APPROXIMATE MIN-MAX MPC FOR LINEAR HYBRID SYSTEMS

This paper presents a Receding Horizon Control (RHC) strategy to robustly control linear hybrid systems subject to bounded additive disturbances. First, the open-loop finite horizon min-max optimal control problem associated with the RHC strategy is presented, defining a mixed-integer optimization p...

Full description

Saved in:
Bibliographic Details
Published inIFAC Proceedings Volumes Vol. 38; no. 1; pp. 622 - 627
Main Authors Botto, M. Ayala, Silva, M., Costa, J. Sá da
Format Journal Article
LanguageEnglish
Published 2005
Subjects
hybrid systems
min-max optimization
mixed logical dynamical systems
model predictive control control
robust control
min-max optimization
model predictive control control
robust control
hybrid systems
mixed logical dynamical systems
Online AccessGet full text
ISSN1474-6670
DOI10.3182/20050703-6-CZ-1902.00504

Cover

Abstract This paper presents a Receding Horizon Control (RHC) strategy to robustly control linear hybrid systems subject to bounded additive disturbances. First, the open-loop finite horizon min-max optimal control problem associated with the RHC strategy is presented, defining a mixed-integer optimization problem. The goal of the min-max formulation is to minimize the worst-case cost of the performance index, while guaranteeing performance/safety constraints for all possible disturbance realizations. Then it will be proved that feasibility at the initial time as well as convexity arguments and set-invariance assumptions are sufficient conditions to guarantee robust stability and performance of the closed-loop system. Simulation results for a perturbed hybrid system will demonstrate the potential of the proposed robust optimal control design.
AbstractList This paper presents a Receding Horizon Control (RHC) strategy to robustly control linear hybrid systems subject to bounded additive disturbances. First, the open-loop finite horizon min-max optimal control problem associated with the RHC strategy is presented, defining a mixed-integer optimization problem. The goal of the min-max formulation is to minimize the worst-case cost of the performance index, while guaranteeing performance/safety constraints for all possible disturbance realizations. Then it will be proved that feasibility at the initial time as well as convexity arguments and set-invariance assumptions are sufficient conditions to guarantee robust stability and performance of the closed-loop system. Simulation results for a perturbed hybrid system will demonstrate the potential of the proposed robust optimal control design.
Author Botto, M. Ayala
Silva, M.
Costa, J. Sá da
Author_xml – sequence: 1
  givenname: M. Ayala
  surname: Botto
  fullname: Botto, M. Ayala
  email: AyalaBotto@dem.ist.utl.pt
– sequence: 2
  givenname: M.
  surname: Silva
  fullname: Silva, M.
– sequence: 3
  givenname: J. Sá da
  surname: Costa
  fullname: Costa, J. Sá da
BookMark eNqFj81qwkAcxPdgodb6DvsCa_-72Y_kGNNYA4mRaEG9LOtmFwJtLEkp9O2baHvuZQYGZpjfA5q0l9YhhCksAhqyJwYgQEFAJElOhEbAFmPCJ2hKueJESgX3aN73zRmYEpQJoaaIxtttVR6yIt6nuMg2pIgPuNgmeFVWOM82aVzh9XFZZc94d9zt02L3iO68eevd_Ndn6HWV7pM1ycuXLIlzYimEfNDAMGUlP3vPFAdpQbGodlRFVILi4qwkA-4Da1TorAwDyutQGO-cMJE1wQyFt13bXfq-c15_dM276b41BT0S6z9iLXVy0iOxvhIP1eWt6oZ_X43rdG8b11pXN52zn7q-NP-P_ACUvFw0
Cites_doi 10.1016/S0005-1098(99)00113-2
10.1007/978-1-4615-1139-7_12
10.1002/rnc.817
