scholarly journals Duality of variable fractional order difference operators and its application in identification

2014 ◽  
Vol 62 (4) ◽  
pp. 809-815 ◽  
Author(s):  
D. Sierociuk ◽  
M. Twardy
Keyword(s):  
System Identification ◽  
Least Squares ◽  
Fractional Order ◽  
Least Squares Estimation ◽  
Difference Operators ◽  
Variable Order ◽  
Fractional Systems ◽  
Order Difference

Abstract The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.

scholarly journals Linear isomorphic spaces of fractional-order difference operators

2021 ◽  
Vol 60 (1) ◽  
pp. 1155-1164 ◽  
Author(s):  
S.A. Mohiuddine ◽  
Kuldip Raj ◽  
M. Mursaleen ◽  
Abdullah Alotaibi
Keyword(s):  
Fractional Order ◽  
Difference Operators ◽  
Order Difference

scholarly journals Multiparameter Fractional Difference Linear Control Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Dorota Mozyrska
Keyword(s):  
Control Systems ◽  
Fractional Order ◽  
Initial Conditions ◽  
Linear Control Systems ◽  
Difference Operators ◽  
Fractional Operators ◽  
Fractional Difference ◽  
Order Difference ◽  
Time Control ◽  
Controllability And Observability

The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.

Local controllability of nonlinear discrete-time fractional order systems

2013 ◽  
Vol 61 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. Mozyrska ◽  
E. Pawłuszewicz
Keyword(s):  
Linear Approximation ◽  
Fractional Order ◽  
Discrete Time ◽  
Local Controllability ◽  
Difference Operators ◽  
Fractional Order Systems ◽  
Discrete Time System ◽  
Controllability Problem ◽  
Time System ◽  
Order Difference

Abstract The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

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