Fractional Order Extremum Seeking Control: Performance and Stability Analysis

In this paper, a novel extremum-seeking control algorithm called fractional order extremum-seeking control is analyzed and benchmarked against the traditional integer order one. Utilizing fractional order operators in extremum-seeking scheme improves the convergence speed, robustness, and performanc...

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Published inIEEE/ASME transactions on mechatronics Vol. 21; no. 3; pp. 1620 - 1628
Main Authors Malek, Hadi, YangQuan Chen
Format Journal Article
LanguageEnglish
Published New York IEEE 01.06.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithm design and analysis
Analytical models
Convergence
Cutoff frequency
Extremum seeking control
fractional order operators
Heuristic algorithms
Mathematical model
nonlinear optimization
Stability analysis
fractional order operators
Extremum-seeking control (ESC)
nonlinear optimization
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Abstract In this paper, a novel extremum-seeking control algorithm called fractional order extremum-seeking control is analyzed and benchmarked against the traditional integer order one. Utilizing fractional order operators in extremum-seeking scheme improves the convergence speed, robustness, and performance of this method without employing additional blocks. Using averaging model, the detailed analysis of fractional order extremum-seeking control is presented. Simulation and experimental results support the mathematical analysis and demonstrate that the proposed scheme outperforms the traditional extremum-seeking algorithm.
AbstractList In this paper, a novel extremum-seeking control algorithm called fractional order extremum-seeking control is analyzed and benchmarked against the traditional integer order one. Utilizing fractional order operators in extremum-seeking scheme improves the convergence speed, robustness, and performance of this method without employing additional blocks. Using averaging model, the detailed analysis of fractional order extremum-seeking control is presented. Simulation and experimental results support the mathematical analysis and demonstrate that the proposed scheme outperforms the traditional extremum-seeking algorithm.
Author Malek, Hadi
YangQuan Chen
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Cites_doi 10.1007/11893257_112
10.1109/TCST.2014.2301172
10.3182/20060719-3-PT-4902.00081
10.1016/j.automatica.2007.10.016
10.1109/81.989172
10.1109/TCST.2012.2223819
10.1016/S0005-1098(99)00183-1
10.1109/TCST.2012.2229465
10.1109/CDC.2006.377021
10.1016/j.mechatronics.2013.02.005
10.1016/j.sysconle.2014.11.005
10.1109/87.370698
10.1016/j.conengprac.2013.02.009
10.1109/ACC.2013.6579832
10.1109/TITS.2015.2414657
10.3390/en7031706
10.1109/ENERGY.2008.4781032
10.1016/j.matcom.2010.10.022
10.1007/978-1-84996-335-0
10.1016/j.automatica.2014.10.027
10.1007/978-1-4471-2224-1
10.1007/s10846-013-9871-1
10.1109/TMECH.2014.2319355
10.1080/0020717031000099100
10.1109/ACC.2010.5530764
10.1007/s12239-010-0072-7
10.1109/TCST.2010.2042296
10.1016/S0167-6911(99)00111-5
10.1109/ACC.2002.1025221
10.3166/ejc.15.331-347
10.1109/ISIE.2007.4374576
10.1007/978-3-642-18101-6
10.1016/j.automatica.2012.05.059
10.1109/IROS.2012.6386180
10.1002/0471669784
10.3182/20080706-5-KR-1001.02417
10.1109/TCST.2008.2008097
10.1109/TCST.2012.2236093
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Extremum-seeking control (ESC)
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References ref35
ref13
ref34
tan (ref17) 0
zhang (ref12) 0
ref15
ref36
ref31
ref33
ref11
ref32
ref10
ref1
monje (ref29) 2010
ref38
ref16
ref19
petras (ref43) 0
singh (ref26) 0
dandois (ref39) 2013; 6
podlubny (ref30) 1999
ref46
ref24
ref45
ref23
ref48
ref47
ref25
ref20
ref41
nesic (ref18) 2009; 15
ref22
ref44
ref21
ref28
petras (ref37) 2009; 12
ref27
ref8
ref7
ref9
ref4
khalil (ref42) 1996
ref3
ref6
ghods (ref14) 2011
ref5
leyva (ref2) 2011; 98
ref40
References_xml – start-page: 14
  year: 0
  ident: ref17
  article-title: Extremum seeking from 1922 to 2010
