Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general fram...

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Main Authors:	Manuel A. Duarte-Mermoud, Javier A. Gallegos, Norelys Aguila-Camacho, Rafael Castro-Linares
Format:	Article
Language:	English
Published:	MDPI AG 2018-09-01
Series:	Algorithms
Subjects:	fractional order systems fractional order observers fractional order adaptive observers robust fractional order observers
Online Access:	http://www.mdpi.com/1999-4893/11/9/136

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spelling	doaj-29123c644f1540b4b23442736f3683862020-11-24T21:22:27ZengMDPI AGAlgorithms1999-48932018-09-0111913610.3390/a11090136a11090136Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant SystemsManuel A. Duarte-Mermoud0Javier A. Gallegos1Norelys Aguila-Camacho2Rafael Castro-Linares3Department of Electrical Engineering, University of Chile, Av. Tupper, Santiago 2007, ChileDepartment of Electrical Engineering, University of Chile, Av. Tupper, Santiago 2007, ChileAdvanced Mining Technology Center, University of Chile, Av. Tupper, Santiago 2007, ChileDepartment of Electrical Engineering, CINVESTAV, Av. IPN, México DF 2508, MexicoAdaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.http://www.mdpi.com/1999-4893/11/9/136fractional order systemsfractional order observersfractional order adaptive observersrobust fractional order observers
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Manuel A. Duarte-Mermoud Javier A. Gallegos Norelys Aguila-Camacho Rafael Castro-Linares
spellingShingle	Manuel A. Duarte-Mermoud Javier A. Gallegos Norelys Aguila-Camacho Rafael Castro-Linares Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems Algorithms fractional order systems fractional order observers fractional order adaptive observers robust fractional order observers
author_facet	Manuel A. Duarte-Mermoud Javier A. Gallegos Norelys Aguila-Camacho Rafael Castro-Linares
author_sort	Manuel A. Duarte-Mermoud
title	Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
title_short	Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
title_full	Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
title_fullStr	Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
title_full_unstemmed	Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems
title_sort	mixed order fractional observers for minimal realizations of linear time-invariant systems
publisher	MDPI AG
series	Algorithms
issn	1999-4893
publishDate	2018-09-01
description	Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.
topic	fractional order systems fractional order observers fractional order adaptive observers robust fractional order observers
url	http://www.mdpi.com/1999-4893/11/9/136
work_keys_str_mv	AT manueladuartemermoud mixedorderfractionalobserversforminimalrealizationsoflineartimeinvariantsystems AT javieragallegos mixedorderfractionalobserversforminimalrealizationsoflineartimeinvariantsystems AT norelysaguilacamacho mixedorderfractionalobserversforminimalrealizationsoflineartimeinvariantsystems AT rafaelcastrolinares mixedorderfractionalobserversforminimalrealizationsoflineartimeinvariantsystems
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Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

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