Optimal Covariance Control for Stochastic Systems Under Chance Constraints

This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although thei...

Full description

Saved in:
Bibliographic Details
Published inIEEE control systems letters Vol. 2; no. 2; pp. 266 - 271
Main Authors Okamoto, Kazuhide, Goldshtein, Maxim, Tsiotras, Panagiotis
Format Journal Article
LanguageEnglish
Published IEEE 01.04.2018
Subjects
Boundary conditions
Gaussian distribution
Linear programming
Linear systems
Optimal control
Optimization
stochastic optimal control
Stochastic systems
uncertain systems
Online AccessGet full text

Cover

Abstract This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this letter, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.
AbstractList This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this letter, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.
Author Goldshtein, Maxim
Okamoto, Kazuhide
Tsiotras, Panagiotis
Author_xml – sequence: 1
  givenname: Kazuhide
  surname: Okamoto
  fullname: Okamoto, Kazuhide
  email: kazuhide@gatech.edu
  organization: Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
– sequence: 2
  givenname: Maxim
  surname: Goldshtein
  fullname: Goldshtein, Maxim
  email: maxg@gatech.edu
  organization: Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
– sequence: 3
  givenname: Panagiotis
  surname: Tsiotras
  fullname: Tsiotras, Panagiotis
  email: tsiotras@gatech.edu
  organization: Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
BookMark eNp9kMtOwzAQRS1UJErpD8AmP5DiV_xYooinKnURumAVOfZENUqTyraQ-vektCDEgtnMLO4ZzZxLNOmHHhC6JnhBCNa3y7J6qxYUE7WgigrM1BmaUi6LnPBCTH7NF2ge4zvGY5RKTPUUvax2yW9Nl5XDhwne9BbGsU9h6LJ2CFmVBrsxMXmbVfuYYBuzde8gZOXmOxtTML5P8Qqdt6aLMD_1GVo_3L-WT_ly9fhc3i1zS4VMeeMod0phRjgAw9aMpbHmbSFdyw3HBEtNtTROgW0sEwIcMaYBzgV1irAZUse9NgwxBmhr65NJ_nC18V1NcH3QUn9pqQ9a6pOWEaV_0F0Yvw_7_6GbI-QB4AdQjAktGfsEVcFxdA
CODEN ICSLBO
CitedBy_id crossref_primary_10_1146_annurev_control_070220_100858
crossref_primary_10_1002_rnc_5636
crossref_primary_10_1109_TIV_2022_3227588
crossref_primary_10_1109_TITS_2022_3152006
crossref_primary_10_1137_20M1339982
crossref_primary_10_1109_LCSYS_2023_3315651
crossref_primary_10_1109_TCST_2023_3291570
crossref_primary_10_1109_TAC_2021_3060704
crossref_primary_10_1016_j_actaastro_2024_03_017
crossref_primary_10_1109_LCSYS_2022_3153094
crossref_primary_10_1002_rnc_7346
crossref_primary_10_1109_TAES_2021_3086956
crossref_primary_10_1002_asjc_1955
crossref_primary_10_1016_j_cpc_2021_108030
crossref_primary_10_1051_cocv_2022060
crossref_primary_10_1016_j_ast_2025_109942
crossref_primary_10_1109_TAC_2023_3331683
crossref_primary_10_1016_j_ast_2024_109464
crossref_primary_10_1109_LCSYS_2024_3409107
crossref_primary_10_1177_02783649251318046
crossref_primary_10_1109_LRA_2019_2901546
crossref_primary_10_1007_s11424_025_4507_7
crossref_primary_10_1016_j_ifacol_2022_09_337
crossref_primary_10_1109_LRA_2022_3196957
crossref_primary_10_1109_TRO_2024_3355375
crossref_primary_10_1109_TAC_2023_3305319
crossref_primary_10_1109_LCSYS_2020_3047132
crossref_primary_10_1109_LCSYS_2022_3181525
crossref_primary_10_1109_TRO_2022_3228128
crossref_primary_10_2514_1_G005704
crossref_primary_10_1016_j_ifacol_2023_10_1277
crossref_primary_10_2514_1_G005426
crossref_primary_10_2514_1_G005964
crossref_primary_10_2514_1_G005941
crossref_primary_10_1109_TITS_2023_3243940
crossref_primary_10_1137_20M135090X
crossref_primary_10_1016_j_automatica_2025_112222
crossref_primary_10_2514_1_G005400
crossref_primary_10_1109_OJCSYS_2022_3212613
crossref_primary_10_20965_jrm_2024_p1082
crossref_primary_10_1016_j_actaastro_2023_04_004
crossref_primary_10_1016_j_ifacol_2023_10_1492
Cites_doi 10.1109/ACC.2016.7526817
10.1080/00207721.2012.670310
10.1109/TRO.2011.2161160
