Using stochastic programming to train neural network approximation of nonlinear MPC laws
To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the NMPC law is approximated via a deep neural network (DNN). To optimize the DNN controller, a novel “optimize and train” architecture is designed...
Uložené v:
| Vydané v: | Automatica (Oxford) Ročník 146; s. 110665 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Ltd
01.12.2022
|
| Predmet: | |
| ISSN: | 0005-1098, 1873-2836 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the NMPC law is approximated via a deep neural network (DNN). To optimize the DNN controller, a novel “optimize and train” architecture is designed, where the processes of data generation and neural network training are combined together to result in a single large-scale stochastic optimization problem. Unlike the conventional “optimize then train” approach, our proposed one directly optimizes the closed-loop performance of the DNN controller over a finite horizon for a number of initial states. The important features of our proposed scheme are that it can deal with set-valued optimal MPC input, and a probabilistic guarantee of constraint satisfaction can be concluded for the closed-loop system without simulating the DNN controller. With our proposed scheme, an increased number of training scenarios leads to improved constraint satisfaction of the derived DNN controller, which is not necessarily true for the “optimize then train” approach. Statistical approaches for validating closed-loop control performance are also discussed. Furthermore, computational methods are introduced to efficiently solve the resulting stochastic optimization problem. The effectiveness of the proposed scheme is extensively illustrated with several numerical simulations. Compared with the conventional “optimize then train” approach, our proposed approach exhibits better closed-loop constraint satisfaction for all considered case studies. |
|---|---|
| AbstractList | To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the NMPC law is approximated via a deep neural network (DNN). To optimize the DNN controller, a novel “optimize and train” architecture is designed, where the processes of data generation and neural network training are combined together to result in a single large-scale stochastic optimization problem. Unlike the conventional “optimize then train” approach, our proposed one directly optimizes the closed-loop performance of the DNN controller over a finite horizon for a number of initial states. The important features of our proposed scheme are that it can deal with set-valued optimal MPC input, and a probabilistic guarantee of constraint satisfaction can be concluded for the closed-loop system without simulating the DNN controller. With our proposed scheme, an increased number of training scenarios leads to improved constraint satisfaction of the derived DNN controller, which is not necessarily true for the “optimize then train” approach. Statistical approaches for validating closed-loop control performance are also discussed. Furthermore, computational methods are introduced to efficiently solve the resulting stochastic optimization problem. The effectiveness of the proposed scheme is extensively illustrated with several numerical simulations. Compared with the conventional “optimize then train” approach, our proposed approach exhibits better closed-loop constraint satisfaction for all considered case studies. |
| ArticleNumber | 110665 |
| Author | Cao, Yankai Hua, Kaixun Li, Yun |
| Author_xml | – sequence: 1 givenname: Yun surname: Li fullname: Li, Yun email: y.li-39@tudelft.nl – sequence: 2 givenname: Kaixun surname: Hua fullname: Hua, Kaixun email: huakaixun@gmail.com – sequence: 3 givenname: Yankai surname: Cao fullname: Cao, Yankai email: yankai.cao@ubc.ca |