10.1109/JPROC.2000.871299
10.1109/ACC.2001.945564
10.1016/S0005-1098(98)00178-2
10.1109/9.704989
10.1137/S0036139997325199
10.1109/9.654885
10.1016/S0005-1098(00)00050-9
10.1109/9.911417
10.1016/S0005-1098(01)00059-0
10.1016/S0005-1098(99)00214-9
ContentType Journal Article
Copyright 2005 IFAC
Copyright_xml – notice: 2005 IFAC
DBID AAYXX
CITATION
DOI 10.3182/20050703-6-CZ-1902.00504
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
EndPage 627
ExternalDocumentID 10_3182_20050703_6_CZ_1902_00504
S1474667016365168
GroupedDBID ALMA_UNASSIGNED_HOLDINGS
OK1
AAYXX
CITATION
ID FETCH-LOGICAL-c1084-c13a27c64bff27406c0729de179160745b76204f3ca78ec68314d85afee5a9ca3
ISSN 1474-6670
IngestDate Tue Jul 01 02:32:39 EDT 2025
Thu Aug 18 14:36:18 EDT 2022
IsPeerReviewed false
IsScholarly false
Issue 1
Keywords min-max optimization
model predictive control control
robust control
hybrid systems
mixed logical dynamical systems
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c1084-c13a27c64bff27406c0729de179160745b76204f3ca78ec68314d85afee5a9ca3
PageCount 6
ParticipantIDs crossref_primary_10_3182_20050703_6_CZ_1902_00504
elsevier_sciencedirect_doi_10_3182_20050703_6_CZ_1902_00504
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2005
2005-00-00
PublicationDateYYYYMMDD 2005-01-01
PublicationDate_xml – year: 2005
  text: 2005
PublicationDecade 2000
PublicationTitle IFAC Proceedings Volumes
PublicationYear 2005
References Mayne, Rawlings, Rao, Scokaert (bib16) 2000; 36
E.C. Kerrigan and J.M. Maciejowski. Robustly stable feedback min-max model predictive control. In
B. de Schutter and T.J.J. van den Boom. Model predictive control for max-min-plus-scaling systems. In
Hedlund, Rantzer (bib10) 1999
pages 208-213, Faro, Portugal, 2004
Blondel, Tsitsiklis (bib4) 2000; 36
E.C. Kerrigan and D.Q. Mayne. Optimal control of constrained, piecewise affine systems with bounded disturbances. In
Las Vegas, Nevada, USA, December 2002
Boyd, Vandenberghe (bib5) 2004
C.G. Cassandras and K. Gokbayrak.
Branicky, Borkar, Mitter (bib6) 1998; 43
chapter Optimal Control for Discrete Event and Hybrid Systems, pages 285-304. Kluwer, 2002
pages 319-324, Arlington, Virginia, USA, 2001
Antsaklis (bib1) 2000; 88
Bemporad, Morari (bib2) 1999; 35
Blanchini (bib3) November 1999; 35
Cassandras, Pepyne, Wardi (bib8) 2001; 46
Heemels, Schumacher, Weiland (bib12) 2000; 60
Denver, Colorado, USA, June 2003
Heemels, de Schutter, Bemporad (bib11) 2001; 37
Mayne, Rakovic (bib15) 2003; 13
Scokaert, Mayne (bib17) 1998; 43
M.P. Silva, L. Pina, A. Bemporad, M. Ayala Botto, and J. Sá da Costa. Robust optimal control of linear hybrid systems: an mld approach. In
10.3182/20050703-6-CZ-1902.00504_bib7
Blondel (10.3182/20050703-6-CZ-1902.00504_bib4) 2000; 36
Scokaert (10.3182/20050703-6-CZ-1902.00504_bib17) 1998; 43
Heemels (10.3182/20050703-6-CZ-1902.00504_bib11) 2001; 37
Heemels (10.3182/20050703-6-CZ-1902.00504_bib12) 2000; 60
Mayne (10.3182/20050703-6-CZ-1902.00504_bib15) 2003; 13
Branicky (10.3182/20050703-6-CZ-1902.00504_bib6) 1998; 43
10.3182/20050703-6-CZ-1902.00504_bib13
Mayne (10.3182/20050703-6-CZ-1902.00504_bib16) 2000; 36
10.3182/20050703-6-CZ-1902.00504_bib14
Cassandras (10.3182/20050703-6-CZ-1902.00504_bib8) 2001; 46
10.3182/20050703-6-CZ-1902.00504_bib18
Antsaklis (10.3182/20050703-6-CZ-1902.00504_bib1) 2000; 88
Blanchini (10.3182/20050703-6-CZ-1902.00504_bib3) 1999; 35
