Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral mode...

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Published inIEEE transactions on automatic control Vol. 59; no. 9; pp. 2385 - 2399
Main Authors Bresch-Pietri, Delphine, Chauvin, Jonathan, Petit, Nicolas
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects
Actuators
Asymptotic properties
Automatic
Backstepping
Control systems
Control theory
Delay
Delays
Engineering Sciences
Equations
Feedback
Fuels
Linear systems
Mathematical models
Robustness
Stability analysis
Stabilization
Backstepping
partial differential equation
time-delay systems
prediction-based feedback
delay differential equation
Time-delay systems
Prediction-based feedback
Delay differential equation
Partial differential equation
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Abstract In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems.
AbstractList In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems.
Author Bresch-Pietri, Delphine
Chauvin, Jonathan
Petit, Nicolas
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  givenname: Nicolas
  surname: Petit
  fullname: Petit, Nicolas
  organization: Centre Autom. et Sysemes, MINES ParisTech, Paris, France
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10.1016/j.ejcon.2013.05.016
10.1109/TAC.1982.1103023
10.1115/1.1569950
10.1109/TAC.1979.1102124
10.1016/j.jprocont.2010.01.008
10.1016/j.automatica.2013.02.019
10.1016/j.automatica.2004.09.006
10.2748/tmj/1113247567
10.1115/1.4005278
10.1016/j.automatica.2013.02.050
10.1109/TNN.2011.2160987
10.1137/1.9780898718645
10.1109/CCA.2008.4629668
10.1016/S0005-1098(03)00167-5
10.1016/S0005-1098(00)00145-X
10.1137/1.9780898718607
10.1016/j.compchemeng.2005.08.003
10.1016/j.jprocont.2009.07.008
10.1109/CDC.1998.760828
10.1016/j.automatica.2012.05.056
10.1109/ACC.2008.4587271
10.1016/j.pecs.2005.08.001
10.2514/2.5947
10.1109/CDC.1991.261456
10.1109/TAC.2012.2208294
10.1016/j.conengprac.2010.06.011
10.1007/978-3-319-01695-5_26
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Issue 9
Keywords Backstepping
partial differential equation
time-delay systems
prediction-based feedback
delay differential equation
Time-delay systems
Prediction-based feedback
Delay differential equation
Partial differential equation
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References smith (ref33) 1959; 6
ref13
ref12
bresch-pietri (ref7) 2012
ref37
ref36
ref14
perry (ref29) 1984; 7
ref31
ref30
ref11
ref32
moon (ref26) 2001; 37
ref1
ref17
ref38
ref16
ref19
ref18
bresch-pietri (ref10) 0
wansheng (ref34) 2010
ref24
ref23
ref25
ref20
balachandran (ref2) 2009
ref22
witrant (ref35) 2005
ref21
ref28
halanay (ref15) 1966; 23
natanzon (ref27) 1999; 222
ref8
ref4
ref3
ref6
ref5
bresch-pietri (ref9) 0
References_xml – ident: ref22
  doi: 10.1007/978-0-8176-4877-0
– start-page: 266
  year: 0
  ident: ref9
  article-title: Invoking Halanay inequality to conclude on closed-loop stability of a process with input-varying delay
  publication-title: Proc IFAC Workshop Time-Delay Syst
– ident: ref5
  doi: 10.1016/j.ejcon.2013.05.016
– ident: ref1
  doi: 10.1109/TAC.1982.1103023
– ident: ref14
  doi: 10.1115/1.1569950
– ident: ref24
  doi: 10.1109/TAC.1979.1102124
– ident: ref12
  doi: 10.1016/j.jprocont.2010.01.008
– volume: 222
  year: 1999
  ident: ref27
  publication-title: Combustion instability
– ident: ref20
  doi: 10.1016/j.automatica.2013.02.019
– ident: ref37
  doi: 10.1016/j.automatica.2004.09.006
– year: 2009
  ident: ref2
  publication-title: Delay Differential Equations Recent Advances and New Directions
– ident: ref18
  doi: 10.2748/tmj/1113247567
– year: 2010
  ident: ref34
  article-title: A generalized halanay inequality for stability of nonlinear neutral functional differential equations
  publication-title: J Inequalities Appl
– ident: ref3
  doi: 10.1115/1.4005278
– volume: 23
  year: 1966
  ident: ref15
  publication-title: Differential Equations Stability Oscillations Time Lags
– ident: ref6
  doi: 10.1016/j.automatica.2013.02.050
– ident: ref23
  doi: 10.1109/TNN.2011.2160987
– year: 2012
  ident: ref7
  publication-title: Robust control of variable time-delay systems Theoretical contributions and applications to engine control
– ident: ref25
  doi: 10.1137/1.9780898718645
– ident: ref32
  doi: 10.1109/CCA.2008.4629668
– ident: ref31
  doi: 10.1016/S0005-1098(03)00167-5
– start-page: 144
  year: 0
  ident: ref10
  article-title: Sufficient condition for prediction-based stabilization of linear system subject to input-dependent input-delay
  publication-title: Proc Amer Control Conf
– volume: 37
  start-page: 307
  year: 2001
  ident: ref26
  article-title: Robust stabilization of uncertain input-delayed systems using reduction method
  publication-title: Automatica
  doi: 10.1016/S0005-1098(00)00145-X
– volume: 6
  start-page: 28
  year: 1959
  ident: ref33
  article-title: A controller to overcome dead time
  publication-title: ISA J
– ident: ref21
  doi: 10.1137/1.9780898718607
– ident: ref16
  doi: 10.1016/j.compchemeng.2005.08.003
– ident: ref38
  doi: 10.1016/j.jprocont.2009.07.008
– ident: ref30
  doi: 10.1109/CDC.1998.760828
– ident: ref8
  doi: 10.1016/j.automatica.2012.05.056
– ident: ref19
  doi: 10.1109/ACC.2008.4587271
– ident: ref13
  doi: 10.1016/j.pecs.2005.08.001
– ident: ref17
  doi: 10.2514/2.5947
– ident: ref28
  doi: 10.1109/CDC.1991.261456
– volume: 7
  year: 1984
  ident: ref29
  publication-title: Perry's Chemical Engineers' Handbook
– year: 2005
  ident: ref35
  publication-title: Stabilisation des systèmes commandés par réseaux
– ident: ref4
  doi: 10.1109/TAC.2012.2208294
– ident: ref36
  doi: 10.1016/j.conengprac.2010.06.011
– ident: ref11
  doi: 10.1007/978-3-319-01695-5_26
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SubjectTerms Actuators
Asymptotic properties
Automatic
Backstepping
Control systems
Control theory
Delay
Delays
Engineering Sciences
Equations
Feedback
Fuels
Linear systems
Mathematical models
Robustness
Stability analysis
Stabilization
Title Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type
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