding Mode ◽  
Variable Structure ◽  
Synchronization Control ◽  
Control Law ◽  
Structure Control ◽  
Synchronization Problem ◽  
Error State

This paper investigates the chaos synchronization problem for a class of uncertain master-slave chaotic systems. Based on the variable structure control theory, a strategy is proposed to guarantee the occurrence of a sliding mode motion of error states when the proposed control law is applied. As expected, the error state is able to drive to zero with match external uncertainties or into a predictable neighborhood of zero with mismatch external uncertainties. Furthermore, a modified continuous sliding mode controller is also proposed to avoid the chattering. Examples of Lorenz system and Chua's circuit are presented to demonstrate the obtained results.

scholarly journals Adaptive Control Synchronization of a Novel Memristive Chaotic System for Secure Communication Applications

Inventions ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 30 ◽  
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Hayder A. A. Al-Kashoash ◽  
Saif Muneam Ramadhan ◽  
Yasir I. A. Al-Yasir
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Data Transmission ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Lyapunov Theory ◽  
Control Law ◽  
Slave System ◽  
Synchronization Mechanism ◽  
Adaptive Control Law

In this paper, a new memristive chaotic system is designed, analyzed, tested, and proposed. An adaptive control synchronization mechanism for both master and slave chaotic systems is also designed. The adaptive control law of this mechanism is derived based on the Lyapunov theory. A single parameter in the slave system has been assumed to be unknown. As the parameters of the master and slave are asymptotically matched, the unknown slave parameters will be identified according to the master’s parameters. The proposed system is used in a secure communication system. The achieved results prove a simple system implementation with a high security of data transmission.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

Adaptive Dynamic Surface Control of Bouc–Wen Hysteretic Systems

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Mansour Peimani ◽  
Mohammad Javad Yazdanpanah ◽  
Naser Khaji
Keyword(s):  
Sliding Mode ◽  
Dynamic Surface Control ◽  
Lyapunov Theory ◽  
Hysteretic Behavior ◽  
Control Law ◽  
Structural Systems ◽  
Control Force ◽  
Dynamic Surface ◽  
Adaptive Dynamic ◽  
Surface Control

This paper develops an adaptive dynamic surface algorithm for designing the control law for uncertain hysteretic structural systems with seismic disturbances that can be converted to a semi strict feedback form. Hysteretic behavior is usually described by Bouc–Wen model for hysteretic structural systems like base isolation systems. Adaptive sliding mode and adaptive backstepping algorithms are also studied and simulated for comparison purposes. The presented simulation results indicate the effectiveness of the proposed control law in reducing displacement, velocity and acceleration responses of the structural system with acceptable control force. Moreover, using dynamic surface control (DSC), the study analyzes the stability of the controlled system based on the Lyapunov theory.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic 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 Nonlinear Hybrid Controller for a Quadrotor Based on Sliding Mode and Backstepping

2015 ◽  
Vol 4 (3) ◽  
pp. 209
Author(s):  
Chuan Lian Zhang ◽  
Kil To Chong
Keyword(s):  
Attitude Control ◽  
Position Control ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Control Law ◽  
Dynamics Modeling ◽  
Hybrid Controller ◽  
Navigation Simulation ◽  
Waypoint Navigation ◽  
Nonlinear Hybrid

<span>In this paper, one nonlinear hybrid controller, based on backstepping and sliding mode, was developed and applied to a quadrotor for waypoint navigation application. After dynamics modeling, the whole quadrotor dynamics system could be divided into two subsystems: rotational system and translational system. Backstepping control law was derived for attitude control whereas sliding mode control law was developed for position control. By using Lyapunov theory and satisfying sliding stable rules, the convergence of system could be guaranteed. A nonlinear equation was proposed to solve the under-actuated problem. To validate the effectiveness of proposed nonlinear hybrid controller, waypoint navigation simulation was performed on the nonlinear hybrid controller. Results showed that the nonlinear hybrid controller finished waypoint navigation successfully.</span>

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