Mixed fractional order adaptive control: Theory and applications

Manuel A. Duarte-Mermud; Libel Bárzaga; Gustavo Ceballos-Benavides

doi:10.1016/j.ifacol.2020.12.2016

Mixed fractional order adaptive control: Theory and applications

Manuel A. Duarte-Mermud^*, Libel Bárzaga^*, Gustavo Ceballos-Benavides

^*Corresponding author for this work

Advanced Mining Technology Center

Research output: Contribution to journal › Conference article › peer-review

4 Scopus citations

Abstract

In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.

Original language	English
Pages (from-to)	1543-1548
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	53
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.2016
State	Published - 2020
Event	21st IFAC World Congress 2020 - Berlin, Germany Duration: 2020 → 2020

Bibliographical note

Publisher Copyright:
Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0)

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/j.ifacol.2020.12.2016

Cite this

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title = "Mixed fractional order adaptive control: Theory and applications",

abstract = "In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.",

keywords = "Adaptive control, Boundedness, Convergence, Fractional order systems, Multi-order fractional systems, Stability",

author = "Duarte-Mermud, {Manuel A.} and Libel B{\'a}rzaga and Gustavo Ceballos-Benavides",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0); 21st IFAC World Congress 2020 ; Conference date: 12-07-2020 Through 17-07-2020",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.2016",

language = "English",

volume = "53",

pages = "1543--1548",

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TY - JOUR

T1 - Mixed fractional order adaptive control

T2 - 21st IFAC World Congress 2020

AU - Duarte-Mermud, Manuel A.

AU - Bárzaga, Libel

AU - Ceballos-Benavides, Gustavo

PY - 2020

Y1 - 2020

N2 - In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.

AB - In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.

KW - Adaptive control

KW - Boundedness

KW - Convergence

KW - Fractional order systems

KW - Multi-order fractional systems

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85107613108&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.2016

DO - 10.1016/j.ifacol.2020.12.2016

M3 - Conference article

AN - SCOPUS:85107613108

SN - 1474-6670

VL - 53

SP - 1543

EP - 1548

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

Y2 - 12 July 2020 through 17 July 2020

ER -

Mixed fractional order adaptive control: Theory and applications

Abstract

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ASJC Scopus subject areas

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