Hedlund (10.3182/20050703-6-CZ-1902.00504_bib10) 1999
Bemporad (10.3182/20050703-6-CZ-1902.00504_bib2) 1999; 35
10.3182/20050703-6-CZ-1902.00504_bib9
Boyd (10.3182/20050703-6-CZ-1902.00504_bib5) 2004
References_xml – volume: 46
  start-page: 398
  year: 2001
  end-page: 415
  ident: bib8
  article-title: Optimal control of a class of hybrid systems
  publication-title: IEEE Transactions on Automatic Control
– reference: Denver, Colorado, USA, June 2003
– volume: 36
  start-page: 1249
  year: 2000
  end-page: 1274
  ident: bib4
  article-title: A survey of computational complexity results in systems and control
  publication-title: Automatica
– reference: Las Vegas, Nevada, USA, December 2002
– year: 1999
  ident: bib10
  article-title: Optimal control of hybrid systems
  publication-title: Proc. IEEE Conference on Decision and Control
– reference: B. de Schutter and T.J.J. van den Boom. Model predictive control for max-min-plus-scaling systems. In
– reference: pages 319-324, Arlington, Virginia, USA, 2001
– volume: 35
  start-page: 407
  year: 1999
  end-page: 427
  ident: bib2
  article-title: Control of systems integrating logic, dynamics, and constraints
  publication-title: Automatica
– volume: 35
  start-page: 1747
  year: November 1999
  end-page: 1768
  ident: bib3
  article-title: Set invariance in control – a survey
  publication-title: Automatica
– volume: 37
  start-page: 1085
  year: 2001
  end-page: 1091
  ident: bib11
  article-title: Equivalence of hybrid dynamical models
  publication-title: Automatica
– reference: E.C. Kerrigan and J.M. Maciejowski. Robustly stable feedback min-max model predictive control. In
– reference: E.C. Kerrigan and D.Q. Mayne. Optimal control of constrained, piecewise affine systems with bounded disturbances. In
– reference: M.P. Silva, L. Pina, A. Bemporad, M. Ayala Botto, and J. Sá da Costa. Robust optimal control of linear hybrid systems: an mld approach. In
– volume: 36
  start-page: 789
  year: 2000
  end-page: 814
  ident: bib16
  article-title: Constrained model predictive control: Stability and optimality
  publication-title: Automatica
– reference: chapter Optimal Control for Discrete Event and Hybrid Systems, pages 285-304. Kluwer, 2002
– reference: pages 208-213, Faro, Portugal, 2004
– volume: 43
  start-page: 31
  year: 1998
  end-page: 45
  ident: bib6
  article-title: A unified framework for hybrid control: model and optimal control theory
  publication-title: IEEE Transactions on Automatic Control
– volume: 88
  start-page: 879
  year: 2000
  end-page: 886
  ident: bib1
  article-title: A brief introduction to the theory and applications of hybrid systems
  publication-title: Proc. IEEE
– volume: 43
  start-page: 1136
  year: 1998
  end-page: 1142
  ident: bib17
  article-title: Min-max feedback model predictive control
  publication-title: IEEE Transations on Automatic Control
– year: 2004
  ident: bib5
  publication-title: Convex Optimization
– volume: 13
  start-page: 261
  year: 2003
  end-page: 279
  ident: bib15
  article-title: Model predictive control of constrained piecewise affine discrete-time systems
  publication-title: International Journal of Robust and Nonlinear Control
– volume: 60
  start-page: 1234
  year: 2000
  end-page: 1269
  ident: bib12
  article-title: Linear complementarity systems
  publication-title: SIAM Journal on Applied Mathematics
– reference: C.G. Cassandras and K. Gokbayrak.
