An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control

In recent years, efficient optimization algorithms for nonlinear model predictive control (NMPC) have been proposed, that significantly reduce the online computational time. In particular, the direct multiple shooting and the sequential quadratic programming (SQP) are used to efficiently solve nonli...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 64; no. 7; pp. 2712 - 2726
Main Authors: Chen, Yutao, Bruschetta, Mattia, Cuccato, Davide, Beghi, Alessandro
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive control
Algorithms
Computer simulation
Computing time
Convergence
Curvature
Dynamical systems
Error detection
Iterative methods
Jacobian matrices
Nonlinear control
Nonlinear dynamics
Nonlinear model predictive control (NMPC)
Nonlinear programming
Nonlinearity
Optimization
partial sensitivity update optimization algorithms
Prediction algorithms
Predictive control
Quadratic programming
real-time iteration (RTI)
Sensitivity
Stiffness
Tuning
ISSN:0018-9286, 1558-2523
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In recent years, efficient optimization algorithms for nonlinear model predictive control (NMPC) have been proposed, that significantly reduce the online computational time. In particular, the direct multiple shooting and the sequential quadratic programming (SQP) are used to efficiently solve nonlinear programming (NLP) problems arising from continuous-time NMPC applications. One of the computationally demanding steps for the online optimization is the computation of sensitivities of the nonlinear dynamics at every sampling instant, especially for systems of large dimensions, strong stiffness, and when using long prediction horizons. In this paper, within the algorithmic framework of the real-time iteration scheme based on multiple shooting, an inexact sensitivity updating scheme is proposed, that performs a partial update of the Jacobian of the constraints in the NLP. Such update is triggered by using a curvature-like measure of nonlinearity, so that only sensitivities exhibiting highly nonlinear behavior are updated, thus adapting to system operating conditions and possibly reducing the computational burden. An advanced tuning strategy for the updating scheme is provided to automatically determine the number of sensitivities being updated, with a guaranteed bounded error on the quadratic programming solution. Numerical and control performance of the scheme is evaluated by means of two simulation examples performed on a dedicated implementation. Local convergence analysis is also presented and a tunable convergence rate is proven, when applied to the SQP method.
AbstractList In recent years, efficient optimization algorithms for nonlinear model predictive control (NMPC) have been proposed, that significantly reduce the online computational time. In particular, the direct multiple shooting and the sequential quadratic programming (SQP) are used to efficiently solve nonlinear programming (NLP) problems arising from continuous-time NMPC applications. One of the computationally demanding steps for the online optimization is the computation of sensitivities of the nonlinear dynamics at every sampling instant, especially for systems of large dimensions, strong stiffness, and when using long prediction horizons. In this paper, within the algorithmic framework of the real-time iteration scheme based on multiple shooting, an inexact sensitivity updating scheme is proposed, that performs a partial update of the Jacobian of the constraints in the NLP. Such update is triggered by using a curvature-like measure of nonlinearity, so that only sensitivities exhibiting highly nonlinear behavior are updated, thus adapting to system operating conditions and possibly reducing the computational burden. An advanced tuning strategy for the updating scheme is provided to automatically determine the number of sensitivities being updated, with a guaranteed bounded error on the quadratic programming solution. Numerical and control performance of the scheme is evaluated by means of two simulation examples performed on a dedicated implementation. Local convergence analysis is also presented and a tunable convergence rate is proven, when applied to the SQP method.