| BookMark | eNqNkN1KAzEQhYNUsFbfIS-wa366u-mNoMU_qOiFBe_CNJvU1G1SktTq25u1guCNXh1mmPnmzDlGA-edRghTUlJC67NVCdvk15CsgpIRxkpKSV1XB2hIRcMLJng9QENCSFVQMhFH6DjGVS7HVLAhep5H65Y4Jq9eIGYI3gS_DLBe9-3kcQpgHXZ6G6DLknY-vGLY5Kl321_1DnuDs6nOOg0B3z9OcQe7eIIODXRRn37rCM2vr56mt8Xs4eZuejErFKciFdmxanlVZTWCGTrmzYKwRQNAKeembTW0ilWNAVYTVTdiPDGTtlELyitdV5SP0Pmeq4KPMWgjlU1fvnrnnaRE9jnJlfzJSfY5yX1OGSB-ATYhfxY-_rN6uV_V-cE3q4OMymqndGuDVkm23v4N-QTvnIz3 |
| CitedBy_id | crossref_primary_10_1002_rnc_70057 crossref_primary_10_3390_act14080402 crossref_primary_10_1007_s40435_024_01426_3 crossref_primary_10_1016_j_patcog_2025_111650 crossref_primary_10_1016_j_jprocont_2024_103228 crossref_primary_10_1016_j_asoc_2025_113882 crossref_primary_10_1016_j_engappai_2024_109009 crossref_primary_10_1016_j_compchemeng_2025_109096 crossref_primary_10_1109_TITS_2023_3342651 crossref_primary_10_1016_j_jprocont_2024_103270 crossref_primary_10_1109_TTE_2025_3543510 crossref_primary_10_1109_TAES_2025_3551283 crossref_primary_10_1016_j_compchemeng_2023_108511 crossref_primary_10_1016_j_ins_2024_120970 crossref_primary_10_1016_j_asr_2024_07_019 crossref_primary_10_1016_j_conengprac_2025_106480 crossref_primary_10_1016_j_jprocont_2024_103302 crossref_primary_10_1002_aic_18644 crossref_primary_10_1016_j_jprocont_2024_103353 crossref_primary_10_1016_j_jprocont_2023_103144 |
| Cites_doi | 10.1016/j.ifacol.2018.09.373 10.1002/rnc.5696 10.1016/j.compchemeng.2017.01.021 10.1016/S0005-1098(01)00174-1 10.1016/0893-6080(90)90005-6 10.1109/TAC.2014.2351991 10.1016/j.compchemeng.2014.09.013 10.1016/j.ifacol.2018.11.036 10.1109/TCYB.2020.2999556 10.1016/j.ifacol.2020.12.546 10.1016/j.compchemeng.2018.08.036 10.1016/j.automatica.2014.11.004 10.1109/LCSYS.2018.2843682 10.1109/TAC.2002.805688 10.1109/TAC.2013.2275667 10.1561/2600000008 10.1109/TCST.2020.3024571 10.1016/j.compchemeng.2019.03.009 10.1016/0005-1098(95)00044-W 10.1016/j.ifacol.2020.12.538 10.1016/j.compchemeng.2020.107174 10.1109/TAC.2009.2031207 10.1016/j.jprocont.2020.06.012 10.1007/s10589-015-9813-x 10.1007/s10107-004-0559-y 10.1016/j.compchemeng.2020.107133 10.1109/TAC.2011.2141410 10.1016/j.automatica.2011.02.029 10.1016/j.ces.2007.05.022 |
| ContentType | Journal Article |
| Copyright | 2022 Elsevier Ltd |
| Copyright_xml | – notice: 2022 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.automatica.2022.110665 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1873-2836 |
| ExternalDocumentID | 10_1016_j_automatica_2022_110665 S0005109822005295 |
| GrantInformation_xml | – fundername: Natural Science and Engineering Research Council of Canada grantid: RGPIN-2019-05499 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 AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABDEX ABFNM ABFRF ABJNI ABMAC ABUCO ABXDB ABYKQ ACBEA ACDAQ ACGFO ACGFS ACNNM ACRLP ADBBV ADEZE ADIYS ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHPGS AI. AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG 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- RIG ROL RPZ RXW SBC SDF SDG SDP SES SET SEW SPC SPCBC SSB SSD SST SSZ T5K T9H TAE TN5 VH1 WH7 WUQ X6Y XFK XPP ZMT ~G- 77I 9DU AATTM AAXKI AAYWO AAYXX ABUFD ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c318t-202cd355202f82f1437b02b7aa1133fddeadc257fa260c67849f9d7cb135e6513 |
| ISICitedReferencesCount | 26 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000878605100002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0005-1098 |
| IngestDate | Sat Nov 29 07:32:04 EST 2025 Tue Nov 18 22:39:59 EST 2025 Fri Feb 23 02:39:39 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Model predictive control Parallel computation Deep neural networks Stochastic optimization Policy learning Nonlinear systems |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c318t-202cd355202f82f1437b02b7aa1133fddeadc257fa260c67849f9d7cb135e6513 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_automatica_2022_110665 crossref_primary_10_1016_j_automatica_2022_110665 elsevier_sciencedirect_doi_10_1016_j_automatica_2022_110665 |
| PublicationCentury | 2000 |
