H2 detector-based state feedback control of continuous-time MJLS subject to uncertain transition rate matrices

This paper uses detector-based mode information to address the H2 state-feedback control problem for continuous-time Markov Jump Linear Systems (MJLS). The focus is on designing robust controllers capable of handling uncertainties affecting both the Markov process and its detector, a less explored s...

Full description

Saved in:
Bibliographic Details
Published inJournal of the Franklin Institute Vol. 361; no. 15
Main Authors da Silva, Lucas P.M., Oliveira, Ricardo C.L.F.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2024
Subjects
Hidden Markov chain
Linear matrix inequalities
Markov jump systems
Polytopic uncertainty
ℚ2 state-feedback control
ℚ2 state-feedback control
Hidden Markov chain
Linear matrix inequalities
Markov jump systems
Polytopic uncertainty
Online AccessGet full text

Cover

Abstract This paper uses detector-based mode information to address the H2 state-feedback control problem for continuous-time Markov Jump Linear Systems (MJLS). The focus is on designing robust controllers capable of handling uncertainties affecting both the Markov process and its detector, a less explored scenario in the literature. The main contribution lies in presenting a new LMI-based algorithm within a suitable synthesis framework to deal with uncertain parameters. A key advantage is the absence of constraints on the optimization variables, even in cases involving structured controllers like decentralized control. To illustrate the effectiveness of the proposed technique, a numerical example based on a linearized model of an unmanned aircraft is provided, showcasing its superiority over existing approaches.
AbstractList This paper uses detector-based mode information to address the H2 state-feedback control problem for continuous-time Markov Jump Linear Systems (MJLS). The focus is on designing robust controllers capable of handling uncertainties affecting both the Markov process and its detector, a less explored scenario in the literature. The main contribution lies in presenting a new LMI-based algorithm within a suitable synthesis framework to deal with uncertain parameters. A key advantage is the absence of constraints on the optimization variables, even in cases involving structured controllers like decentralized control. To illustrate the effectiveness of the proposed technique, a numerical example based on a linearized model of an unmanned aircraft is provided, showcasing its superiority over existing approaches.
ArticleNumber 107123
Author Oliveira, Ricardo C.L.F.
da Silva, Lucas P.M.
Author_xml – sequence: 1
  givenname: Lucas P.M.
  orcidid: 0000-0002-0591-3453
  surname: da Silva
  fullname: da Silva, Lucas P.M.
  organization: Faculdade de Engenharia, Universidade Federal de Mato Grosso (UFMT), Cuiabá, MT, Brazil
– sequence: 2
  givenname: Ricardo C.L.F.
  orcidid: 0000-0002-8225-7058
  surname: Oliveira
  fullname: Oliveira, Ricardo C.L.F.
  email: ricfow@dt.fee.unicamp.br
  organization: Faculdade de Engenharia Elétrica e de Computação, Universidade Estadual de Campinas (UNICAMP), Campinas, SP, Brazil
BookMark eNo9kM1OAyEUhVnUxLb6DPICU_mbwVk2jVrNGBfqmjBwSZi2kADj80utcXX_cs85-VZoEWIAhO4o2VBCu_tpM7mkw-How4YRJupWUsYXaEnquSGEs2u0ynmqo6SELFHYM2yhgCkxNaPOYHEuugB2AHbU5oBNDCXFI47ut_VhjnNuij8BfnsdPnCex6m-4xLxHAykon3ApabIvvgYcDqrnXRJ3kC-QVdOHzPc_tU1-np6_Nztm-H9-WW3HRpglJfGtGAtZ1QAc4ZQcJ3mnRG007o3vZWWSC4ob6V8sMK1IEmrKdcCeudEx0e-RtuLLlSTbw9JZeOhxrM-1bDKRq8oUWdoalL_0NQZmrpA4z8ovmo1
ContentType Journal Article
Copyright 2024 The Franklin Institute
Copyright_xml – notice: 2024 The Franklin Institute
DOI 10.1016/j.jfranklin.2024.107123
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
ExternalDocumentID S0016003224005441
GrantInformation_xml – fundername: Brazilian agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES)
  grantid: 001
  funderid: http://dx.doi.org/10.13039/501100002322
– fundername: Project Stic-Amsud/CAPES NetConHybSDP
  grantid: 22-STIC-09
– fundername: National Council for Scientific and Technological Development (CNPq)
  funderid: http://dx.doi.org/10.13039/501100003593
GroupedDBID --K
--M
-DZ
-~X
.~1
0R~
1B1
1RT
1~.