– volume: 35
  start-page: 1747
  issue: 11
  year: 1999
  ident: 10.3182/20050703-6-CZ-1902.00504_bib3
  article-title: Set invariance in control – a survey
  publication-title: Automatica
  doi: 10.1016/S0005-1098(99)00113-2
– ident: 10.3182/20050703-6-CZ-1902.00504_bib7
  doi: 10.1007/978-1-4615-1139-7_12
– volume: 13
  start-page: 261
  issue: 3-4
  year: 2003
  ident: 10.3182/20050703-6-CZ-1902.00504_bib15
  article-title: Model predictive control of constrained piecewise affine discrete-time systems
  publication-title: International Journal of Robust and Nonlinear Control
  doi: 10.1002/rnc.817
– volume: 88
  start-page: 879
  issue: 7
  year: 2000
  ident: 10.3182/20050703-6-CZ-1902.00504_bib1
  article-title: A brief introduction to the theory and applications of hybrid systems
  publication-title: Proc. IEEE
  doi: 10.1109/JPROC.2000.871299
– ident: 10.3182/20050703-6-CZ-1902.00504_bib18
– year: 2004
  ident: 10.3182/20050703-6-CZ-1902.00504_bib5
– ident: 10.3182/20050703-6-CZ-1902.00504_bib9
  doi: 10.1109/ACC.2001.945564
– volume: 35
  start-page: 407
  issue: 3
  year: 1999
  ident: 10.3182/20050703-6-CZ-1902.00504_bib2
  article-title: Control of systems integrating logic, dynamics, and constraints
  publication-title: Automatica
  doi: 10.1016/S0005-1098(98)00178-2
– year: 1999
  ident: 10.3182/20050703-6-CZ-1902.00504_bib10
  article-title: Optimal control of hybrid systems
  publication-title: Proc. IEEE Conference on Decision and Control
– volume: 43
  start-page: 1136
  issue: 8
  year: 1998
  ident: 10.3182/20050703-6-CZ-1902.00504_bib17
  article-title: Min-max feedback model predictive control
  publication-title: IEEE Transations on Automatic Control
  doi: 10.1109/9.704989
– ident: 10.3182/20050703-6-CZ-1902.00504_bib13
– volume: 60
  start-page: 1234
  issue: 4
  year: 2000
  ident: 10.3182/20050703-6-CZ-1902.00504_bib12
  article-title: Linear complementarity systems
  publication-title: SIAM Journal on Applied Mathematics
  doi: 10.1137/S0036139997325199
– volume: 43
  start-page: 31
  issue: 1
  year: 1998
  ident: 10.3182/20050703-6-CZ-1902.00504_bib6
  article-title: A unified framework for hybrid control: model and optimal control theory
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/9.654885
– volume: 36
  start-page: 1249
  issue: 9
  year: 2000
  ident: 10.3182/20050703-6-CZ-1902.00504_bib4
  article-title: A survey of computational complexity results in systems and control
  publication-title: Automatica
  doi: 10.1016/S0005-1098(00)00050-9
– ident: 10.3182/20050703-6-CZ-1902.00504_bib14
– volume: 46
  start-page: 398
  issue: 3
  year: 2001
  ident: 10.3182/20050703-6-CZ-1902.00504_bib8
  article-title: Optimal control of a class of hybrid systems
  publication-title: IEEE Transactions on Automatic Control
  doi: 10.1109/9.911417
– volume: 37
  start-page: 1085
  issue: 7
  year: 2001
  ident: 10.3182/20050703-6-CZ-1902.00504_bib11
  article-title: Equivalence of hybrid dynamical models
  publication-title: Automatica
  doi: 10.1016/S0005-1098(01)00059-0
– volume: 36
  start-page: 789
  issue: 6
  year: 2000
  ident: 10.3182/20050703-6-CZ-1902.00504_bib16
  article-title: Constrained model predictive control: Stability and optimality
  publication-title: Automatica
  doi: 10.1016/S0005-1098(99)00214-9
SSID ssib027512557
ssib036250806
ssib001723113
ssib001723112
ssib046627245
ssib028086724
Score 1.338922
Snippet This paper presents a Receding Horizon Control (RHC) strategy to robustly control linear hybrid systems subject to bounded additive disturbances. First, the...