Author Chen, Yutao
Bruschetta, Mattia
Cuccato, Davide
Beghi, Alessandro
Author_xml – sequence: 1
  givenname: Yutao
  orcidid: 0000-0001-6748-2866
  surname: Chen
  fullname: Chen, Yutao
  email: yutao.chen@dei.unipd.it
  organization: Department of Information Engineering, University of Padova, Padova, Italy
– sequence: 2
  givenname: Mattia
  orcidid: 0000-0003-0769-4191
  surname: Bruschetta
  fullname: Bruschetta, Mattia
  email: mattia.bruschetta@dei.unipd.it
  organization: Department of Information Engineering, University of Padova, Padova, Italy
– sequence: 3
  givenname: Davide
  orcidid: 0000-0002-9718-7291
  surname: Cuccato
  fullname: Cuccato, Davide
  email: davide.cuccato@dei.unipd.it
  organization: Department of Information Engineering, University of Padova, Padova, Italy
– sequence: 4
  givenname: Alessandro
  orcidid: 0000-0003-2252-2179
  surname: Beghi
  fullname: Beghi, Alessandro
  email: beghi@dei.unipd.it
  organization: Department of Information Engineering, University of Padova, Padova, Italy
BookMark eNp9UE1LAzEQDaJgW70LXgKet2ay2TR7LMUv8KNQPXlYYnaikW1Ss6nQf29qxYMHT8PMe29m3huSfR88EnICbAzA6vPH6WzMGagxV3JSg9wjA6gqVfCKl_tkwDJU1Bk7JMO-f8-tFAIG5Hnq6bTVq-Q-kc51TE53dIG-d3ni0oY-rVqdnH-lC_OGS6Q2RHqp-0Tvg--cRx3pXWixo_OIrTPfe2bBpxi6I3Jgddfj8U8dkafLi8fZdXH7cHUzm94WhteQCiEMTmwlNExqrDTWzJhWCGGVBstrq6QV2ZGo4AUASmGMgNYaLpELy2BSjsjZbu8qho819ql5D-vo88mGc6GklIpVmSV3LBND30e0jXEpW9v-ql3XAGu2QTY5yGYbZPMTZBayP8JVdEsdN_9JTncSh4i_dJUt1KUqvwDNgX-h
CODEN IETAA9
CitedBy_id crossref_primary_10_1016_j_jfranklin_2022_03_013
crossref_primary_10_1109_ACCESS_2021_3060018
crossref_primary_10_1109_TMECH_2022_3163692
crossref_primary_10_1109_LCSYS_2024_3408711
crossref_primary_10_1016_j_asr_2023_05_051
crossref_primary_10_1109_TSMC_2022_3177271
crossref_primary_10_1080_00207179_2022_2087739
crossref_primary_10_1007_s12239_024_00029_3
crossref_primary_10_1109_TCST_2020_3022462
crossref_primary_10_3390_s21165372
crossref_primary_10_1049_iet_cta_2019_0168
crossref_primary_10_1109_TIV_2022_3153633
Cites_doi 10.1016/j.ifacol.2017.08.1528
10.1080/1055678021000060829
10.1016/S1474-6670(17)43213-7
10.1007/BF01580110
10.1109/CDC.2017.8264305
10.1109/ICIF.2005.1591858
10.1016/j.automatica.2008.06.011
10.3182/20080706-5-KR-1001.00329
10.1080/00207179.2016.1222553
10.1016/S0959-1524(01)00023-3
10.1137/1.9780898718935.ch1
10.1109/TCST.2012.2231960
10.1016/j.ifacol.2015.11.258
10.1109/CCA.2016.7588014
10.1007/3-540-10861-0
10.1021/ie020783s
10.1016/S1474-6670(17)61205-9
10.1111/j.2517-6161.1980.tb01094.x
10.1007/BFb0067703
10.1007/978-3-642-01094-1_37
10.3182/20120823-5-NL-3013.00085
10.1145/838250.838251
10.1016/j.jprocont.2012.01.008
10.1137/1.9780898719383
10.1080/10556780903027500
10.5772/37638
10.1016/j.automatica.2011.08.020
10.1016/S1570-7946(04)80055-5
10.1002/oca.2152
10.1137/120876915
10.1016/j.ifacol.2016.10.139
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019
DBID 97E
RIA
RIE
AAYXX
CITATION
7SC
7SP
7TB
8FD
FR3
JQ2
L7M
L~C
L~D
DOI 10.1109/TAC.2018.2867916
DatabaseName IEEE Xplore (IEEE)
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Computer and Information Systems Abstracts
Electronics & Communications Abstracts
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Technology Research Database
Computer and Information Systems Abstracts – Academic
Mechanical & Transportation Engineering Abstracts
Electronics & Communications Abstracts
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
Engineering Research Database
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts Professional
DatabaseTitleList Technology Research Database
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1558-2523
EndPage 2726
ExternalDocumentID 10_1109_TAC_2018_2867916
8451938
Genre orig-research
GroupedDBID -~X
.DC
0R~
29I
3EH
4.4
5GY
5VS
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABQJQ
ABVLG
ACGFO
ACGFS
ACIWK
ACNCT
AENEX
AETIX
AGQYO
AGSQL
AHBIQ
AI.
