Shrinking economic MPC of constrained nonlinear systems: An event‐triggered constraint relaxation approach
This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for...
Saved in:
| Published in | International journal of robust and nonlinear control Vol. 34; no. 15; pp. 10424 - 10436 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
01.10.2024
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1049-8923 1099-1239 |
| DOI | 10.1002/rnc.7521 |
Cover
| Abstract | This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example. |
|---|---|
| AbstractList | This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example. |
| Author | Mu, Jianbin He, Defeng Tian, Yu |
| Author_xml | – sequence: 1 givenname: Yu orcidid: 0009-0004-3550-6375 surname: Tian fullname: Tian, Yu organization: Zhejiang University of Technology – sequence: 2 givenname: Defeng orcidid: 0000-0002-8183-2372 surname: He fullname: He, Defeng email: hdfzj@zjut.edu.cn organization: Zhejiang University of Technology – sequence: 3 givenname: Jianbin surname: Mu fullname: Mu, Jianbin organization: Zhejiang University of Technology |
| BookMark | eNp1kMtOwzAQRS1UJNqCxCdYYsMmxY-4jtlVES-pPETZR447aVNSu9gp0B2fwDfyJbgUsWM1d3TPzJVuD3Wss4DQMSUDSgg789YMpGB0D3UpUSqhjKvOVqcqyRTjB6gXwoKQ6LG0i5rJ3Nf2ubYzDMZZt6wNvn3IsatwXEPrdW1himNIE4X2OGxCC8twjkcWwyvY9uvjs_X1bAY-cn83LfbQ6Hfd1s5ivVp5p838EO1Xuglw9Dv7aHJ58ZRfJ-P7q5t8NE4MEylNWFoaIbisqoxm3IghCCBMcqWnrBJSAk8ZZKUwAqalpIxIU0pFhiURvOK8j052X2PoyxpCWyzc2tsYWHBKFcnIMGOROt1RxrsQPFTFytdL7TcFJcW2ySI2WWybjGiyQ9_qBjb_csXjXf7DfwOvIHiE |
| Cites_doi | 10.3182/20120823-5-NL-3013.00058 10.1109/TAC.2016.2537741 10.1016/j.jprocont.2020.05.009 10.1109/TAC.2019.2905223 10.1109/TCYB.2017.2695499 10.1016/j.jprocont.2014.05.009 10.1016/j.automatica.2016.05.004 10.1109/TAC.2022.3200967 10.1016/j.automatica.2014.03.015 10.1016/j.jprocont.2023.102992 10.1016/j.automatica.2014.10.128 10.1109/TFUZZ.2019.2891236 10.1016/j.automatica.2020.108803 10.1016/j.automatica.2021.109992 10.1109/TCYB.2019.2908389 10.1109/TIE.2018.2874581 10.1016/j.automatica.2022.110364 10.1109/TCYB.2019.2963141 10.1109/ACC.2009.5160732 10.1109/TAC.2018.2868997 10.1016/j.jfranklin.2017.11.040 10.1016/j.jprocont.2014.03.010 10.1016/j.jprocont.2016.05.002 10.1002/rnc.3549 10.1016/j.automatica.2021.109499 10.1109/TIE.2019.2939994 10.1002/rnc.4033 |
| ContentType | Journal Article |
| Copyright | 2024 John Wiley & Sons Ltd. 2024 John Wiley & Sons, Ltd. |
| Copyright_xml | – notice: 2024 John Wiley & Sons Ltd. – notice: 2024 John Wiley & Sons, Ltd. |
| DBID | AAYXX CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D |
| DOI | 10.1002/rnc.7521 |
| DatabaseName | 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 | CrossRef Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1099-1239 |
| EndPage | 10436 |
| ExternalDocumentID | 10_1002_rnc_7521 RNC7521 |
| Genre | article |
| GrantInformation_xml | – fundername: National Nature Science Foundation of China funderid: 62173303 – fundername: Central Guidance Project for Local Scientific and Technological Development funderid: 2023ZY1045 |
