Robust MPC with event-triggered learning for unknown linear time-varying systems
This paper is concerned with robust model predictive control (MPC) for unknown linear time-varying (LTV) systems where all time-varying system matrices are assumed to belong to an unknown polytope. Based on the current observation only, an event-triggered learning scheme involving a model estimation...
Saved in:
| Published in | Automatica (Oxford) Vol. 179; p. 112434 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2025
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 |
| DOI | 10.1016/j.automatica.2025.112434 |
Cover
Loading…
| Abstract | This paper is concerned with robust model predictive control (MPC) for unknown linear time-varying (LTV) systems where all time-varying system matrices are assumed to belong to an unknown polytope. Based on the current observation only, an event-triggered learning scheme involving a model estimation and a polytope learning is proposed, leading to the reduction of the number of learning iterations and the guarantee of the convergence of learning. With the learned polytope, a robust MPC controller subject to a mixed state-input constraint is purposely designed to minimize the upper bound of a worst-case infinite horizon objective function with a discount factor. A matching error is constructed to connect two consecutive learned polytopes and accordingly the input-to-state stability is analyzed. Two examples are used to show the effectiveness of the proposed approach. |
|---|---|
| AbstractList | This paper is concerned with robust model predictive control (MPC) for unknown linear time-varying (LTV) systems where all time-varying system matrices are assumed to belong to an unknown polytope. Based on the current observation only, an event-triggered learning scheme involving a model estimation and a polytope learning is proposed, leading to the reduction of the number of learning iterations and the guarantee of the convergence of learning. With the learned polytope, a robust MPC controller subject to a mixed state-input constraint is purposely designed to minimize the upper bound of a worst-case infinite horizon objective function with a discount factor. A matching error is constructed to connect two consecutive learned polytopes and accordingly the input-to-state stability is analyzed. Two examples are used to show the effectiveness of the proposed approach. |
| ArticleNumber | 112434 |
| Author | Deng, Li Chen, Tongwen Shu, Zhan |
| Author_xml | – sequence: 1 givenname: Li surname: Deng fullname: Deng, Li email: ld@ualberta.ca – sequence: 2 givenname: Zhan surname: Shu fullname: Shu, Zhan email: zshu1@ualberta.ca – sequence: 3 givenname: Tongwen surname: Chen fullname: Chen, Tongwen email: tchen@ualberta.ca |
| BookMark | eNqFkEtLAzEUhbOoYFv9D_kDM-ZO5rnU4gsqFtF1yONOTe0kkqQt_fdOqeDS1eGeyzkcvhmZOO-QEAosBwb1zSaXu-QHmayWecGKKgcoSl5OyJQxVmXAuvaSzGLcjGcJbTElqzevdjHRl9WCHmz6pLhHl7IU7HqNAQ3dogzOujXtfaA79-X8wdGtdaNNkx0w28twPP3jMSYc4hW56OU24vWvzsnHw_374ilbvj4-L26XmS7qKmW81lAbbrpKApSKcwV90_PKKJBaKSgbNEWnKyWhak2jeNlJUyiFneoQG83npD336uBjDNiL72CHcYsAJk40xEb80RAnGuJMY4zenaM47ttbDCJqi06jsQF1Esbb_0t-AL1wc_k |
| Cites_doi | 10.1109/TAC.2019.2959924 10.1109/TAC.2020.3030877 10.1016/j.automatica.2003.07.007 10.1016/0005-1098(96)00063-5 10.1016/S0005-1098(01)00028-0 10.1007/978-3-540-24743-2_30 10.1109/TAC.2023.3276909 10.1109/TAC.2022.3191760 10.1016/j.automatica.2020.109009 10.1016/j.automatica.2020.108974 10.1016/j.automatica.2018.10.019 10.1109/TAC.2020.3000182 10.1016/j.automatica.2023.110961 10.1109/TAC.2024.3357417 10.1016/j.automatica.2019.06.025 10.1109/TAC.2020.3024161 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier Ltd |