AIBXA
AKJIK
AKQYR
ALLEH
ALMA_UNASSIGNED_HOLDINGS
ASUFR
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CS3
DU5
EBS
EJD
F5P
HZ~
H~9
IAAWW
IBMZZ
ICLAB
IDIHD
IFIPE
IFJZH
IPLJI
JAVBF
LAI
M43
MS~
O9-
OCL
P2P
RIA
RIE
RNS
TAE
TN5
VH1
VJK
~02
AAYXX
CITATION
7SC
7SP
7TB
8FD
FR3
JQ2
L7M
L~C
L~D
RIG
ID FETCH-LOGICAL-c291t-44ce7f54a179e5ae90ccd444f8a1f29f86f4791451b11134cc41dfc26e24f0173
IEDL.DBID RIE
ISICitedReferencesCount 18
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000473489700005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0018-9286
IngestDate Mon Jun 30 10:22:17 EDT 2025
Sat Nov 29 05:40:51 EST 2025
Tue Nov 18 20:57:51 EST 2025
Wed Aug 27 05:52:03 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 7
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-c291t-44ce7f54a179e5ae90ccd444f8a1f29f86f4791451b11134cc41dfc26e24f0173
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-9718-7291
0000-0003-2252-2179
0000-0001-6748-2866
0000-0003-0769-4191
PQID 2248666805
PQPubID 85475
PageCount 15
ParticipantIDs crossref_citationtrail_10_1109_TAC_2018_2867916
crossref_primary_10_1109_TAC_2018_2867916
proquest_journals_2248666805
ieee_primary_8451938
PublicationCentury 2000
PublicationDate 2019-07-01
PublicationDateYYYYMMDD 2019-07-01
PublicationDate_xml – month: 07
  year: 2019
  text: 2019-07-01
  day: 01
PublicationDecade 2010
PublicationPlace New York
PublicationPlace_xml – name: New York
PublicationTitle IEEE transactions on automatic control
PublicationTitleAbbrev TAC
PublicationYear 2019
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References ref35
ref13
ref34
ref12
ref37
ref15
ref14
ref31
li (ref33) 0
ref32
ref10
guay (ref29) 1996
ref2
(ref39) 2017
ref1
kühl (ref11) 2007
ref17
ref19
fiacco (ref36) 1983
ref18
enns (ref42) 2010
andersson (ref38) 2013
ref24
ref23
leineweber (ref7) 1999
ref26
ref25
chen (ref20) 0
ref41
ref22
ref44
wirsching (ref16) 0
ref21
ref43
ref28
ref27
nocedal (ref8) 2006
diehl (ref4) 2001
ref9
ref3
niu (ref30) 0
ref6
ref5
ref40
References_xml – ident: ref22
  doi: 10.1016/j.ifacol.2017.08.1528
– ident: ref43
  doi: 10.1080/1055678021000060829
– ident: ref32
  doi: 10.1016/S1474-6670(17)43213-7
– year: 2017
  ident: ref39
  article-title: HPIPM
– ident: ref35
  doi: 10.1007/BF01580110
– year: 2006
  ident: ref8
  publication-title: Numerical Optimization
– start-page: 1780
  year: 0
  ident: ref20
  article-title: A fast nonlinear model predictive control strategy for real-time motion control of mechanical systems
  publication-title: Proc IEEE Int Conf Adv Intell Mechatronics
– ident: ref21
  doi: 10.1109/CDC.2017.8264305
– start-page: 591
  year: 0
  ident: ref16
  article-title: Fast nmpc of a chain of masses connected by springs