| GroupedDBID | .3N .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 31~ 33P 3SF 3WU 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AAHQN AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABEML ABIJN ABJNI ACAHQ ACBWZ ACCFJ ACCZN ACGFO ACGFS ACIWK ACPOU ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN ADZOD AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFWVQ AFZJQ AHBTC AI. AIAGR AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BY8 CMOOK CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE G-S G.N GNP GODZA H.T H.X HF~ HGLYW HHY HHZ HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M59 MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- P2P P2W P2X P4D PALCI Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RX1 RYL SAMSI SUPJJ TUS UB1 V2E VH1 W8V W99 WBKPD WH7 WIH WIK WJL WLBEL WOHZO WQJ WRC WWI WXSBR WYISQ XG1 XV2 ZZTAW ~IA ~WT AAMMB AAYXX AEFGJ AEYWJ AGHNM AGQPQ AGXDD AGYGG AIDQK AIDYY AIQQE AMVHM CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c2541-24bc5537ff8183c56e5e02739ad2f577e342e8b5c5edb71207cb7906b053f33 |
| IEDL.DBID | DR2 |
| ISSN | 1049-8923 |
| IngestDate | Fri Jul 25 12:05:29 EDT 2025 Wed Oct 01 01:47:53 EDT 2025 Wed Jan 22 17:15:43 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 15 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2541-24bc5537ff8183c56e5e02739ad2f577e342e8b5c5edb71207cb7906b053f33 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0009-0004-3550-6375 0000-0002-8183-2372 |
| PQID | 3119080682 |
| PQPubID | 1026344 |
| PageCount | 13 |
| ParticipantIDs | proquest_journals_3119080682 crossref_primary_10_1002_rnc_7521 wiley_primary_10_1002_rnc_7521_RNC7521 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | October 2024 2024-10-00 20241001 |
| PublicationDateYYYYMMDD | 2024-10-01 |
| PublicationDate_xml | – month: 10 year: 2024 text: October 2024 |
| PublicationDecade | 2020 |
| PublicationPlace | Hoboken, USA |
| PublicationPlace_xml | – name: Hoboken, USA – name: Bognor Regis |
| PublicationTitle | International journal of robust and nonlinear control |
| PublicationYear | 2024 |
| Publisher | John Wiley & Sons, Inc Wiley Subscription Services, Inc |
| Publisher_xml | – name: John Wiley & Sons, Inc – name: Wiley Subscription Services, Inc |
| References | 2018; 28 2019; 51 2017; 48 2021; 127 2009 2023; 127 2022; 68 2014; 24 2016; 72 2018; 66 2018; 64 2022; 135 2022; 142 2019; 64 2020; 51 2018; 355 2020; 92 2019; 67 2019; 27 2016; 62 2014 2020; 114 2012; 45 2014; 50 2016; 26 2016; 44 e_1_2_9_11_1 e_1_2_9_10_1 e_1_2_9_13_1 e_1_2_9_12_1 e_1_2_9_15_1 e_1_2_9_14_1 e_1_2_9_17_1 e_1_2_9_16_1 e_1_2_9_19_1 e_1_2_9_18_1 Tran T (e_1_2_9_5_1) 2014 e_1_2_9_20_1 e_1_2_9_22_1 e_1_2_9_21_1 e_1_2_9_24_1 e_1_2_9_23_1 e_1_2_9_8_1 e_1_2_9_7_1 e_1_2_9_6_1 e_1_2_9_4_1 e_1_2_9_3_1 e_1_2_9_2_1 e_1_2_9_9_1 e_1_2_9_26_1 e_1_2_9_25_1 e_1_2_9_28_1 e_1_2_9_27_1 e_1_2_9_29_1 |
| References_xml | – volume: 135 year: 2022 article-title: Event‐triggered output quantized control of discrete Markovian singular systems publication-title: Automatica – volume: 28 start-page: 2513 issue: 6 year: 2018 end-page: 2527 article-title: Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control publication-title: Int J Robust Nonlinear Control – volume: 92 start-page: 1 year: 2020 end-page: 18 article-title: Interactions between control and process design under economic model predictive control publication-title: J Process Control – volume: 44 start-page: 162 year: 2016 end-page: 183 article-title: Fast NMPC schemes for regulatory and economic NMPC–A review publication-title: J Process Control – volume: 64 start-page: 4780 