| Copyright_xml | – notice: 2025 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.automatica.2025.112434 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| ExternalDocumentID | 10_1016_j_automatica_2025_112434 S0005109825003280 |
| GrantInformation_xml | – fundername: Natural Sciences and Engineering Research Council of Canada (NSERC) funderid: http://dx.doi.org/10.13039/501100000038 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 23N 3R3 4.4 457 4G. 5GY 5VS 6TJ 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AATTM AAXKI AAXUO AAYWO ABFNM ABFRF ABJNI ABMAC ABUCO ABWVN ABXDB ACBEA ACDAQ ACGFO ACGFS ACNNM ACRLP ACRPL ACVFH ADBBV ADCNI ADEZE ADIYS ADMUD ADNMO ADTZH AEBSH AECPX AEFWE AEIPS AEKER AENEX AEUPX AFFNX AFJKZ AFPUW AFTJW AGCQF AGHFR AGQPQ AGUBO AGYEJ AHHHB AHJVU AHPGS AI. AIEXJ AIGII AIIUN AIKHN AITUG AKBMS AKRWK AKYEP ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU APLSM APXCP ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFKBS EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HLZ HVGLF HZ~ H~9 IHE J1W JJJVA K-O KOM LG9 LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- ROL RPZ RXW SBC SDF SDG SDP SES SET SEW SPC SPCBC SSB SSD SST SSZ T5K T9H TAE TN5 VH1 WH7 WUQ X6Y XPP ZMT ~G- AAYXX AFXIZ AGRNS BNPGV CITATION RIG SSH |
| ID | FETCH-LOGICAL-c265t-36c16d3d95a114b33b1f7f35db1acbb147ed29c5ba158d7b349ad2bbe9b9ee7c3 |
| IEDL.DBID | .~1 |
| ISSN | 0005-1098 |
| IngestDate | Thu Jul 24 02:16:15 EDT 2025 Sat Aug 23 17:12:24 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Unknown linear time-varying (LTV) systems Event-triggered learning Input-to-state stability Robust model predictive control (MPC) |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c265t-36c16d3d95a114b33b1f7f35db1acbb147ed29c5ba158d7b349ad2bbe9b9ee7c3 |
| ParticipantIDs | crossref_primary_10_1016_j_automatica_2025_112434 elsevier_sciencedirect_doi_10_1016_j_automatica_2025_112434 |
| PublicationCentury | 2000 |
| PublicationDate | September 2025 2025-09-00 |
| PublicationDateYYYYMMDD | 2025-09-01 |
| PublicationDate_xml | – month: 09 year: 2025 text: September 2025 |
| PublicationDecade | 2020 |
| PublicationTitle | Automatica (Oxford) |
| PublicationYear | 2025 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Deng, Shu, Chen (b3) 2024; 69 Berberich, Köhler, Müller, Allgöwer (b1) 2021; 66 Jiang, Wang (b6) 2001; 37 Breschi, Chiuso, Formentin (b2) 2023; 152 Persis, Tesi (b10) 2020; 65 Kvasnica, M., Grieder, P., & Baotić, M. (2004). Multi-Parametric Toolbox (MPT). In Zhang, Shi (b16) 2020; 117 (pp. 448–462). Zou, Su, Li, Niu, Li (b18) 2019; 99 Solowjow, Trimpe (b12) 2020; 117 Esfahani, Gros (b5) 2022 Ding, Xi, Li (b4) 2008; 40 Terzi, Fagiano, Farina, Scattolini (b13) 2019; 108 Verhoek, Abbas, Tóth, Haesaert (b14) 2021 Zheng, Shi, Shi, Wang (b17) 2023; 68 Schlüter, Solowjow, Trimpe (b11) 2021; 66 Nortmann, Mylvaganam (b9) 2023; 68 Kothare, Balakrishnan, Morari (b7) 1996; 32 Zanon, Gros (b15) 2021; 66 Kothare (10.1016/j.automatica.2025.112434_b7) 1996; 32 Esfahani (10.1016/j.automatica.2025.112434_b5) 2022 Schlüter (10.1016/j.automatica.2025.112434_b11) 2021; 66 Solowjow (10.1016/j.automatica.2025.112434_b12) 2020; 117 Zheng (10.1016/j.automatica.2025.112434_b17) 2023; 68 Ding (10.1016/j.automatica.2025.112434_b4) 2008; 40 Verhoek (10.1016/j.automatica.2025.112434_b14) 2021 Berberich (10.1016/j.automatica.2025.112434_b1) 2021; 66 Zhang (10.1016/j.automatica.2025.112434_b16) 2020; 117 Breschi (10.1016/j.automatica.2025.112434_b2) 2023; 152 Deng (10.1016/j.automatica.2025.112434_b3) 2024; 69 Jiang (10.1016/j.automatica.2025.112434_b6) 2001; 37 Persis (10.1016/j.automatica.2025.112434_b10) 2020; 65 Zanon (10.1016/j.automatica.2025.112434_b15) 2021; 66 Zou (10.1016/j.automatica.2025.112434_b18) 2019; 99 Terzi (10.1016/j.automatica.2025.112434_b13) 2019; 108 10.1016/j.automatica.2025.112434_b8 Nortmann (10.1016/j.automatica.2025.112434_b9) 2023; 68 |
| References_xml | – start-page: 1 year: 2022 end-page: 6 ident: b5 article-title: Policy gradient reinforcement learning for uncertain polytopic LPV systems based on MHE-MPC publication-title: 6th IFAC conference on intelligent control and automation sciences – volume: 66 start-page: 4485 year: 2021 end-page: 4498 ident: b11 article-title: Event-triggered learning for linear quadratic control publication-title: IEEE Transactions on Automatic Control – volume: 68 start-page: 4888 year: 2023 end-page: 4895 ident: b9 article-title: Direct data-driven control of linear time-varying systems publication-title: IEEE Transactions on Automatic Control – volume: 68 start-page: 3469 year: 2023 end-page: 3484 ident: b17 article-title: Nonparameteric event-triggered learning with applications to adaptive model predictive control publication-title: IEEE Transactions on Automatic Control – volume: 69 start-page: 4773 year: 2024 end-page: 4780 ident: b3 article-title: Event-triggered robust MPC with terminal inequality constraints: A data-driven approach publication-title: IEEE Transactions on Automatic Control – volume: 40 start-page: 163 year: 2008 end-page: 167 ident: b4 article-title: A synthesis approach of on-line constrained robust model predictive control publication-title: Automatica – volume: 99 start-page: 92 year: 2019 end-page: 98 ident: b18 article-title: Event-triggered distributed predictive control for asynchronous coordination of multi-agent systems publication-title: Automatica – volume: 108 year: 2019 ident: b13 article-title: Learning-based predictive control for linear systems: A unitary approach publication-title: Automatica – start-page: 101 year: 2021 end-page: 108 ident: b14 article-title: Data-driven predictive control for linear parameter-varying systems publication-title: 4th IFAC Workshop on Linear Parameter Varying Systems – volume: 117 year: 2020 ident: b16 article-title: Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties publication-title: Automatica – volume: 32 start-page: 440 year: 1996 end-page: 444 ident: b7 article-title: Robust constrained model predictive control using linear matrix inequalities publication-title: Automatica – reference: Kvasnica, M., Grieder, P., & Baotić, M. (2004). Multi-Parametric Toolbox (MPT). In – volume: 65 start-page: 909 year: 2020 end-page: 924 ident: b10 article-title: Formulas for data-driven control: Stabilization, optimality, and robustness publication-title: IEEE Transactions on Automatic Control – volume: 66 start-page: 3638 year: 2021 end-page: 3652 ident: b15 article-title: Safe reinforcement learning using robust MPC publication-title: IEEE Transactions on Automatic Control – volume: 152 year: 2023 ident: b2 article-title: Data-driven predictive control in a stochastic setting: A unified