  publication-title: Proc IEEE Int Conf Control Appl IEEE Int Symp Intell Control Comput Aided Control Syst Des
– ident: ref31
  doi: 10.1109/ICIF.2005.1591858
– ident: ref5
  doi: 10.1016/j.automatica.2008.06.011
– ident: ref17
  doi: 10.3182/20080706-5-KR-1001.00329
– year: 2001
  ident: ref4
  article-title: Real-time optimization for large scale nonlinear processes
– year: 2007
  ident: ref11
  publication-title: MUSCOD-II User's Manual
– ident: ref14
  doi: 10.1080/00207179.2016.1222553
– ident: ref13
  doi: 10.1016/S0959-1524(01)00023-3
– ident: ref15
  doi: 10.1137/1.9780898718935.ch1
– ident: ref41
  doi: 10.1109/TCST.2012.2231960
– ident: ref44
  doi: 10.1016/j.ifacol.2015.11.258
– ident: ref24
  doi: 10.1109/CCA.2016.7588014
– year: 1983
  ident: ref36
  publication-title: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming
– ident: ref10
  doi: 10.1007/3-540-10861-0
– ident: ref27
  doi: 10.1021/ie020783s
– ident: ref1
  doi: 10.1016/S1474-6670(17)61205-9
– ident: ref28
  doi: 10.1111/j.2517-6161.1980.tb01094.x
– ident: ref3
  doi: 10.1007/BFb0067703
– ident: ref23
  doi: 10.1007/978-3-642-01094-1_37
– start-page: 1
  year: 0
  ident: ref30
  article-title: Curvature nonlinearity measure and filter divergence detector for nonlinear tracking problems
  publication-title: Proc 11th Inter Conf Info Fusion
– ident: ref25
  doi: 10.3182/20120823-5-NL-3013.00085
– start-page: 1073
  year: 0
  ident: ref33
  article-title: Measure of nonlinearity for stochastic systems
  publication-title: Proc 15th Int Conf Inf Fusion
– ident: ref9
  doi: 10.1145/838250.838251
– year: 2013
  ident: ref38
  article-title: A general-purpose software framework for dynamic optimization
– ident: ref18
  doi: 10.1016/j.jprocont.2012.01.008
– ident: ref2
  doi: 10.1137/1.9780898719383
– ident: ref34
  doi: 10.1080/10556780903027500
– ident: ref6
  doi: 10.5772/37638
– ident: ref12
  doi: 10.1016/j.automatica.2011.08.020
– ident: ref26
  doi: 10.1016/S1570-7946(04)80055-5
– ident: ref40
  doi: 10.1002/oca.2152
– year: 2010
  ident: ref42
  publication-title: It's A Nonlinear World
– ident: ref37
  doi: 10.1137/120876915
– ident: ref19
  doi: 10.1016/j.ifacol.2016.10.139
– year: 1996
  ident: ref29
  article-title: Measurement of nonlinearity in chemical process control
– year: 1999
  ident: ref7
  article-title: Efficient reduced SQP methods for the optimization of chemical processes described by large sparse DAE models
SSID ssj0016441
Score 2.443209
Snippet In recent years, efficient optimization algorithms for nonlinear model predictive control (NMPC) have been proposed, that significantly reduce the online...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 2712
SubjectTerms Adaptive control
Algorithms
Computer simulation
Computing time
Convergence
Curvature
Dynamical systems
Error detection