1~5
29L
4.4
41~
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AACTN
AAEDT
AAEDW
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXKI
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFRF
ABJNI
ABMAC
ABTAH
ABUCO
ABXDB
ACCUC
ACDAQ
ACGFO
ACGFS
ACIWK
ACNCT
ACNNM
ACRLP
ACZNC
ADEZE
ADGUI
ADJOM
ADMUD
ADTZH
AEBSH
AECPX
AEFWE
AEKER
AETEA
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHPAA
AHZHX
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
APLSM
ARUGR
AXJTR
BJAXD
BKOJK
BLXMC
CS3
D1Z
EBS
EFJIC
EJD
EO8
EO9
EP2
EP3
F5P
FA8
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HAMUX
HMJ
HVGLF
HZ~
H~9
IHE
J1W
JJJVA
KOM
LY7
M26
M41
MHUIS
MO0
MVM
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SCC
SDF
SDG
SES
SET
SEW
SME
SPC
SPCBC
SSB
SSD
SST
SSV
SSW
SSZ
T5K
TN5
UHS
VOH
WH7
WUQ
XOL
XPP
ZCG
ZMT
ZY4
~02
~G-
ID FETCH-LOGICAL-e213t-c5edd3214e2fc01ef6a36c416aa9c9d7d0734135778d4f5e705a13a4e9ff463b3
IEDL.DBID .~1
ISSN 0016-0032
IngestDate Sat Sep 07 15:50:24 EDT 2024
IsPeerReviewed true
IsScholarly true
Issue 15
Keywords ℚ2 state-feedback control
Hidden Markov chain
Linear matrix inequalities
Markov jump systems
Polytopic uncertainty
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-e213t-c5edd3214e2fc01ef6a36c416aa9c9d7d0734135778d4f5e705a13a4e9ff463b3
ORCID 0000-0002-0591-3453
0000-0002-8225-7058
ParticipantIDs elsevier_sciencedirect_doi_10_1016_j_jfranklin_2024_107123
PublicationCentury 2000
PublicationDate October 2024
PublicationDateYYYYMMDD 2024-10-01
PublicationDate_xml – month: 10
  year: 2024
  text: October 2024
PublicationDecade 2020
PublicationTitle Journal of the Franklin Institute
PublicationYear 2024
Publisher Elsevier Inc
Publisher_xml – name: Elsevier Inc
References Ducard (b33) 2009
Morais, Braga, Oliveira, Peres (b16) 2015; 52
Boyd, El Ghaoui, Feron, Balakrishnan (b27) 1994
Vargas, Agulhari, Oliveira, Preciado (b6) 2021; 67
Todorov, Fragoso (b13) 2010
Morais, Braga, Oliveira, Peres (b25) 2013; 7
Andersen, Andersen (b32) 2000; vol. 33
Shi, Li (b4) 2015; 13
Todorov, Fragoso (b9) 2013; 49
Dong, Yang (b12) 2008; 44
Rodrigues, Todorov, Fragoso (b18) 2018
de Oliveira, Costa (b22) 2017; 28
Oliveira, Peres (b30) 2007; 52
Costa, Fragoso, Todorov (b2) 2013
Geromel, Bernussou, Peres (b34) 1994; 30
Morais, Braga, Oliveira, Peres (b11) 2016; 26
Felipe, Oliveira (b24) 2021; 66
M. Herceg, M. Kvasnica, C.N. Jones, M. Morari, Multi-Parametric Toolbox 3.0, in: Proceedings of the 2013 European Control Conference, Zurich, Switzerland, 2013, pp. 502–510.
