scholarly journals Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongjuan Liu ◽  
Zhiliang Zhu ◽  
Hai Yu ◽  
Qian Zhu
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Order System ◽  
Coupling Scheme ◽  
Fractional Order Systems ◽  
Parameter Mismatch ◽  
Loop Control ◽  
Modified Projective Synchronization

A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS) of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL) control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.

scholarly journals Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Jinman He ◽  
Fangqi Chen ◽  
Qinsheng Bi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Inverse Matrix ◽  
Projective Synchronization ◽  
Control Parameters ◽  
Complete Synchronization ◽  
External Disturbances ◽  
Modified Projective Synchronization ◽  
Projective Matrix

This paper is concerned with the quasi-matrix and quasi-inverse-matrix projective synchronization between two nonidentical delayed fractional order neural networks subjected to external disturbances. First, the definitions of quasi-matrix and quasi-inverse-matrix projective synchronization are given, respectively. Then, in order to realize two types of synchronization for delayed and disturbed fractional order neural networks, two sufficient conditions are established and proved by constructing appropriate Lyapunov function in combination with some fractional order differential inequalities. And their estimated synchronization error bound is obtained, which can be reduced to the required standard as small as what we need by selecting appropriate control parameters. Because of the generality of the proposed synchronization, choosing different projective matrix and controllers, the two synchronization types can be reduced to some common synchronization types for delayed fractional order neural networks, like quasi-complete synchronization, quasi-antisynchronization, quasi-projective synchronization, quasi-inverse projective synchronization, quasi-modified projective synchronization, quasi-inverse-modified projective synchronization, and so on. Finally, as applications, two numerical examples with simulations are employed to illustrate the efficiency and feasibility of the new synchronization analysis.

An Approach to Design Controllers for MIMO Fractional Order System Based on RFN Method

2021 ◽  
Author(s):  
Tingxue Li ◽  
Dingyu Xue ◽  
Xinshu Cui
Keyword(s):  
Fractional Order ◽  
Controller Design ◽  
Order System ◽  
Fractional Order Systems ◽  
Control Effect ◽  
Loop Control ◽  
Single Input Single Output ◽  
Single Output ◽  
Single Input ◽  
Value Decomposition

Abstract Fractional calculus has attracted more and more attention and is applied in different fields. However the controller design techniques for fractional order systems mostly focus on single input single output (SISO) ones. This paper deals with the design of controllers for multiple inputs multiple outputs (MIMO) fractional order systems. A method to synthetize controller based on the eigenvalue function and singular value decomposition (SVD) is proposed with aid of fractional order transfer function (FOTF) MATLAB toolbox for the computation and fitting. Instead of setting specification to the controller, the method proposed aiming at achieving the target closed-loop control effect of the system as a whole. Several models evolved from fractional-order Proportional-Integral-Derivative (fPID) controller are selected to form the designed multivariable controller. The effectiveness and robustness of the proposed method are illustrated by an example via simulation.

scholarly journals Control Techniques for a Class of Fractional Order Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2357
Author(s):  
Mircea Ivanescu ◽  
Ioan Dumitrache ◽  
Nirvana Popescu ◽  
Decebal Popescu
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Fractional Order ◽  
Closed Loop ◽  
Fractional Order Systems ◽  
Loop Control ◽  
Order Linear ◽  
Control Techniques ◽  
The Stability ◽  
Nonlinear Components

The paper discusses several control techniques for a class of systems described by fractional order equations. The paper presents the unit frequency criteria that ensure the closed loop control for: Fractional Order Linear Systems, Fractional Order Linear Systems with nonlinear components, Time Delay Fractional Order Linear Systems, Time Delay Fractional Order Linear Systems with nonlinear components. The stability criterion is proposed for the systems composed of fractional order subsystems. These techniques are used in two applications: Soft Exoskeleton Glove Control, studied as a nonlinear model with time delay and Disabled Man-Wheelchair model, analysed as a fractional-order multi-system.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Fractional-order Kalman filters for continuous-time fractional-order systems involving correlated and uncorrelated process and measurement noises

2018 ◽  
Vol 41 (7) ◽  
pp. 1933-1947 ◽  
Author(s):  
Fanghui Liu ◽  
Zhe Gao ◽  
Chao Yang ◽  
Ruicheng Ma
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
Equation Model ◽  
Order System ◽  
Fractional Order Systems ◽  
Derivative Method ◽  
Measurement Noises ◽  
Computation Load ◽  
Average Derivative

This paper presents fractional-order Kalman filters using the fractional-order average derivative method for linear fractional-order systems involving process and measurement noises. By using the fractional-order average derivative method, a difference equation model is obtained by discretizing the investigated continuous-time fractional-order system, and the accuracy of state estimation is improved. Meanwhile, compared with the Tustin generating function, the fractional-order average derivative method proposed in this paper can reduce computation load and save calculation time. Two kinds of fractional-order Kalman filters are given, for the correlated and uncorrelated cases, in terms of the process and measurement noises for linear fractional-order systems, respectively. Finally, simulation results are illustrated to verify the effectiveness of the proposed Kalman filters using the fractional-order average derivative method.

Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques

2019 ◽  
Vol 234 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Bahram Yaghooti ◽  
Ali Siahi Shadbad ◽  
Kaveh Safavi ◽  
Hassan Salarieh
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Closed Loop Control ◽  
Loop Control ◽  
Closed Loop Control System ◽  
Loop Control System

In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractional-order chaotic systems using fractional-order sliding mode control. The controller structure and adaptation laws are chosen such that asymptotic stability of the closed-loop control system is guaranteed. The adaptation laws are being calculated from a proper sliding surface using the Lyapunov stability theory. This method guarantees the closed-loop control system robustness against the system uncertainties and external disturbances. Eventually, the presented method is used to synchronize two fractional-order gyro and Duffing systems, and the numerical simulation results demonstrate the effectiveness of this method.

scholarly journals A Closed-Loop Brain Stimulation Control System Design Based on Brain-Machine Interface for Epilepsy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Moshu Qian ◽  
Guanghua Zhong ◽  
Xinggang Yan ◽  
Heyuan Wang ◽  
Yang Cui
Keyword(s):  
Control System ◽  
Fractional Order ◽  
Brain Stimulation ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Brain Machine Interface ◽  
Machine Interface ◽  
Electromagnetic Disturbances ◽  
Stimulation Control

In this study, a closed-loop brain stimulation control system scheme for epilepsy seizure abatement is designed by brain-machine interface (BMI) technique. In the controller design process, the practical parametric uncertainties involving cerebral blood flow, glucose metabolism, blood oxygen level dependence, and electromagnetic disturbances in signal control are considered. An appropriate transformation is introduced to express the system in regular form for design and analysis. Then, sufficient conditions are developed such that the sliding motion is asymptotically stable. Combining Caputo fractional order definition and neural network (NN), a finite time fractional order sliding mode (FFOSM) controller is designed to guarantee reachability of the sliding mode. The stability and reachability analysis of the closed-loop tracking control system gives the guideline of parameter selection, and simulation results based on comprehensive comparisons are carried out to demonstrate the effectiveness of proposed approach.

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