10.1109/ACC.2010.5530976
10.1080/00207178708933880
10.1515/9781400833344
10.1109/MCS.2016.2602087
10.1109/ACC.2016.7526814
10.1016/j.jprocont.2016.03.005
10.1016/j.automatica.2018.01.029
10.1287/opre.36.1.145
10.1109/TAC.1987.1104443
10.1103/PhysRevLett.101.033601
10.2514/6.2009-5876
10.1109/CDC.2013.6761117
10.1016/S0005-1098(96)00188-4
10.1109/9.256389
10.1109/CDC.2016.7798422
10.1109/CDC.1985.268547
10.1109/TAC.2015.2457784
10.1109/TAC.2015.2457791
10.1109/CDC.2017.8264189
ContentType Journal Article
DBID 97E
RIA
RIE
AAYXX
CITATION
DOI 10.1109/LCSYS.2018.2826038
DatabaseName IEEE All-Society Periodicals Package (ASPP) 2005–Present
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
EISSN 2475-1456
EndPage 271
ExternalDocumentID 10_1109_LCSYS_2018_2826038
8336973
Genre orig-research
GrantInformation_xml – fundername: Ito Foundation USA-FUTI Scholarship
– fundername: ARO
  grantid: W911NF-16-1-0390
  funderid: 10.13039/100000183
– fundername: NSF
  grantid: CPS-1544814
  funderid: 10.13039/100000001
– fundername: Funai Foundation for Information Technology
GroupedDBID 0R~
6IK
97E
AAJGR
AASAJ
AAWTH
ABAZT
ABJNI
ABQJQ
ABVLG
ACGFS
AGQYO
AHBIQ
AKJIK
ALMA_UNASSIGNED_HOLDINGS
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
EBS
EJD
IFIPE
IPLJI
JAVBF
OCL
RIA
RIE
AAYXX
CITATION
RIG
ID FETCH-LOGICAL-c267t-bd24d880314ee30caaaa9094f57df4a401079297ad8ecbc366ed1aabe4462d813
IEDL.DBID RIE
ISSN 2475-1456
IngestDate Thu Apr 24 22:59:40 EDT 2025
Tue Jul 01 04:06:32 EDT 2025
Wed Aug 27 02:50:21 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
https://doi.org/10.15223/policy-029
https://doi.org/10.15223/policy-037
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c267t-bd24d880314ee30caaaa9094f57df4a401079297ad8ecbc366ed1aabe4462d813
ORCID 0000-0002-2295-1646
0000-0001-7563-4129
0000-0003-4222-8356
PageCount 6
ParticipantIDs crossref_citationtrail_10_1109_LCSYS_2018_2826038
ieee_primary_8336973
crossref_primary_10_1109_LCSYS_2018_2826038
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2018-April
2018-4-00
PublicationDateYYYYMMDD 2018-04-01
PublicationDate_xml – month: 04
  year: 2018
  text: 2018-April
PublicationDecade 2010
PublicationTitle IEEE control systems letters
PublicationTitleAbbrev LCSYS
PublicationYear 2018
Publisher IEEE
Publisher_xml – name: IEEE
References iwasaki (ref5) 1992
ref11
ref10
schrödinger (ref14) 1931
ref2
ref17
ref16
ref19
ref18
(ref31) 2017
kantorovich (ref15) 1942; 37
ref24
ref23
ref26
carvalho (ref29) 2014
ref20
ref22
ref21
ridderhof (ref13) 2018
shahrokhi (ref1) 2016
ref28
bernstein (ref25) 2009; 41
ref27
ref8
ref7
ref9
ref4
ref3
chen (ref12) 0
ref6
grant (ref30) 2014
References_xml – ident: ref17
  doi: 10.1109/ACC.2016.7526817
– ident: ref21
  doi: 10.1080/00207721.2012.670310
– year: 2017
  ident: ref31
  publication-title: The Mosek Optimization Toolbox for MATLAB Manual Version 7 1
– start-page: 2866
  year: 1992
  ident: ref5
  article-title: Quadratic optimization for fixed order linear controllers via covariance control
  publication-title: Proc Amer Control Conf
– ident: ref28
  doi: 10.1109/TRO.2011.2161160
– ident: ref24
  doi: 10.1109/ACC.2010.5530976
– year: 2014
  ident: ref29
  article-title: Stochastic predictive control of autonomous vehicles in uncertain environments
  publication-title: Proc Int Symp Adv Veh Control
– ident: ref8
  doi: 10.1080/00207178708933880
– volume: 41
  year: 2009
  ident: ref25
  publication-title: Matrix Mathematics Theory Facts and Formulas
  doi: 10.1515/9781400833344
– ident: ref23
  doi: 10.1109/MCS.2016.2602087
– ident: ref18
  doi: 10.1109/ACC.2016.7526814
– ident: ref22
  doi: 10.1016/j.jprocont.2016.03.005
– ident: ref20
  doi: 10.1016/j.automatica.2018.01.029
– ident: ref26
  doi: 10.1287/opre.36.1.145
– year: 2016
  ident: ref1
