A New Approximation Algorithm of Fractional Order System Models Based Optimization

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Li Meng ◽  
Dingyu Xue
Keyword(s):  
Approximation Algorithm ◽  
Fractional Order ◽  
Approximation Scheme ◽  
Original System ◽  
Order System ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Frequency Domains ◽  
Approximate System ◽  
Phase Fitting

This paper proposes a new approximation scheme which is an extension to the well-established Charef’s approximation method for fractional order systems. The method relaxes the constraints on the locations of the pole-zero pairs of the approximate system, which provides more flexibility and space for approximate system to approach the original system as close as possible. The approximate system based on an optimization process performs not only a good magnitude fitting but also a good phase fitting. The benefits from using the proposed scheme are illustrated by numerical examples in frequency domains.

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.

scholarly journals Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach

2020 ◽  
Vol 4 (1) ◽  
pp. 8
Author(s):  
Xuefeng Zhang ◽  
Yuqing Yan
Keyword(s):  
Fractional Order ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Fractional Order Systems ◽  
Lmi Approach ◽  
Numerical Examples ◽  
Necessary And Sufficient

This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions.

scholarly journals Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yiheng Wei ◽  
Hamid Reza Karimi ◽  
Jinwen Pan ◽  
Qing Gao ◽  
Yong Wang
Keyword(s):  
Time Series ◽  
Series Expansion ◽  
Fractional Order ◽  
Disturbance Observer ◽  
Higher Order ◽  
Transient Dynamics ◽  
Fractional Order Systems ◽  
Weighted Function ◽  
Numerical Examples ◽  
The Stability

This paper is concerned with the problem of designing disturbance observer for fractional order systems, of which the disturbance is in time series expansion. The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. In addition, the result is also extended to estimate slope forms disturbance and higher order disturbance of fractional order systems. The efficacy of the proposed method is validated through numerical examples.

Model Predictive Control of General Fractional Order Systems Using a General Purpose Optimal Control Problem Solver: RIOTS

2019 ◽  
Author(s):  
Sina Dehghan ◽  
Tiebiao Zhao ◽  
YangQuan Chen ◽  
Taymaz Homayouni
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Fractional Order ◽  
Predictive Control ◽  
Order System ◽  
Problem Solver ◽  
Fractional Order Systems ◽  
Application Process ◽  
Order Model ◽  
Integer Order

Abstract RIOTS is a Matlab toolbox capable of solving a very general form of integer order optimal control problems. In this paper, we present an approach for implementing Model Predictive Control (MPC) to control a general form of fractional order systems using RIOTS toolbox. This approach is based on time-response-invariant approximation of fractional order system with an integer order model to be used as the internal model in MPC. The implementation of this approach is demonstrated to control a coupled MIMO commensurate fractional order model. Moreover, the performance and its application process is compared to examples reported in the literature.

Stability analysis of fractional-order systems with double noncommensurate orders for matrix case

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhuang Jiao ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Simple Algorithm ◽  
Inverse Laplace Transform ◽  
Order System ◽  
Necessary Condition ◽  
Fractional Order Systems ◽  
Numerical Inverse Laplace Transform ◽  
Laplace Transform Technique ◽  
Matrix Case

AbstractBounded-input bounded-output stability issues for fractional-order linear time invariant (LTI) system with double noncommensurate orders for the matrix case have been established in this paper. Sufficient and necessary condition of stability is given, and a simple algorithm to test the stability for this kind of fractional-order systems is presented. Based on the numerical inverse Laplace transform technique, time-domain responses for fractional-order system with double noncommensurate orders are shown in numerical examples to illustrate the proposed results.

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.

LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER

2011 ◽  
Vol 25 (29) ◽  
pp. 3951-3964 ◽  
Author(s):  
HAO ZHU ◽  
ZHONGSHI HE ◽  
SHANGBO ZHOU
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Stability Theorem ◽  
Nonlinear Observer ◽  
Order System ◽  
Fractional Order Systems ◽  
Lag Synchronization ◽  
Systematic Method ◽  
Fractional System ◽  
The Stability

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation.

scholarly journals On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Parameter Dependent ◽  
Lyapunov Technique

In this paper, the problem of stabilization and observer design of parameter-dependent perturbed fractional-order systems is investigated. Sufficient conditions on the practical Mittag–Leffler and Mittag–Leffler stability are given based on the Lyapunov technique. Firstly, the problem of stabilization using the state feedback is developed. Secondly, under some sufficient hypotheses, an observer design which provides an estimation of the state is constructed. Finally, numerical examples are provided to validate the contributed results.

scholarly journals Some Fundamental Properties on the Sampling Free Nabla Laplace Transform

2019 ◽  
Author(s):  
Yiheng Wei ◽  
Yuquan Chen ◽  
Yong Wang ◽  
YangQuan Chen
Keyword(s):  
System Theory ◽  
Laplace Transform ◽  
Fractional Order ◽  
Fractional Order System ◽  
The Other ◽  
Order System ◽  
Fractional Order Systems ◽  
Fundamental Properties ◽  
Other Hand

Abstract Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its development. In this paper, 14 lemmas are listed to conclude the existing properties and 14 theorems are developed to describe the innovative features. On one hand, these properties make the Ntransform more effective and efficient. On the other hand, they enrich the discrete fractional order system theory.

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