scholarly journals Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo ◽  
Guanjun Li ◽  
Heng Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Control ◽  
Control Input ◽  
Saturated Control ◽  
Laplace Transform Technique

In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 <α≤ 1 and 1 <α< 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method.

Using Active Sliding Mode Controller Antisynchronization of Fractional-Order Chaotic Systems with Uncertainties and Disturbances

2013 ◽  
Vol 411-414 ◽  
pp. 1779-1786
Author(s):  
Hong Zhang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
External Disturbances ◽  
Active Sliding Mode Control ◽  
Derivative Method ◽  
Method Analysis

The antisynchronization behavior of fractional-order chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical fractional-order chaotic systems with different initial conditions and two different fractional-order chaotic systems with terms of uncertainties and external disturbances are derived based on the fractional-order derivative method. Analysis and numerical simulations are shown for validation purposes.

scholarly journals State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Control Method ◽  
Input Saturation ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Feedback Control Method ◽  
Linear State

We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems With One Control Input

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Pitcha Khamsuwan ◽  
Suwat Kuntanapreeda
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Direct Method ◽  
Output Feedback Control ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Input ◽  
Unified Chaotic Systems ◽  
System Output

This paper focuses on stabilization of fractional-order unified chaotic systems. In contrast to existing methods in literature, the proposed method requires only the system output for feedback and uses only one control input. The controller consists of a state feedback control law and a dynamic estimator. Sufficient stability conditions are derived using a fractional-order extension of the Lyapunov direct method and a new lemma of the Caputo fractional derivative. The conditions are expressed in the form of linear matrix inequalities (LMIs). All the parameters of the controller can be simultaneously obtained by solving the LMIs. Numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed method.

Reduced-order anti-synchronization of the projections of the fractional order hyperchaotic and chaotic systems

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Mayank Srivastava ◽  
Saurabh Agrawal ◽  
Subir Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Sufficient Conditions ◽  
Transformation Theory ◽  
Reduced Order ◽  
Hyperchaotic Lorenz System ◽  
Fractional Orders ◽  
Active Control Method

AbstractThe article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

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