de Oliveira, Costa, Fragoso, Stadtmann (b19) 2022; 95
Stadtmann, Costa (b21) 2017; 62
de Oliveira, Bernussou, Geromel (b14) 1999; 37
Bernussou, Peres, Geromel (b31) 1989; 13
de Oliveira, Costa (b20) 2021; Vols. V. III, 41
Morais, Braga, Lacerda, Oliveira, Peres (b10) 2015; 29
de Oliveira, Skelton (b36) 2001; vol. 268
Cardeliquio, Fioravanti, Gonçalves (b8) 2014
Agulhari, Felipe, Oliveira, Peres (b26) 2019; 45
Shi, Yu (b3) 2009; 54
Stadtmann, Costa (b28) 2018; 2
Costa, Fragoso, Marques (b1) 2005
Cao, Niu, Peng (b7) 2024; 69
Oliveira, Vargas, do Val, Peres (b15) 2009; 82
de Oliveira (b29) 2018
Oliveira, Vargas, do Val, Peres (b5) 2014; 22
Rodrigues, Todorov, Fragoso (b17) 2017; 90
Stadtmann, Costa (b23) 2015
References_xml – start-page: 2237
  year: 2014
  end-page: 2241
  ident: b8
  article-title: and
  publication-title: Proceedings of the 2014 European Control Conference
– reference: M. Herceg, M. Kvasnica, C.N. Jones, M. Morari, Multi-Parametric Toolbox 3.0, in: Proceedings of the 2013 European Control Conference, Zurich, Switzerland, 2013, pp. 502–510.
– volume: 22
  start-page: 1915
  year: 2014
  end-page: 1919
  ident: b5
  article-title: Mode-independent
  publication-title: IEEE Trans. Control Syst. Technol.
– start-page: 5604
  year: 2018
  end-page: 5609
  ident: b18
  article-title: Mean square stability and
  publication-title: Proceedings of the 2018 IEEE Conference on Decision and Control
– volume: vol. 268
  start-page: 241
  year: 2001
  end-page: 257
  ident: b36
  article-title: Stability tests for constrained linear systems
  publication-title: Perspectives in Robust Control
– volume: 62
  start-page: 4031
  year: 2017
  end-page: 4037
  ident: b21
  article-title: Control of continuous-time hidden Markov jump linear systems
  publication-title: IEEE Trans. Autom. Control
– volume: 7
  start-page: 1665
  year: 2013
  end-page: 1674
  ident: b25
  article-title: control of discrete-time Markov jump linear systems with uncertain transition probability matrix: Improved linear matrix inequality relaxations and multi-simplex modeling
  publication-title: IET Control Theory Appl.
– volume: 13
  start-page: 65
  year: 1989
  end-page: 72
  ident: b31
  article-title: A linear programming oriented procedure for quadratic stabilization of uncertain systems
  publication-title: Systems Control Lett.
– volume: 67
  start-page: 6234
  year: 2021
  end-page: 6239
  ident: b6
  article-title: Robust stability analysis of linear parameter-varying systems with Markov jumps
  publication-title: IEEE Trans. Autom. Control
– start-page: 7165
  year: 2015
  end-page: 7170
  ident: b23
  article-title: Mean square stability and
  publication-title: Proceedings of the 54th IEEE Conference on Decision and Control
– volume: vol. 33
  start-page: 197
  year: 2000
  end-page: 232
  ident: b32
  article-title: The MOSEK interior point optimizer for linear programming: An implementation of the homogeneous algorithm
  publication-title: High Performance Optimization
– volume: 2
  start-page: 845
  year: 2018
  end-page: 850
  ident: b28
  article-title: Exponential hidden Markov models for
  publication-title: IEEE Control Syst. Lett.