| PublicationDate | December 2022 2022-12-00 |
| PublicationDateYYYYMMDD | 2022-12-01 |
| PublicationDate_xml | – month: 12 year: 2022 text: December 2022 |
| PublicationDecade | 2020 |
| PublicationTitle | Automatica (Oxford) |
| PublicationYear | 2022 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Parisini, Zoppoli (b26) 1995; 31 Patrinos, Bemporad (b27) 2013; 59 Vaupel, Hamacher, Caspari, Mhamdi, Kevrekidis, Mitsos (b34) 2020; 92 Cao, Gopaluni (b11) 2020; 53 Maddalena, Moraes, Waltrich, Jones (b25) 2020; 53 Jerez, Goulart, Richter, Constantinides, Kerrigan, Morari (b19) 2014; 59 Zhang, Bujarbaruah, Borrelli (b39) 2020; 29 Stathopoulos, Shukla, Szuecs, Pu, Jones (b32) 2016; 3 Karg, Alamo, Lucia (b21) 2021; 31 Kang, Cao, Word, Laird (b20) 2014; 71 Bonzanini, Paulson, Makrygiorgos, Mesbah (b7) 2021; 145 Cao, Fuentes-Cortes, Chen, Zavala (b10) 2017; 99 Calafiore, Dabbene, Tempo (b9) 2011; 47 Domahidi, Zeilinger, Morari, Jones (b15) 2011 Karg, Lucia (b22) 2020; 50 Hertneck, Köhler, Trimpe, Allgöwer (b16) 2018; 2 Wächter, Biegler (b36) 2006; 106 Bemporad, Borrelli, Morari (b3) 2002; 47 Hornik, Stinchcombe, White (b17) 1990; 3 Bemporad, Oliveri, Poggi, Storace (b5) 2011; 56 Zavala, Laird, Biegler (b38) 2008; 63 Jalving, Cao, Zavala (b18) 2019; 125 Chan, Paulson, Mesbah (b13) 2021 Bemporad, Morari, Dua, Pistikopoulos (b4) 2002; 38 Birge, Louveaux (b6) 2011 Rodriguez, Nicholson, Laird, Zavala (b30) 2018; 119 Boyd, Parikh, Chu (b8) 2011 Yoo, Kim, Kim, Lee (b37) 2021; 144 Alamo, Tempo, Luque, Ramirez (b2) 2015; 52 Tempo, Bai, Dabbene (b33) 1996 Cao, Laird, Zavala (b12) 2016; 64 Karg, Lucia (b23) 2021 Paulson, Mesbah (b28) 2018; 51 Safran, Shamir (b31) 2017 Von Luxburg, Schölkopf (b35) 2011 Alamo, Tempo, Camacho (b1) 2009; 54 Kumar, Tulsyan, Gopaluni, Loewen (b24) 2018; 51 Chiang, Petra, Zavala (b14) 2014 Raff, Huber, Nagy, Allgower (b29) 2006 Alamo (10.1016/j.automatica.2022.110665_b2) 2015; 52 Karg (10.1016/j.automatica.2022.110665_b23) 2021 Wächter (10.1016/j.automatica.2022.110665_b36) 2006; 106 Patrinos (10.1016/j.automatica.2022.110665_b27) 2013; 59 Maddalena (10.1016/j.automatica.2022.110665_b25) 2020; 53 Paulson (10.1016/j.automatica.2022.110665_b28) 2018; 51 Bemporad (10.1016/j.automatica.2022.110665_b5) 2011; 56 Chiang (10.1016/j.automatica.2022.110665_b14) 2014 Vaupel (10.1016/j.automatica.2022.110665_b34) 2020; 92 Hertneck (10.1016/j.automatica.2022.110665_b16) 2018; 2 Raff (10.1016/j.automatica.2022.110665_b29) 2006 Cao (10.1016/j.automatica.2022.110665_b12) 2016; 64 Tempo (10.1016/j.automatica.2022.110665_b33) 1996 Domahidi (10.1016/j.automatica.2022.110665_b15) 2011 Bemporad (10.1016/j.automatica.2022.110665_b4) 2002; 38 Karg (10.1016/j.automatica.2022.110665_b22) 2020; 50 Von Luxburg (10.1016/j.automatica.2022.110665_b35) 2011 Bonzanini (10.1016/j.automatica.2022.110665_b7) 2021; 145 Yoo (10.1016/j.automatica.2022.110665_b37) 2021; 144 Cao (10.1016/j.automatica.2022.110665_b11) 2020; 53 Birge (10.1016/j.automatica.2022.110665_b6) 2011 Cao (10.1016/j.automatica.2022.110665_b10) 2017; 99 Alamo (10.1016/j.automatica.2022.110665_b1) 2009; 54 Zavala (10.1016/j.automatica.2022.110665_b38) 2008; 63 Stathopoulos (10.1016/j.automatica.2022.110665_b32) 2016; 3 Parisini (10.1016/j.automatica.2022.110665_b26) 1995; 31 Kumar (10.1016/j.automatica.2022.110665_b24) 2018; 51 Chan (10.1016/j.automatica.2022.110665_b13) 2021 Jalving (10.1016/j.automatica.2022.110665_b18) 2019; 125 Calafiore (10.1016/j.automatica.2022.110665_b9) 2011; 47 Kang (10.1016/j.automatica.2022.110665_b20) 2014; 71 Boyd (10.1016/j.automatica.2022.110665_b8) 2011 Bemporad (10.1016/j.automatica.2022.110665_b3) 2002; 47 Jerez (10.1016/j.automatica.2022.110665_b19) 2014; 59 Hornik (10.1016/j.automatica.2022.110665_b17) 1990; 3 Rodriguez (10.1016/j.automatica.2022.110665_b30) 2018; 119 Zhang (10.1016/j.automatica.2022.110665_b39) 2020; 29 Safran (10.1016/j.automatica.2022.110665_b31) 2017 Karg (10.1016/j.automatica.2022.110665_b21) 2021; 31 |
