Design of Optimal Fractional Luenberger Observers for Linear Fractional-Order Systems

2017 ◽  
Author(s):  
Arman Dabiri ◽  
Eric A. Butcher
Keyword(s):  
Banach Space ◽  
Spectral Radius ◽  
Fractional Order ◽  
State Transition ◽  
Design Method ◽  
Design Methods ◽  
The State ◽  
Transition Operator ◽  
Fractional Order Systems ◽  
Numerical Example

Optimal fractional Luenberger observers for linear fractional-order systems are developed using the fractional Chebyshev collocation (FCC) method. It is shown that the design method has advantages over existing Luenberger design methods for fractional order systems. To accomplish this, the state transition operator for the solution of linear fractional-order systems is defined in a Banach space and discretized using the FCC method. In addition, the discretized state transition operator is obtained by using the FCC method. Next, the optimal observer gains are obtained by minimizing the spectral radius of the state transition operator for the observer,while ensuring that the observer responds faster than the controller. Finally, a numerical example is provided to demonstrate the validity and the efficiency of the proposed method.

Optimal observer-based feedback control for linear fractional-order systems with periodic coefficients

2019 ◽  
Vol 25 (7) ◽  
pp. 1379-1392 ◽  
Author(s):  
Arman Dabiri ◽  
Eric A. Butcher
Keyword(s):  
Banach Space ◽  
Feedback Control ◽  
Fractional Order ◽  
Closed Loop ◽  
State Transition ◽  
Fractional Order Systems ◽  
Chebyshev Collocation Method ◽  
Periodic Coefficients ◽  
A New Technique ◽  
Transition Operators

This paper proposes a new technique to design an optimal observer-based feedback control for linear fractional-order systems with constant or periodic coefficients. The proposed observer-based feedback control assures the fastest convergence of the closed-loop system’s states. For this purpose, a state-transition operator is defined in a Banach space and approximated using the fractional Chebyshev collocation method. It is shown that periodic gains of the controller and observer can be independently tuned by minimizing the spectral radius of their associated state-transition operators. The validity and efficiency of the proposed method are demonstrated through two illustrative examples.

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.

Functional interval observer design for singular fractional-order systems with disturbances

2020 ◽  
pp. 014233122094489
Author(s):  
Dinh Cong Huong ◽  
Dao Thi Hai Yen
Keyword(s):  
Fractional Order ◽  
Design Method ◽  
Observer Design ◽  
Effective Algorithm ◽  
Fractional Order Systems ◽  
Full State ◽  
Simulation Results ◽  
Interval Observer ◽  
Interval Observers ◽  
State Functions

In this study, we consider the problem of designing functional interval observers for a class of singular fractional-order systems. The goal of this work is to design not a full state interval observer for singular fractional-order systems, but to design an observer for state functions of this kind of systems. Conditions for the existence of such functional interval observers are given and an effective algorithm for computing unknown observer matrices is provided in this study. Two numerical examples and simulation results are provided to illustrate the effectiveness of the proposed design method.

Global Stabilization for a class of nonlinear fractional-order systems

2019 ◽  
Vol 10 (01) ◽  
pp. 1941009 ◽  
Author(s):  
Taide Liu ◽  
Feng Wang ◽  
Wanchun Lu ◽  
Xuhuan Wang
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Global Stabilization ◽  
Fractional Order Systems ◽  
Closed Loop System ◽  
Integer Order ◽  
Backstepping Algorithm

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method.

scholarly journals Combination synchronization of fractional order n-chaotic systems using active backstepping design

2019 ◽  
Vol 8 (1) ◽  
pp. 597-608 ◽  
Author(s):  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Design Method ◽  
Backstepping Design ◽  
Fractional Order Systems ◽  
Combination Synchronization

Abstract In this article, a scheme using active backstepping design method is proposed to achieve combination synchronization of n number of fractional order chaotic systems. In the proposed method the controllers are designed with the help of a new lemma and Lyapunov function in a systematic way. Synchronization among three/four fractional order systems have been shown as examples of synchronization of n-chaotic systems. Numerical simulation and graphical results clearly exhibit that the method of this new procedure is easy to implement and reliable for synchronization of fractional order chaotic systems.

scholarly journals Fault Tolerant Control for Interval Fractional-Order Systems with Sensor Failures

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Hao Shen
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Fault Tolerant ◽  
Design Method ◽  
Fault Tolerant Control ◽  
Fractional Order Systems ◽  
Sensor Faults ◽  
Sensor Fault ◽  
Interval Parameters ◽  
Output Feedback Controller

The problem of robust fault tolerant control for continuous-time fractional-order (FO) systems with interval parameters and sensor faults of0<α<2has been investigated. By establishing sensor fault model and state observer, an observer-based FO output feedback controller is developed such that the closed-loop FO system is asymptotically stable, not only when all sensor components are working well, but also in the presence of sensor components failures. Finally, numerical simulation examples are given to illustrate the application of the proposed design method.

scholarly journals Solution of linear fractional order systems with variable coefficients

2020 ◽  
Vol 23 (3) ◽  
pp. 753-763
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Transition Matrix ◽  
State Transition ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Fractional Order Systems ◽  
Initial Value ◽  
Theoretical Results

AbstractThe paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann–Liouville derivatives. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by an example.

On Observability of Fractional Order Systems

2009 ◽  
Author(s):  
Jocelyn Sabatier ◽  
Mathieu Merveillaut ◽  
Ludovic Fenetau ◽  
Alain Oustaloup
Keyword(s):  
Parabolic Equation ◽  
State Space ◽  
Fractional Order ◽  
The State ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
System State ◽  
Fractional Systems ◽  
Real State

In this paper, fractional order system observability is discussed. A representation of these systems that involves a classical linear integer system and a system described by a parabolic equation is used to define the system real state and to conclude that the system state cannot be observed. However, it is also shown that the state space like representation usually encountered in the literature for fractional systems, can be used to design Luenberger like observers that permit an estimation of important variables in the system.

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