– volume: 49
  start-page: 735
  year: 2013
  end-page: 747
  ident: b9
  article-title: A new perspective on the robustness of Markov jump linear systems
  publication-title: Automatica
– volume: 66
  start-page: 4365
  year: 2021
  end-page: 4370
  ident: b24
  article-title: An LMI-based algorithm to compute robust stabilizing feedback gains directly as optimization variables
  publication-title: IEEE Trans. Autom. Control
– year: 2009
  ident: b33
  article-title: Fault-Tolerant Flight Control and Guidance Systems: Practical Methods for Small Unmanned Aerial Vehicles
– volume: 13
  start-page: 1
  year: 2015
  end-page: 16
  ident: b4
  article-title: A survey on Markovian jump systems: modeling and design
  publication-title: Int. J. Control Autom. Syst.
– volume: 82
  start-page: 470
  year: 2009
  end-page: 481
  ident: b15
  article-title: Robust stability,
  publication-title: Internat. J. Control
– volume: 54
  start-page: 1668
  year: 2009
  end-page: 1674
  ident: b3
  article-title: Output feedback stabilization of networked control systems with random delays modeled by Markov chains
  publication-title: IEEE Trans. Autom. Control
– year: 2018
  ident: b29
  article-title: Estimating and Control of Markov Jump Linear Systems with Partial Observation of the Operation Mode
– volume: 45
  start-page: 36:1
  year: 2019
  end-page: 36:25
  ident: b26
  article-title: Algorithm 998: The robust LMI parser — A toolbox to construct LMI conditions for uncertain systems
  publication-title: ACM Trans. Math. Software
– year: 2005
  ident: b1
  article-title: Discrete-Time Markovian Jump Linear Systems
– volume: 90
  start-page: 2178
  year: 2017
  end-page: 2196
  ident: b17
  article-title: Control of continuous-time Markov jump linear systems with detector-based mode information
  publication-title: Internat. J. Control
– volume: Vols. V. III, 41
  start-page: 87
  year: 2021
  end-page: 107
  ident: b20
  article-title: Control of continuous-time Markov jump linear systems with partial information
  publication-title: Modern Trends in Controlled Stochastic Processes: Theory and Applications
– volume: 95
  start-page: 716
  year: 2022
  end-page: 728
  ident: b19
  article-title: Dynamic output feedback control for continuous-time Markov jump linear systems with hidden Markov models
  publication-title: Internat. J. Control
– volume: 28
  start-page: 1261
  year: 2017
  end-page: 1280
  ident: b22
  article-title: Mixed
  publication-title: Internat. J. Robust Nonlinear Control
– volume: 30
  start-page: 1565
  year: 1994
  end-page: 1578
  ident: b34
  article-title: Decentralized control through parameter space optimization
  publication-title: Automatica
– volume: 69
  start-page: 3531
  year: 2024
  end-page: 3543
  ident: b7
  article-title: Finite-time stabilization of uncertain Markovian jump systems: An adaptive gain-scheduling control method
  publication-title: IEEE Trans. Autom. Control
– volume: 44
  start-page: 1431
  year: 2008
  end-page: 1436
  ident: b12
  article-title: Robust
  publication-title: Automatica
– year: 1994
  ident: b27
  article-title: Linear Matrix Inequalities in System and Control Theory
– volume: 52
  start-page: 317
  year: 2015
  end-page: 321
  ident: b16
  article-title: state feedback control for MJLS with uncertain probabilities
  publication-title: Automatica
– volume: 29
  start-page: 1207
  year: 2015
  end-page: 1223
  ident: b10
  article-title: and
  publication-title: Internat. J. Adapt. Control Signal Process.
– volume: 37
  start-page: 261
  year: 1999
  end-page: 265
  ident: b14
  article-title: A new discrete-time robust stability condition
  publication-title: Systems Control Lett.
– volume: 52
  start-page: 1334
  year: 2007
  end-page: 1340
  ident: b30
  article-title: Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations
  publication-title: IEEE Trans. Autom. Control
– year: 2013
  ident: b2
  article-title: Continuous-Time Markov Jump Linear Systems
– start-page: 6499
  year: 2010
  end-page: 6504
  ident: b13
  article-title: On the state-feedback robust control of continuous-time infinite Markov jump linear systems
  publication-title: Proceedings of the 49th IEEE Conference on Decision and Control
– volume: 26
  start-page: 599
  year: 2016
  end-page: 612
  ident: b11
  article-title: And
  publication-title: Internat. J. Robust Nonlinear Control
SSID ssj0017100
Score 2.3894846
Snippet This paper uses detector-based mode information to address the H2 state-feedback control problem for continuous-time Markov Jump Linear Systems (MJLS). The...