| References_xml | – start-page: 651 year: 2011 end-page: 706 ident: b35 article-title: Statistical learning theory: Models, concepts, and results publication-title: Handbook of the history of logic, Vol. 10 – year: 2011 ident: b8 article-title: Distributed optimization and statistical learning via the alternating direction method of multipliers – volume: 53 start-page: 11362 year: 2020 end-page: 11367 ident: b25 article-title: A neural network architecture to learn explicit MPC controllers from data publication-title: IFAC-PapersOnLine – volume: 47 start-page: 1974 year: 2002 end-page: 1985 ident: b3 article-title: Model predictive control based on linear programming — the explicit solution publication-title: IEEE Transactions on Automatic Control – volume: 47 start-page: 1279 year: 2011 end-page: 1293 ident: b9 article-title: Research on probabilistic methods for control system design publication-title: Automatica – volume: 54 start-page: 2545 year: 2009 end-page: 2559 ident: b1 article-title: Randomized strategies for probabilistic solutions of uncertain feasibility and optimization problems publication-title: IEEE Transactions on Automatic Control – volume: 64 start-page: 379 year: 2016 end-page: 406 ident: b12 article-title: Clustering-based preconditioning for stochastic programs publication-title: Computational Optimization and Applications – volume: 145 year: 2021 ident: b7 article-title: Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks publication-title: Computers & Chemical Engineering – start-page: 3475 year: 2021 end-page: 3481 ident: b13 article-title: Deep learning-based approximate nonlinear model predictive control with offset-free tracking for embedded applications publication-title: 2021 American control conference (ACC) – volume: 59 start-page: 3238 year: 2014 end-page: 3251 ident: b19 article-title: Embedded online optimization for model predictive control at megahertz rates publication-title: IEEE Transactions on Automatic Control – start-page: 149 year: 2021 end-page: 156 ident: b23 article-title: Reinforced approximate robust nonlinear model predictive control publication-title: 2021 23rd international conference on process control (PC) – volume: 59 start-page: 18 year: 2013 end-page: 33 ident: b27 article-title: An accelerated dual gradient-projection algorithm for embedded linear model predictive control publication-title: IEEE Transactions on Automatic Control – volume: 63 start-page: 4834 year: 2008 end-page: 4845 ident: b38 article-title: Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems publication-title: Chemical Engineering Science – volume: 125 start-page: 134 year: 2019 end-page: 154 ident: b18 article-title: Graph-based modeling and simulation of complex systems publication-title: Computers & Chemical Engineering – volume: 2 start-page: 543 year: 2018 end-page: 548 ident: b16 article-title: Learning an approximate model predictive controller with guarantees publication-title: IEEE Control Systems Letters – volume: 99 start-page: 185 year: 2017 end-page: 197 ident: b10 article-title: Scalable modeling and solution of stochastic multiobjective optimization problems publication-title: Computers & Chemical Engineering – volume: 31 start-page: 8855 year: 2021 end-page: 8876 ident: b21 article-title: Probabilistic performance validation of deep learning-based robust NMPC controllers publication-title: International Journal of Robust and Nonlinear Control – start-page: 3424 year: 1996 end-page: 3428 ident: b33 article-title: Probabilistic robustness analysis: Explicit bounds for the minimum number of samples publication-title: Proceedings of 35th IEEE conference on decision and control, Vol. 3 – start-page: 2979 year: 2017 end-page: 2987 ident: b31 article-title: Depth-width tradeoffs in approximating natural functions with neural networks publication-title: International conference on machine learning – volume: 29 