SourceID crossref
elsevier
SourceType Index Database
Publisher
StartPage 622
SubjectTerms hybrid systems
min-max optimization
mixed logical dynamical systems
model predictive control control
robust control
Title APPROXIMATE MIN-MAX MPC FOR LINEAR HYBRID SYSTEMS
URI https://dx.doi.org/10.3182/20050703-6-CZ-1902.00504
Volume 38
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9NAEF5BuXBBRYAoFOQDN2sD9j4rTlaUKilyGpIUpb2sdte2VKlKEAQk-PXMPmyHUlToZRU5yjj2fJr9ZmZnBqE34PNkpGoqrIWVmNaywkcVYJkZ3hBibd5YFxoop3x8Rk9WbNWOuI_VJVszsD9vrCu5i1bhGujVVcn-h2Y7oXABPoN-YQUNw_pPOi5ms_npalIWy1FaTqa4LFZpOQM2ejoHqzQdFfN0fO6Oz6SL88VyFOPPkYpOjothqBPw-9fX9JM3VH3YfLP1I5bScpAWP_RVZ78Xl1ffdfiiy2BsIgs9GaQLn3vP0ujqtxEFtmP-qKCY8zDKo7WPRP6Bg2DseKgojvsmDzX-100y2AzX4tXdx1kXzPHwAgMLcX1SWZg8_HsX7Gu7U3dmELwVJ0u1khRXwwvlJCkv6T56kAuRuWOdHz7uZAIFMNiesuQCGA7rM725BJ9O9B3rYT8HytpnnqlrkJ_7WdfdywkHwtyfefu3x7qZ5ewwl-U-ehRdjqQI-HmM7tXrJyjbwU4SsZMAdhLAThKwkwTsJBE7T9HZ8Wg5HOM4PgPb7J2ksBKdC8upaZpcAHGzrkt8VbuGtByYIzPCDSNoiNVC1pZLktFKMt3UNdNHVpNnaG-9WdfPUSKJsYYxnRlgc7yi0gqbGWop01XNWH6AsvZx1efQJUXdpq8D9L59LyqyvcDiFCDn1l-_uMMdX6KHvvGuD6Ador3tl2_1K6CUW_PaY-YXQ3tYAg
linkProvider Colorado Alliance of Research Libraries
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=APPROXIMATE+MIN-MAX+MPC+FOR+LINEAR+HYBRID+SYSTEMS&rft.jtitle=IFAC+Proceedings+Volumes&rft.au=Botto%2C+M.+Ayala&rft.au=Silva%2C+M.&rft.au=Costa%2C+J.+S%C3%A1+da&rft.date=2005&rft.issn=1474-6670&rft.volume=38&rft.issue=1&rft.spage=622&rft.epage=627&rft_id=info:doi/10.3182%2F20050703-6-CZ-1902.00504&rft.externalDBID=n%2Fa&rft.externalDocID=10_3182_20050703_6_CZ_1902_00504
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1474-6670&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1474-6670&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1474-6670&client=summon