issue: 11 year: 2019 end-page: 4787 article-title: Robust self‐triggered MPC with adaptive prediction horizon for perturbed nonlinear systems publication-title: IEEE Trans Automat Contr – volume: 67 start-page: 7104 issue: 8 year: 2019 end-page: 7113 article-title: H‐infinity load frequency control of networked power systems via an event‐triggered scheme publication-title: IEEE Trans Ind Electron – volume: 64 start-page: 2606 issue: 6 year: 2018 end-page: 2613 article-title: Output consensus of heterogeneous linear multi‐agent systems with adaptive event‐triggered control publication-title: IEEE Trans Automat Contr – volume: 51 start-page: 5921 issue: 12 year: 2020 end-page: 5929 article-title: Integral‐type event‐triggered model predictive control of nonlinear systems with additive disturbance publication-title: IEEE Trans Cybern – volume: 66 start-page: 6393 issue: 8 year: 2018 end-page: 6403 article-title: Input‐to‐state stability of perturbed nonlinear systems with event‐triggered receding horizon control scheme publication-title: IEEE Trans Ind Electron – volume: 24 start-page: 1156 issue: 8 year: 2014 end-page: 1178 article-title: A tutorial review of economic model predictive control methods publication-title: J Process Control – volume: 114 year: 2020 article-title: Self‐triggered MPC with performance guarantee using relaxed dynamic programming publication-title: Automatica – start-page: 2236 year: 2009 end-page: 2242 – year: 2014 – volume: 127 year: 2021 article-title: Robust MPC for disturbed nonlinear discrete‐time systems via a composite self‐triggered scheme publication-title: Automatica – volume: 51 start-page: 3093 issue: 6 year: 2019 end-page: 3102 article-title: Event‐triggered active MPC for nonlinear multiagent systems with packet losses publication-title: IEEE Trans Cybern – volume: 26 start-page: 4072 issue: 18 year: 2016 end-page: 4087 article-title: Economic MPC with a contractive constraint for nonlinear systems publication-title: Int J Robust Nonlinear Control – volume: 27 start-page: 1793 issue: 9 year: 2019 end-page: 1806 article-title: Adaptive event‐triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and actuator failure publication-title: IEEE Trans Fuzzy Syst – volume: 50 start-page: 2967 issue: 12 year: 2014 end-page: 2986 article-title: Model predictive control: recent developments and future promise publication-title: Automatica – volume: 68 start-page: 3806 year: 2022 end-page: 3813 article-title: Robust nonlinear MPC with variable prediction horizon: an adaptive event‐triggered approach publication-title: IEEE Trans Automat Contr – volume: 62 start-page: 177 issue: 1 year: 2016 end-page: 189 article-title: Self‐triggered model predictive control for nonlinear input‐affine dynamical systems via adaptive control samples selection publication-title: IEEE Trans Automat Contr – volume: 48 start-page: 1397 issue: 5 year: 2017 end-page: 1405 article-title: Aperiodic robust model predictive control for constrained continuous‐time nonlinear systems: an event‐triggered approach publication-title: IEEE Trans Cybern – volume: 50 start-page: 1507 issue: 5 year: 2014 end-page: 1513 article-title: Event‐triggered robust model predictive control of continuous‐time nonlinear systems publication-title: Automatica – volume: 142 year: 2022 article-title: Self‐triggered MPC with