start-page: 2102 year: 2020 end-page: 2114 ident: b39 article-title: Near-optimal rapid MPC using neural networks: A primal-dual policy learning framework publication-title: IEEE Transactions on Control Systems Technology – start-page: 513 year: 2011 end-page: 519 ident: b15 article-title: Learning a feasible and stabilizing explicit model predictive control law by robust optimization publication-title: 2011 50th IEEE conference on decision and control and European control conference – volume: 51 start-page: 523 year: 2018 end-page: 534 ident: b28 article-title: Nonlinear model predictive control with explicit backoffs for stochastic systems under arbitrary uncertainty publication-title: IFAC-PapersOnLine – volume: 144 start-page: 107133 year: 2021 ident: b37 article-title: Reinforcement learning based optimal control of batch processes using Monte-Carlo deep deterministic policy gradient with phase segmentation publication-title: Computers & Chemical Engineering – volume: 51 start-page: 512 year: 2018 end-page: 517 ident: b24 article-title: A deep learning architecture for predictive control publication-title: IFAC-PapersOnLine – volume: 119 start-page: 315 year: 2018 end-page: 325 ident: b30 article-title: Benchmarking ADMM in nonconvex NLPs publication-title: Computers & Chemical Engineering – year: 2011 ident: b6 article-title: Introduction to stochastic programming – volume: 106 start-page: 25 year: 2006 end-page: 57 ident: b36 article-title: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming publication-title: Mathematical Programming – volume: 92 start-page: 261 year: 2020 end-page: 270 ident: b34 article-title: Accelerating nonlinear model predictive control through machine learning publication-title: Journal of Process Control – volume: 52 start-page: 160 year: 2015 end-page: 172 ident: b2 article-title: Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms publication-title: Automatica – volume: 56 start-page: 2883 year: 2011 end-page: 2897 ident: b5 article-title: Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations publication-title: IEEE Transactions on Automatic Control – volume: 3 start-page: 551 year: 1990 end-page: 560 ident: b17 article-title: Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks publication-title: Neural Networks – volume: 71 start-page: 563 year: 2014 end-page: 573 ident: b20 article-title: An interior-point method for efficient solution of block-structured NLP problems using an implicit Schur-complement decomposition publication-title: Computers & Chemical Engineering – volume: 31 start-page: 1443 year: 1995 end-page: 1451 ident: b26 article-title: A receding-horizon regulator for nonlinear systems and a neural approximation publication-title: Automatica – volume: 53 start-page: 11319 year: 2020 end-page: 11324 ident: b11 article-title: Deep neural network approximation of nonlinear model predictive control publication-title: IFAC-PapersOnLine – start-page: 1 year: 2014 end-page: 7 ident: b14 article-title: Structured nonconvex optimization of large-scale energy systems using PIPS-NLP publication-title: Power systems computation conference (PSCC) – volume: 3 start-page: 249 year: 2016 end-page: 362 ident: b32 article-title: Operator splitting methods in control publication-title: Foundations and Trends in Systems and Control – volume: 38 start-page: 3 year: 2002 end-page: 20 ident: b4 article-title: The explicit linear quadratic regulator for constrained systems publication-title: Automatica – volume: 50 start-page: 3866 year: 2020 end-page: 3878 ident: b22 article-title: Efficient representation and approximation of model predictive control laws via deep learning publication-title: IEEE Transactions on Cybernetics – start-page: 237 year: 2006 end-page: 242 ident: b29 article-title: Nonlinear model predictive control of a four tank system: An experimental stability study publication-title: 2006 IEEE conference on computer aided