framework publication-title: Automatica – volume: 117 year: 2020 ident: b12 article-title: Event-triggered learning publication-title: Automatica – volume: 66 start-page: 1702 year: 2021 end-page: 1717 ident: b1 article-title: Data-driven model predictive control with stability and robustness guarantees publication-title: IEEE Transactions on Automatic Control – reference: (pp. 448–462). – volume: 37 start-page: 857 year: 2001 end-page: 869 ident: b6 article-title: Input-to-state stability for discrete-time nonlinear systems publication-title: Automatica – start-page: 1 year: 2022 ident: 10.1016/j.automatica.2025.112434_b5 article-title: Policy gradient reinforcement learning for uncertain polytopic LPV systems based on MHE-MPC – volume: 65 start-page: 909 issue: 3 year: 2020 ident: 10.1016/j.automatica.2025.112434_b10 article-title: Formulas for data-driven control: Stabilization, optimality, and robustness publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2019.2959924 – volume: 66 start-page: 4485 issue: 10 year: 2021 ident: 10.1016/j.automatica.2025.112434_b11 article-title: Event-triggered learning for linear quadratic control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2020.3030877 – volume: 40 start-page: 163 year: 2008 ident: 10.1016/j.automatica.2025.112434_b4 article-title: A synthesis approach of on-line constrained robust model predictive control publication-title: Automatica doi: 10.1016/j.automatica.2003.07.007 – volume: 32 start-page: 440 issue: 10 year: 1996 ident: 10.1016/j.automatica.2025.112434_b7 article-title: Robust constrained model predictive control using linear matrix inequalities publication-title: Automatica doi: 10.1016/0005-1098(96)00063-5 – volume: 37 start-page: 857 issue: 6 year: 2001 ident: 10.1016/j.automatica.2025.112434_b6 article-title: Input-to-state stability for discrete-time nonlinear systems publication-title: Automatica doi: 10.1016/S0005-1098(01)00028-0 – ident: 10.1016/j.automatica.2025.112434_b8 doi: 10.1007/978-3-540-24743-2_30 – volume: 68 start-page: 4888 issue: 8 year: 2023 ident: 10.1016/j.automatica.2025.112434_b9 article-title: Direct data-driven control of linear time-varying systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2023.3276909 – volume: 68 start-page: 3469 issue: 6 year: 2023 ident: 10.1016/j.automatica.2025.112434_b17 article-title: Nonparameteric event-triggered learning with applications to adaptive model predictive control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2022.3191760 – volume: 117 year: 2020 ident: 10.1016/j.automatica.2025.112434_b12 article-title: Event-triggered learning publication-title: Automatica doi: 10.1016/j.automatica.2020.109009 – volume: 117 year: 2020 ident: 10.1016/j.automatica.2025.112434_b16 article-title: Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties publication-title: Automatica doi: 10.1016/j.automatica.2020.108974 – start-page: 101 year: 2021 ident: 10.1016/j.automatica.2025.112434_b14 article-title: Data-driven predictive control for linear parameter-varying systems – volume: 99 start-page: 92 year: 2019 ident: 10.1016/j.automatica.2025.112434_b18 article-title: Event-triggered distributed predictive control for asynchronous coordination of multi-agent systems publication-title: Automatica doi: 10.1016/j.automatica.2018.10.019 – volume: 66 start-page: 1702 issue: 4 year: 2021 ident: 10.1016/j.automatica.2025.112434_b1 article-title: Data-driven model predictive control with stability