  publication-title: Proc 29th Chin Control Conf
– ident: ref22
  doi: 10.1007/11893257_112
– ident: ref6
  doi: 10.1109/TCST.2014.2301172
– year: 0
  ident: ref26
  article-title: Improving performance of extremum-seeking control applied to a supercritical-CO2 closed brayton cycle in a solar thermal power plant
– ident: ref31
  doi: 10.3182/20060719-3-PT-4902.00081
– ident: ref19
  doi: 10.1016/j.automatica.2007.10.016
– ident: ref34
  doi: 10.1109/81.989172
– ident: ref1
  doi: 10.1109/TCST.2012.2223819
– ident: ref38
  doi: 10.1016/S0005-1098(99)00183-1
– start-page: 873
  year: 0
  ident: ref43
  article-title: Digital fractional order controllers realized by PIC microprocessor: Experimental results
  publication-title: Proc Int Carpathian Control Conf
– ident: ref7
  doi: 10.1109/TCST.2012.2229465
– ident: ref48
  doi: 10.1109/CDC.2006.377021
– ident: ref33
  doi: 10.1016/j.mechatronics.2013.02.005
– ident: ref25
  doi: 10.1016/j.sysconle.2014.11.005
– start-page: 2765
  year: 0
  ident: ref12
  article-title: Extremum seeking control of a nonholonomic mobile robot with limited field of view
  publication-title: Proc Amer Control Conf
– ident: ref9
  doi: 10.1109/87.370698
– ident: ref3
  doi: 10.1016/j.conengprac.2013.02.009
– volume: 98
  start-page: 529
  year: 2011
  ident: ref2
  article-title: MPPT based on sinusoidal extremum-seeking control in PV generation
  publication-title: Int J Photoenergy
– ident: ref36
  doi: 10.1109/ACC.2013.6579832
– ident: ref45
  doi: 10.1109/TITS.2015.2414657
– ident: ref4
  doi: 10.3390/en7031706
– ident: ref5
  doi: 10.1109/ENERGY.2008.4781032
– ident: ref16
  doi: 10.1016/j.matcom.2010.10.022
– year: 2010
  ident: ref29
  publication-title: Fractional-order Systems and Controls Fundamentals and Applications (Advances in Industrial Control)
  doi: 10.1007/978-1-84996-335-0
– ident: ref24
  doi: 10.1016/j.automatica.2014.10.027
– volume: 6
  start-page: 1
  year: 2013
  ident: ref39
  article-title: NARX modeling and extremum-seeking control of a separation
  publication-title: Aerospace Lab Journal
– ident: ref8
  doi: 10.1007/978-1-4471-2224-1
– ident: ref13
  doi: 10.1007/s10846-013-9871-1
– year: 2011
  ident: ref14
  article-title: Extremum seeking for mobile robots
– ident: ref46
  doi: 10.1109/TMECH.2014.2319355
– ident: ref20
  doi: 10.1080/0020717031000099100
– ident: ref23
  doi: 10.1109/ACC.2010.5530764
– year: 1999
  ident: ref30
  publication-title: Fractional Differential Equations An Introduction to Fractional Derivatives Fractional Differential Equations Some Methods of Their Solution and Some of Their Applications
– ident: ref47
  doi: 10.1007/s12239-010-0072-7
– ident: ref44
  doi: 10.1109/TCST.2010.2042296
– ident: ref41
  doi: 10.1016/S0167-6911(99)00111-5
– ident: ref15
  doi: 10.1109/ACC.2002.1025221
– volume: 15
  start-page: 331
  year: 2009
  ident: ref18
  article-title: Extremum seeking control: Convergence analysis
  publication-title: Eur J Control
  doi: 10.3166/ejc.15.331-347
– ident: ref28
  doi: 10.1109/ISIE.2007.4374576
– ident: ref32
  doi: 10.1007/978-3-642-18101-6
– ident: ref27
  doi: 10.1016/j.automatica.2012.05.059
– volume: 12
  start-page: 269
  year: 2009
  ident: ref37
  article-title: Stability of fractional order systems with rational order: A survey
  publication-title: Fractional Calculus Appl Anal
– ident: ref21
  doi: 10.1109/IROS.2012.6386180
– ident: ref40
  doi: 10.1002/0471669784
– ident: ref35
  doi: 10.3182/20080706-5-KR-1001.02417
– ident: ref10
  doi: 10.1109/TCST.2008.2008097
– ident: ref11
  doi: 10.1109/TCST.2012.2236093
– year: 1996
  ident: ref42
  publication-title: Nonlinear Systems
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SubjectTerms Algorithm design and analysis
Analytical models
Convergence
Cutoff frequency
Extremum seeking control
fractional order operators
Heuristic algorithms
Mathematical model
nonlinear optimization
Stability analysis
Title Fractional Order Extremum Seeking Control: Performance and Stability Analysis
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