Iterative methods
Jacobian matrices
Nonlinear control
Nonlinear dynamics
Nonlinear model predictive control (NMPC)
Nonlinear programming
Nonlinearity
Optimization
partial sensitivity update optimization algorithms
Prediction algorithms
Predictive control
Quadratic programming
real-time iteration (RTI)
Sensitivity
Stiffness
Tuning
Title An Adaptive Partial Sensitivity Updating Scheme for Fast Nonlinear Model Predictive Control
URI https://ieeexplore.ieee.org/document/8451938
https://www.proquest.com/docview/2248666805
Volume 64
WOSCitedRecordID wos000473489700005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Electronic Library (IEL)
  customDbUrl:
  eissn: 1558-2523
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0016441
  issn: 0018-9286
  databaseCode: RIE
  dateStart: 19630101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3Na8IwFH-o7LAd9uXG3NzIYZfBqrambXIUmewkggrCDiVNkzFwVbTu7997bS3CxmC3HpLQvo-8l76X3w_g0U0w6iWeckTs4gHF7fuOCoV0QhtgdisVWpnNySbC8VgsFnJSg-fqLowxJm8-Mx16zGv5yUrv6FdZVxAWSl_UoR6GQXFXq6oYUFwvdl10YE9UJcme7M4GQ-rhEh2P0OWI2fwgBOWcKj824jy6jM7-917ncFpmkWxQqP0Caia9hJMDbMEmvA1SNkjUmrYzNiEDwQlTalcv-CLYfE03G9J3NkW9fRqG2SsbqW3GxgV6htowIkpbssmGijn5OsOisf0K5qOX2fDVKZkUHO1JN3M41ya0PlfofsZXRva0TjjnVijXetKKwHKUDH5GTNTzXGvuJlZ7gfG4RZ_tX0MjXaXmBlg_plqhJ4OQx1wYP7Y-hlnftYZwXjRvQXcv3EiXMOPEdrGM8uNGT0aojojUEZXqaMFTNWNdQGz8MbZJ4q_GlZJvQXuvv6j0wW2EyYnAw5no-be_z7qDY1xbFs23bWhkm525hyP9lX1sNw-5eX0DfvPLug
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60CurBVxXrcw9eBNM26SbZPZZiUdRSaAuCh7DZ7IpQY0mrv9-ZJA2CInjLYTePmZ2d2czM9wFcugl6vcRTjohdPKC4Hd9RoZBOaAOMbqXCVWZzsolwMBBPT3K4AtdVL4wxJi8-M026zHP5ybv-oF9lLUFYKB2xCmvEnFV2a1U5A_Lsxb6LJuyJKinZlq1xt0dVXKLpEb4ccZt_c0I5q8qPrTj3L_2d_73ZLmyXcSTrForfgxWT7sPWN3TBOjx3U9ZN1Iw2NDakJYITRlSwXjBGsMmMehvSFzZCzb0ZhvEr66v5gg0K_AyVMaJKm7JhRumc_D69orT9ACb9m3Hv1im5FBztSXfhcK5NaH2u0ACNr4xsa51wzq1QrvWkFYHlKBn8jJjI57nW3E2s9gLjcYtW2zmEWvqemiNgnZiyhZ4MQh5zYfzY-uhofdcaQnrRvAGtpXAjXQKNE9_FNMoPHG0ZoToiUkdUqqMBV9WMWQGy8cfYOom_GldKvgGnS_1FpRXOIwxPBB7PRNs__n3WBWzcjh8fooe7wf0JbOJzZFGKewq1RfZhzmBdfy5e59l5vtS-AEZKzwM
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=An+Adaptive+Partial+Sensitivity+Updating+Scheme+for+Fast+Nonlinear+Model+Predictive+Control&rft.jtitle=IEEE+transactions+on+automatic+control&rft.au=Chen%2C+Yutao&rft.au=Bruschetta%2C+Mattia&rft.au=Cuccato%2C+Davide&rft.au=Beghi%2C+Alessandro&rft.date=2019-07-01&rft.issn=0018-9286&rft.eissn=1558-2523&rft.volume=64&rft.issue=7&rft.spage=2712&rft.epage=2726&rft_id=info:doi/10.1109%2FTAC.2018.2867916&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TAC_2018_2867916
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9286&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9286&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9286&client=summon