SourceID elsevier
SourceType Publisher
SubjectTerms Hidden Markov chain
Linear matrix inequalities
Markov jump systems
Polytopic uncertainty
ℚ2 state-feedback control
Title H2 detector-based state feedback control of continuous-time MJLS subject to uncertain transition rate matrices
URI https://dx.doi.org/10.1016/j.jfranklin.2024.107123
Volume 361
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELaqssCAeIpn5YHVNHGcF1tVUYVCu0ClbpEd21KLSBBNV347d05atTPKkliJFF2c--7s7-4j5IFbbpM0gjS1iDwmdBgxaT3BVBwqD46CG9zRnUyjbCbG83DeIcNNLQzSKlvf3_h0563bkX5rzf73YoE1vj6gdeBYkKikhRXsIsZZ_vi7pXn42L2m8caQOcPdexyvpW2V0SFR5AJGYx91i7awtAM1oxNy3MaIdNC8xinpmPKMHO10DjwnZcapNrVbcmeIRJq60iBqAY2ULD5py0GnlXWni3INOT5DKXk6Gb-909Va4RIMrSsK0NYQA2iNyOVIXBRbSNAv18DfrC7IbPT8McxYK53ADPeDmhWh0Ro1iAy3hecbG8kgKiD4kjItUh1r-LMBvsI4TrSwoYm9UPqBFCa1VkSBCi5Jt6xKc0Wo0jrR2EcekF0IlSisMAwS7Qtlpeb6mjxtzJXvfbkcnHK-IZEt862tc7R13tj65j8P35JDvGqodXekW_-szT2ECLXquTnQIweDl9ds-gccb74P
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZKGYAB8RRvPLCaJo7zYkMVVShtF1qpW2THttQiUkTTld_OnZNWZUZZIieRokt835393X2EPHDLbZJGkKYWkceEDiMmrSeYikPlwVFwgzu6w1GUTUR_Gk5bpLuuhUFaZeP7a5_uvHUz0mms2fmazbDG1we0DhwLEpW0dsiugOmLMgaPPxueh4_ta2p3DKkz3P6H5DW3jTQ6ZIpcwGjso3DRBpe2sKZ3RA6bIJE-1-9xTFqmPCEHW60DT0mZcapN5dbcGUKRpq42iFqAIyWLD9qQ0OnCutNZuYIkn6GWPB32B-90uVK4BkOrBQVsq5kBtELociwuij0k6Kfr4G-WZ2TSexl3M9ZoJzDD_aBiRWi0RhEiw23h-cZGMogKiL6kTItUxxqmNuBXGMeJFjY0sRdKP5DCpNaKKFDBOWmXi9JcEKq0TjQ2kgdoF0IlCksMg0T7Qlmpub4kT2tz5X8-XQ5eOV-zyOb5xtY52jqvbX31n4fvyV42Hg7ywevo7Zrs45WaZ3dD2tX3ytxCvFCpO_c__AK20r-d
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=H2+detector-based+state+feedback+control+of+continuous-time+MJLS+subject+to+uncertain+transition+rate+matrices&rft.jtitle=Journal+of+the+Franklin+Institute&rft.au=da+Silva%2C+Lucas+P.M.&rft.au=Oliveira%2C+Ricardo+C.L.F.&rft.date=2024-10-01&rft.pub=Elsevier+Inc&rft.issn=0016-0032&rft.volume=361&rft.issue=15&rft_id=info:doi/10.1016%2Fj.jfranklin.2024.107123&rft.externalDocID=S0016003224005441
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0016-0032&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0016-0032&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0016-0032&client=summon