performance guarantee for tracking piecewise constant reference signals publication-title: Automatica – volume: 355 start-page: 753 issue: 2 year: 2018 end-page: 773 article-title: Lexicographic MPC with multiple economic criteria for constrained nonlinear systems publication-title: J Franklin Inst – volume: 72 start-page: 73 year: 2016 end-page: 83 article-title: Robust self‐triggered MPC for constrained linear systems: a tube‐based approach publication-title: Automatica – volume: 45 start-page: 342 issue: 17 year: 2012 end-page: 348 article-title: Self‐triggered MPC for constrained linear systems and quadratic costs publication-title: IFAC Proc Vol – volume: 127 year: 2023 article-title: Event‐triggered economic MPC with relaxed contractive constraints publication-title: J Process Control – volume: 24 start-page: 1179 issue: 8 year: 2014 end-page: 1186 article-title: On the performance of economic model predictive control with self‐tuning terminal cost publication-title: J Process Control – ident: e_1_2_9_11_1 doi: 10.3182/20120823-5-NL-3013.00058 – ident: e_1_2_9_12_1 doi: 10.1109/TAC.2016.2537741 – ident: e_1_2_9_4_1 doi: 10.1016/j.jprocont.2020.05.009 – ident: e_1_2_9_23_1 doi: 10.1109/TAC.2019.2905223 – ident: e_1_2_9_9_1 doi: 10.1109/TCYB.2017.2695499 – ident: e_1_2_9_3_1 doi: 10.1016/j.jprocont.2014.05.009 – ident: e_1_2_9_13_1 doi: 10.1016/j.automatica.2016.05.004 – ident: e_1_2_9_25_1 doi: 10.1109/TAC.2022.3200967 – ident: e_1_2_9_14_1 doi: 10.1016/j.automatica.2014.03.015 – ident: e_1_2_9_22_1 doi: 10.1016/j.jprocont.2023.102992 – ident: e_1_2_9_29_1 doi: 10.1016/j.automatica.2014.10.128 – ident: e_1_2_9_15_1 doi: 10.1109/TFUZZ.2019.2891236 – ident: e_1_2_9_21_1 doi: 10.1016/j.automatica.2020.108803 – ident: e_1_2_9_19_1 doi: 10.1016/j.automatica.2021.109992 – ident: e_1_2_9_10_1 doi: 10.1109/TCYB.2019.2908389 – ident: e_1_2_9_18_1 doi: 10.1109/TIE.2018.2874581 – ident: e_1_2_9_20_1 doi: 10.1016/j.automatica.2022.110364 – ident: e_1_2_9_26_1 doi: 10.1109/TCYB.2019.2963141 – ident: e_1_2_9_8_1 doi: 10.1109/ACC.2009.5160732 – ident: e_1_2_9_17_1 doi: 10.1109/TAC.2018.2868997 – ident: e_1_2_9_28_1 doi: 10.1016/j.jfranklin.2017.11.040 – ident: e_1_2_9_2_1 doi: 10.1016/j.jprocont.2014.03.010 – ident: e_1_2_9_7_1 doi: 10.1016/j.jprocont.2016.05.002 – ident: e_1_2_9_27_1 doi: 10.1002/rnc.3549 – volume-title: ISARC. Proceedings of the International Symposium on Automation and Robotics in Construction year: 2014 ident: e_1_2_9_5_1 – ident: e_1_2_9_24_1 doi: 10.1016/j.automatica.2021.109499 – ident: e_1_2_9_16_1 doi: 10.1109/TIE.2019.2939994 – ident: e_1_2_9_6_1 doi: 10.1002/rnc.4033 |
| SSID | ssj0009924 |
| Score | 2.4137344 |
| Snippet | This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to... |
| SourceID | proquest crossref wiley |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 10424 |
| SubjectTerms | Algorithms Constraints Continuously stirred tank reactors Control systems Design optimization economic optimization event‐triggered control model predictive control Nonlinear control Nonlinear systems Performance prediction Predictive control Stability |
| Title | Shrinking economic MPC of constrained nonlinear systems: An event‐triggered constraint relaxation approach |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Frnc.7521 https://www.proquest.com/docview/3119080682 |
