scholarly journals Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Paul Yaovi Dousseh ◽  
Cyrille Ainamon ◽  
Clément Hodévèwan Miwadinou ◽  
Adjimon Vincent Monwanou ◽  
Jean Bio Chabi Orou
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Stability Theory ◽  
Financial System ◽  
Adaptive Synchronization ◽  
Control Law ◽  
State Variables ◽  
Unknown Constant ◽  
Theoretical Results ◽  
Adaptive Control Law

In this paper, adaptive control and adaptive synchronization of an integer and fractional order new financial system with unknown constant parameters are studied. Based on Lyapunov’s stability theory, an adaptive control law is designed to asymptotically stabilize the state variables of the system to the origin in integer and fractional order cases. By the same theory, an adaptive synchronization law is designed to perform the identical synchronization of the new financial system in the cases of integer and fractional order with unknown constant parameters. Numerical simulations are carried out in order to show the efficiency of the theoretical results.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Adaptive Synchronization for Hyperchaotic Liu System

2022 ◽  
Vol 9 ◽  
Author(s):  
Shunjie Li ◽  
Yawen Wu ◽  
Gang Zheng
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Control Schemes ◽  
Liu System ◽  
Adaptive Control Law

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

scholarly journals Adaptive Anti-synchronization of Identical and Non-identical 4-D Chaotic Systems

2012 ◽  
pp. 160-164
Author(s):  
H. Najafizadegan ◽  
M. Khoeiniha ◽  
H. Zarabadipour
Keyword(s):  
Adaptive Control ◽  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Unknown Parameters ◽  
Different Chaotic Systems ◽  
Adaptive Control Law

In this paper, we investigate the chaos anti-synchronization between two identical and different chaotic systems with fully unknown parameters via adaptive control. Based on the Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are designed such that the two different chaotic systems can be anti-synchronized asymptotically. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

A road-adaptive control law for semi-active suspensions

1999 ◽  
Vol 13 (10) ◽  
pp. 667-676 ◽  
Author(s):  
Youngjoo Cho ◽  
Byung Suk Song ◽  
Kyongsu Yi
Keyword(s):  
Adaptive Control ◽  
Control Law ◽  
Active Suspensions ◽  
Adaptive Control Law

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

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