Recursive set-membership parameter estimation of fractional systems using orthotopic approach

2018 ◽  
Vol 40 (15) ◽  
pp. 4185-4197 ◽  
Author(s):  
Saif Eddine Hamdi ◽  
Messaoud Amairi ◽  
Mohamed Aoun
Keyword(s):  
Parameter Estimation ◽  
System Parameter ◽  
A Priori ◽  
Fractional Order Systems ◽  
Fractional Systems ◽  
Order Estimation ◽  
Set Membership ◽  
Equation Error ◽  
Bounded Error ◽  
Fractional System

In this paper, set-membership parameter estimation of linear fractional-order systems is addressed for the case of unknown-but-bounded equation error. In such bounded-error context with a-priori known noise bounds, the main goal is to characterize the set of all feasible parameters. This characterization is performed using an orthotopic strategy adapted for fractional system parameter estimation. In the case of a fractional commensurate system, an iterative algorithm is proposed to deal with commensurate-order estimation. The performances of the proposed algorithm are illustrated by a numerical example via a Monte Carlo simulation.

scholarly journals Recursive set membership estimation for output–error fractional models with unknown–but–bounded errors

2016 ◽  
Vol 26 (3) ◽  
pp. 543-553 ◽  
Author(s):  
Messaoud Amairi
Keyword(s):  
A Priori ◽  
Ellipsoid Algorithm ◽  
Fractional Systems ◽  
Output Error ◽  
Set Membership ◽  
Equation Error ◽  
Fractional Models ◽  
Bounded Error ◽  
Optimal Bounding Ellipsoid ◽  
New Formulation

Abstract This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

Initial Conditions and Initialization of Fractional Systems

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Massinissa Tari ◽  
Nezha Maamri ◽  
Jean-Claude Trigeassou
Keyword(s):  
Initial Conditions ◽  
Fractional Order Systems ◽  
Fractional Systems ◽  
Infinite Dimensional ◽  
State Variable ◽  
Future Behavior ◽  
Fractional Integrator ◽  
True State ◽  
Fractional System ◽  
Dimensional Variable

In this paper, the initialization of fractional order systems is analyzed. The objective is to prove that the usual pseudostate variable x(t) is unable to predict the future behavior of the system, whereas the infinite dimensional variable z(ω, t) fulfills the requirements of a true state variable. Two fractional systems, a fractional integrator and a one-derivative fractional system, are analyzed with the help of elementary tests and numerical simulations. It is proved that the dynamic behaviors of these two fractional systems differ completely from that of their integer order counterparts. More specifically, initialization of these systems requires knowledge of z(ω,t0) initial condition.

Transient Stability Ranking Technique based on System Parameter Estimation and Extended Equal-Area Criterion

2008 ◽  
Vol 128 (1) ◽  
pp. 101-109 ◽  
Author(s):  
Akira Takeuchi ◽  
Takashi Sato ◽  
Kouya Takafuji ◽  
Hideaki Nishiiri ◽  
Kotaro Takasaki ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
System Parameter ◽  
Transient Stability ◽  
Equal Area ◽  
Stability Ranking ◽  
Ranking Technique

scholarly journals Set-membership identifiability of nonlinear models and related parameter estimation properties

2016 ◽  
Vol 26 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Carine Jauberthie ◽  
Louise Travé-MassuyèEs ◽  
Nathalie Verdière
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Dynamic System ◽  
Nonlinear Models ◽  
Differential Algebra ◽  
Related Parameter ◽  
Set Membership ◽  
Estimation Problems ◽  
The Mathematical Model

Abstract Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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