| Volume | 34 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVEBS databaseName: EBSCOhost Mathematics Source - HOST customDbUrl: eissn: 1099-1239 dateEnd: 20241105 omitProxy: false ssIdentifier: ssj0009924 issn: 1049-8923 databaseCode: AMVHM dateStart: 20120801 isFulltext: true titleUrlDefault: https://www.ebsco.com/products/research-databases/mathematics-source providerName: EBSCOhost – providerCode: PRVWIB databaseName: Wiley Online Library - Core collection (SURFmarket) issn: 1049-8923 databaseCode: DR2 dateStart: 19960101 customDbUrl: isFulltext: true eissn: 1099-1239 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009924 providerName: Wiley-Blackwell |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3NSsNAEF6kJz34L1arrCDe0iab_Um8lWIpQou0CgUPIbuZKChV0hTEk4_gM_ok7mYTUwVBPOWSgcnszM43YeYbhE65l3hJrJgjGaUO5Sx1JBHSAYA4kG6gZGqGk4cjPrihl1M2LbsqzSyM5Yf4-uFmIqO4r02Ax3LeqUlDMx0_ghUz5J7Pi2pqXDNHhaHdZ6sBsBNoEFPxzrqkUwl-z0Q1vFwGqUWW6W-g20o_21zy0F7ksq1ef1A3_u8DNtF6CT5x13rLFlqB2TZaW6Ik3EGPk_vMrlPAUM4s4-FVDz-lWBkoaTZKQIJnVoE4w5YKen6OuzNcsEF9vL3nuuS_M0tAa5kcm6mZl8IPcEVkvosm_Yvr3sApNzI4SheSnkOoVIz5Ik11nvcV48DAEOKEcUJSJgT4lEAgmWKQSOERVygpQpdLHeqp7--hhlYP9hFO0tjzQVCIgdJQl4jK4xpLgMZzCUto0EQn1dlEz5Z2I7IEyyTSdouM3ZqoVR1aVAbePPI9jXAClwekic4K6_8qH41HPfM8-OuLh2iVaEhjW_laqJFnCzjSkCSXx4XzfQI79uCy |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ1LS8QwEMeHRQ_qwbe4PiOIt2qbJk2rp2VxWR-7yO4KHoTSpFMFZZXdCuLJj-Bn9JOYNFtXBUE89dJAOsl0fhMy_wHYDbzUSxPFHckZc1jAM0dSIR1ETELphkpmpji51Q6al-z0il9V4KishbH6EJ8HbsYziv-1cXBzIH0wVg0daAcS3BSRT7JApymGiDpj7agosh1tNQI7ocaYUnnWpQflyO-xaAyYXzG1iDONObguZ2ivl9ztP-VyX738EG_85yfMw-yIP0nNbpgFqGB_EWa-qBIuwX33dmA7KhAclS2T1kWdPGREGZo0TSUwJX07g2RArBr08JDU-qQQhHp_fct11n9j-oCOx-TEFM48F1uBlFrmy9BtHPfqTWfUlMFROpf0HMqk4twXWaZDva94gByNJk6UpDTjQqDPKIaSK46pFB51hZIicgOpvT3z_RWY0NPDVSBplng-CoYJMhbpLFF5gcYJ1EiX8pSFVdgpFyd-tMobsdVYprG2W2zsVoWNctXike8NY9_TkBO6QUirsFeY_9fxcaddN8-1v764DVPNXus8Pj9pn63DNNWEY2_2bcBEPnjCTU0oudwqduIHT4Dk0w |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1fS9xAEB9EQdoH_7XF06uuIL5Fk81uNrFPx9nDf3eItuCDELK7sxYq53GXA_HJj-Bn7CfpbvbiXQuC-JSXDExmZ3Z-E2Z-A7CbRDrSheKB5IwFLOEmkFTIABGLVIapksYNJ3d7yfFPdnrNr-fgWz0L4_khXn64ucio7msX4DjQ5mDKGjq0ASS4GyJfYDxLXT_f0eWUOyrL_EZbC4GD1MKYmnk2pAe15L-5aAowZ2FqlWc6y3BTa-jbS37vj0u5rx7_I2985yeswNIEf5KWd5hVmMP-GnycYSX8BHdXv4Z-owLBydgy6V60yb0hyqFJt1QCNel7DYoh8WzQo0PS6pOKEOrP03Npq_5btwd0KlMSNzjzULkCqbnMP8NV5_uP9nEwWcoQKFtLRgFlUnEeC2Nsqo8VT5Cj48TJCk0NFwJjRjGVXHHUUkQ0FEqKLEykjXYTx19g3qqH60C0KaIYBcMCGctslaiixMIJtJBOc83SBuzUh5MPPPNG7jmWaW7tlju7NaBZn1o-ib1RHkcW5KRhktIG7FXmf1U-v-y13XPjrS9uw-LFUSc_P-mdbcIHagGOb-xrwnw5HONXC1BKuVU54l8d8uRX |
| 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=Shrinking+economic+MPC+of+constrained+nonlinear+systems%3A+An+event%E2%80%90triggered+constraint+relaxation+approach&rft.jtitle=International+journal+of+robust+and+nonlinear+control&rft.au=Tian%2C+Yu&rft.au=He%2C+Defeng&rft.au=Mu%2C+Jianbin&rft.date=2024-10-01&rft.pub=John+Wiley+%26+Sons%2C+Inc&rft.issn=1049-8923&rft.eissn=1099-1239&rft.volume=34&rft.issue=15&rft.spage=10424&rft.epage=10436&rft_id=info:doi/10.1002%2Frnc.7521&rft.externalDBID=10.1002%252Frnc.7521&rft.externalDocID=RNC7521 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1049-8923&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1049-8923&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1049-8923&client=summon |