and robustness guarantees publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2020.3000182 – volume: 152 year: 2023 ident: 10.1016/j.automatica.2025.112434_b2 article-title: Data-driven predictive control in a stochastic setting: A unified framework publication-title: Automatica doi: 10.1016/j.automatica.2023.110961 – volume: 69 start-page: 4773 issue: 7 year: 2024 ident: 10.1016/j.automatica.2025.112434_b3 article-title: Event-triggered robust MPC with terminal inequality constraints: A data-driven approach publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2024.3357417 – volume: 108 year: 2019 ident: 10.1016/j.automatica.2025.112434_b13 article-title: Learning-based predictive control for linear systems: A unitary approach publication-title: Automatica doi: 10.1016/j.automatica.2019.06.025 – volume: 66 start-page: 3638 issue: 8 year: 2021 ident: 10.1016/j.automatica.2025.112434_b15 article-title: Safe reinforcement learning using robust MPC publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2020.3024161 |
| SSID | ssj0004182 |
| Score | 2.4826694 |
| Snippet | This paper is concerned with robust model predictive control (MPC) for unknown linear time-varying (LTV) systems where all time-varying system matrices are... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 112434 |
| SubjectTerms | Event-triggered learning Input-to-state stability Robust model predictive control (MPC) Unknown linear time-varying (LTV) systems |
| Title | Robust MPC with event-triggered learning for unknown linear time-varying systems |
| URI | https://dx.doi.org/10.1016/j.automatica.2025.112434 |
| Volume | 179 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3Pa8IwFA7iLtth7CdzPySHXTNNk7QNO4lM3IYiY4K3kjRR3KGKtjvub19e06KDwQ47tjRQvr6-fC9873sI3UvBIjO3gri9XhJu4J9LuSKhigNHyB1RKlWVo3E4nPKXmZg1UL_uhQFZZZX7fU4vs3V1p1Oh2Vkvl9DjCwElXYnTBVM4qNs5jyDKH752Mg9OY-8YXjpuyrhS83iNlyryVemMCg5EgYB-Gs7471vU3rYzOEHHFV_EPf9Kp6hhszN0tOcieI4mbytdbHM8mvQxHKvi0pSJ5K7uXsAkTlxNhlhgR1BxkcExWoaBXqoNhtny5FNtoNsJe1vn7QWaDp7e-0NSDUogaRCKnLAwpaFhRgrlyhvNmKbzaM6E0VSlWlMeWRPIVGhFRWwizbhUJtDaSi2tjVJ2iZrZKrNXCAeh4wDuaRobxU0axcyGge5qx1SMK3aCFqI1Nsna-2EktVDsI9nhmQCeicezhR5rEJMf3zZxafvP1df_Wn2DDuHKq8JuUTPfFPbO0Yhct8s4aaOD3vPrcPwNvk3I_Q |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3Pa8IwFH6IHrYdxn4y9zOHXYs2adqGnUQmdf5AhoK3kDRRtkMVrfv7lzQtOhjssGvbQPmavve98L3vATwzSiK10NQzuZ55gbL_XBoILxQxNoTcEKVCVTkah8kseJvTeQ26VS-MlVWWsd_F9CJal1daJZqt9ceH7fG1G4qZEqdtTeFM3d6w7lS0Do1Of5CM9-2RfuxMwwvTTRaXgh4n8xK7fFWYo1oTIkxtS01Agt-z1EHm6Z3BaUkZUce91TnUdHYBJwdGgpcweV_J3TZHo0kX2ZNVVPgyebkpvZd2GCcqh0MskeGoaJfZk7QMWYYpNsiOl_e-xMY2PCHn7Ly9glnvddpNvHJWgpfikOYeCVM_VEQxKkyFIwmR_iJaEKqkL1Ip_SDSCrOUSuHTWEWSBEwoLKVmkmkdpeQa6tkq0zeAcGhogHnaj5UIVBrFRIdYtqUhK8rUO7gJfoUNXztLDF5pxT75Hk9u8eQOzya8VCDyH5-Xm8j95-rbf61-gqNkOhryYX88uINje8eJxO6hnm92-sGwilw-lrvmG68Sy64 |
| 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=Robust+MPC+with+event-triggered+learning+for+unknown+linear+time-varying+systems&rft.jtitle=Automatica+%28Oxford%29&rft.au=Deng%2C+Li&rft.au=Shu%2C+Zhan&rft.au=Chen%2C+Tongwen&rft.date=2025-09-01&rft.issn=0005-1098&rft.volume=179&rft.spage=112434&rft_id=info:doi/10.1016%2Fj.automatica.2025.112434&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_automatica_2025_112434 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0005-1098&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0005-1098&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0005-1098&client=summon |