  article-title: Algorithms for shaping a particle swarm with a shared control input using boundary interaction
  publication-title: arXiv preprint arXiv 1609 01830
– ident: ref9
  doi: 10.1109/TAC.1987.1104443
– ident: ref2
  doi: 10.1103/PhysRevLett.101.033601
– ident: ref27
  doi: 10.2514/6.2009-5876
– ident: ref3
  doi: 10.1109/CDC.2013.6761117
– ident: ref7
  doi: 10.1016/S0005-1098(96)00188-4
– ident: ref6
  doi: 10.1109/9.256389
– ident: ref19
  doi: 10.1109/CDC.2016.7798422
– year: 1931
  ident: ref14
  publication-title: Über die Umkehrung der Naturgesetze
– year: 2014
  ident: ref30
  publication-title: CVX Matlab Software for Disciplined Convex Programming Version 2 1
– start-page: 611
  year: 2018
  ident: ref13
  article-title: Uncertainty quantication and control during Mars powered descent and landing using covariance steering
  publication-title: Proc AIAA Guid Navigat Control Conf
– ident: ref4
  doi: 10.1109/CDC.1985.268547
– year: 0
  ident: ref12
  article-title: Optimal steering of a linear stochastic system to a final probability distribution, part III
  publication-title: IEEE Trans Autom Control
– volume: 37
  start-page: 227
  year: 1942
  ident: ref15
  article-title: On the transfer of masses
  publication-title: Dokl Akad Nauk SSSR
– ident: ref10
  doi: 10.1109/TAC.2015.2457784
– ident: ref11
  doi: 10.1109/TAC.2015.2457791
– ident: ref16
  doi: 10.1109/CDC.2017.8264189
SSID ssj0001827029
Score 2.4433017
Snippet This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our...
SourceID crossref
ieee
SourceType Enrichment Source
Index Database
Publisher
StartPage 266
SubjectTerms Boundary conditions
Gaussian distribution
Linear programming
Linear systems
Optimal control
Optimization
stochastic optimal control
Stochastic systems
uncertain systems
Title Optimal Covariance Control for Stochastic Systems Under Chance Constraints
URI https://ieeexplore.ieee.org/document/8336973
Volume 2
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LSwMxEA5tT158UMX6Igdvutt9ZpOjLEopVg-1UE9LHlMEtSt268Ff7yS7rUVE3NMSEggzYWe-7HzfEHIecGAiUdrTGCy9xPDUE7FgnsiECjEEqZkjCo_u2GCSDKfptEUu11wYAHDFZ-DbV_cv35R6aa_K-jyOmcjiNmkjcKu5Wt_3Kdwyq8SKFxOI_m0-fhzb4i3uI65ggaWgbMSejWYqLpbc7JDRahd1Ccmzv6yUrz9_CDT-d5u7ZLtJKulVfQr2SAvmXTK8x6_BKw7n5QcCYutdmteF6RQzVTquSv0krUwzbWTLqWuCRC3hoJ67cA0kqsU-mdxcP-QDr-mc4OmIZZWnTIRm51aaHiAOtMRHIJCbpZmZJRIxVZBhXpRJw0ErHTMGJpRSAYLDyPAwPiCdeTmHQ0KzBDFEmiqlEExFWvLECAhlGIAV_plFPRKubFroRlbcbu6lcPAiEIXzQ2H9UDR-6JGL9Zq3WlTjz9lda-P1zMa8R78PH5Mtu7gurjkhnep9CaeYN1TqzB2YL671wDY
linkProvider IEEE
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV07T8MwELZKGWDhoYIoTw9skDRPxx5RRFVKW4a2UpkivyokoEE0ZeDXc3bSUiGEyBRZTmTdWbn7nPu-Q-jSo5qwSEhHQrB0IkVjh4WMOCxhwocQJKaWKNwfkM446k7iSQ1dr7gwWmtbfKZdc2v_5atcLsxRWYuGIWFJuIE2Ie7HQcnW-j5RoYZbxZbMGI-1eunwcWjKt6gLyIJ4hoSyFn3W2qnYaNLeRf3lOsoikmd3UQhXfv6QaPzvQvfQTpVW4ptyH-yjmp41UPcBvgevMJzmHwCJjX9xWpamY8hV8bDI5RM3Qs24Ei7Htg0SNpSDcu7ctpAo5gdo3L4dpR2n6p3gyIAkhSNUAIanRpxe69CTHC4GUG4aJ2oacUBVXgKZUcIV1VLIkBCtfM6FBngYKOqHh6g-y2f6COEkAhQRx0IIgFOB5DRSTPvc97SR_pkGTeQvbZrJSljcLO4lswDDY5n1Q2b8kFV-aKKr1TNvpazGn7MbxsarmZV5j38fvkBbnVG_l_XuBvcnaNu8qCy1OUX14n2hzyCLKMS53Txf5OLDgA
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=Optimal+Covariance+Control+for+Stochastic+Systems+Under+Chance+Constraints&rft.jtitle=IEEE+control+systems+letters&rft.au=Okamoto%2C+Kazuhide&rft.au=Goldshtein%2C+Maxim&rft.au=Tsiotras%2C+Panagiotis&rft.date=2018-04-01&rft.pub=IEEE&rft.eissn=2475-1456&rft.volume=2&rft.issue=2&rft.spage=266&rft.epage=271&rft_id=info:doi/10.1109%2FLCSYS.2018.2826038&rft.externalDocID=8336973
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2475-1456&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2475-1456&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2475-1456&client=summon