Analysis of fractional order error models in adaptive systems: Mixed order cases

N. Aguila-Camacho; J. Gallegos; M. A. Duarte-Mermoud

doi:10.1515/fca-2019-0058

Analysis of fractional order error models in adaptive systems: Mixed order cases

N. Aguila-Camacho
, J. Gallegos
, M. A. Duarte-Mermoud

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

This paper presents the properties of two fractional order error models (FOEM) that arise in the analysis of fractional order adaptive systems (FOAS). Cases where the fractional order is the same for every equation in these two FOEM were analyzed in a previous work, obtaining useful results. However, those cases where the fractional orders are different in the equations of FOEM (mixed order cases) have not been addressed before. This paper treats the analysis of some of these mixed order cases, proving boundedness of all the signals and convergence to zero of the mean value of the squared norm of the output error. A model reference adaptive control (MRAC) scheme for an integer order plant using fractional adaptive laws for estimating the controller parameters is presented at the end of the paper, which shows the applicability and importance of the proposed results.

Original language	English
Pages (from-to)	1113-1132
Number of pages	20
Journal	Fractional Calculus and Applied Analysis
Volume	22
Issue number	4
DOIs	https://doi.org/10.1515/fca-2019-0058
State	Published - 1 Aug 2019
Externally published	Yes

Keywords

Adaptive systems
Fractional systems
Mixed order error models
Model reference adaptive control
Simulation
Stability

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10.1515/fca-2019-0058

Cite this

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title = "Analysis of fractional order error models in adaptive systems: Mixed order cases",

abstract = "This paper presents the properties of two fractional order error models (FOEM) that arise in the analysis of fractional order adaptive systems (FOAS). Cases where the fractional order is the same for every equation in these two FOEM were analyzed in a previous work, obtaining useful results. However, those cases where the fractional orders are different in the equations of FOEM (mixed order cases) have not been addressed before. This paper treats the analysis of some of these mixed order cases, proving boundedness of all the signals and convergence to zero of the mean value of the squared norm of the output error. A model reference adaptive control (MRAC) scheme for an integer order plant using fractional adaptive laws for estimating the controller parameters is presented at the end of the paper, which shows the applicability and importance of the proposed results.",

keywords = "Adaptive systems, Fractional systems, Mixed order error models, Model reference adaptive control, Simulation, Stability",

author = "N. Aguila-Camacho and J. Gallegos and Duarte-Mermoud, \{M. A.\}",

note = "Publisher Copyright: {\textcopyright} 2019 Diogenes Co., Sofia",

year = "2019",

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doi = "10.1515/fca-2019-0058",

language = "English",

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TY - JOUR

T1 - Analysis of fractional order error models in adaptive systems

T2 - Mixed order cases

AU - Aguila-Camacho, N.

AU - Gallegos, J.

AU - Duarte-Mermoud, M. A.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - This paper presents the properties of two fractional order error models (FOEM) that arise in the analysis of fractional order adaptive systems (FOAS). Cases where the fractional order is the same for every equation in these two FOEM were analyzed in a previous work, obtaining useful results. However, those cases where the fractional orders are different in the equations of FOEM (mixed order cases) have not been addressed before. This paper treats the analysis of some of these mixed order cases, proving boundedness of all the signals and convergence to zero of the mean value of the squared norm of the output error. A model reference adaptive control (MRAC) scheme for an integer order plant using fractional adaptive laws for estimating the controller parameters is presented at the end of the paper, which shows the applicability and importance of the proposed results.

AB - This paper presents the properties of two fractional order error models (FOEM) that arise in the analysis of fractional order adaptive systems (FOAS). Cases where the fractional order is the same for every equation in these two FOEM were analyzed in a previous work, obtaining useful results. However, those cases where the fractional orders are different in the equations of FOEM (mixed order cases) have not been addressed before. This paper treats the analysis of some of these mixed order cases, proving boundedness of all the signals and convergence to zero of the mean value of the squared norm of the output error. A model reference adaptive control (MRAC) scheme for an integer order plant using fractional adaptive laws for estimating the controller parameters is presented at the end of the paper, which shows the applicability and importance of the proposed results.

KW - Adaptive systems

KW - Fractional systems

KW - Mixed order error models

KW - Model reference adaptive control

KW - Simulation

KW - Stability

UR - https://www.scopus.com/pages/publications/85074435015

U2 - 10.1515/fca-2019-0058

DO - 10.1515/fca-2019-0058

M3 - Article

AN - SCOPUS:85074435015

SN - 1311-0454

VL - 22

SP - 1113

EP - 1132

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 4

ER -

Analysis of fractional order error models in adaptive systems: Mixed order cases

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