control system design, 2006 IEEE international conference on control applications, 2006 IEEE international symposium on intelligent control – volume: 51 start-page: 512 issue: 18 year: 2018 ident: 10.1016/j.automatica.2022.110665_b24 article-title: A deep learning architecture for predictive control publication-title: IFAC-PapersOnLine doi: 10.1016/j.ifacol.2018.09.373 – start-page: 3424 year: 1996 ident: 10.1016/j.automatica.2022.110665_b33 article-title: Probabilistic robustness analysis: Explicit bounds for the minimum number of samples – year: 2011 ident: 10.1016/j.automatica.2022.110665_b8 – start-page: 3475 year: 2021 ident: 10.1016/j.automatica.2022.110665_b13 article-title: Deep learning-based approximate nonlinear model predictive control with offset-free tracking for embedded applications – volume: 31 start-page: 8855 issue: 18 year: 2021 ident: 10.1016/j.automatica.2022.110665_b21 article-title: Probabilistic performance validation of deep learning-based robust NMPC controllers publication-title: International Journal of Robust and Nonlinear Control doi: 10.1002/rnc.5696 – start-page: 149 year: 2021 ident: 10.1016/j.automatica.2022.110665_b23 article-title: Reinforced approximate robust nonlinear model predictive control – volume: 99 start-page: 185 year: 2017 ident: 10.1016/j.automatica.2022.110665_b10 article-title: Scalable modeling and solution of stochastic multiobjective optimization problems publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2017.01.021 – start-page: 513 year: 2011 ident: 10.1016/j.automatica.2022.110665_b15 article-title: Learning a feasible and stabilizing explicit model predictive control law by robust optimization – volume: 38 start-page: 3 issue: 1 year: 2002 ident: 10.1016/j.automatica.2022.110665_b4 article-title: The explicit linear quadratic regulator for constrained systems publication-title: Automatica doi: 10.1016/S0005-1098(01)00174-1 – volume: 3 start-page: 551 issue: 5 year: 1990 ident: 10.1016/j.automatica.2022.110665_b17 article-title: Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks publication-title: Neural Networks doi: 10.1016/0893-6080(90)90005-6 – volume: 59 start-page: 3238 issue: 12 year: 2014 ident: 10.1016/j.automatica.2022.110665_b19 article-title: Embedded online optimization for model predictive control at megahertz rates publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2014.2351991 – volume: 71 start-page: 563 year: 2014 ident: 10.1016/j.automatica.2022.110665_b20 article-title: An interior-point method for efficient solution of block-structured NLP problems using an implicit Schur-complement decomposition publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2014.09.013 – volume: 51 start-page: 523 issue: 20 year: 2018 ident: 10.1016/j.automatica.2022.110665_b28 article-title: Nonlinear model predictive control with explicit backoffs for stochastic systems under arbitrary uncertainty publication-title: IFAC-PapersOnLine doi: 10.1016/j.ifacol.2018.11.036 – volume: 50 start-page: 3866 issue: 9 year: 2020 ident: 10.1016/j.automatica.2022.110665_b22 article-title: Efficient representation and approximation of model predictive control laws via deep learning publication-title: IEEE Transactions on Cybernetics doi: 10.1109/TCYB.2020.2999556 – volume: 53 start-page: 11362 issue: 2 year: 2020 ident: 10.1016/j.automatica.2022.110665_b25 article-title: A neural network architecture to learn explicit MPC controllers from data publication-title: IFAC-PapersOnLine doi: 10.1016/j.ifacol.2020.12.546 – volume: 119 start-page: 315 year: 2018 ident: 10.1016/j.automatica.2022.110665_b30 article-title: Benchmarking ADMM in nonconvex NLPs publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2018.08.036 – start-page: 2979 year: 2017 ident: 10.1016/j.automatica.2022.110665_b31 article-title: Depth-width tradeoffs in approximating natural functions with neural networks – volume: 52 start-page: 160 year: 2015 ident: 10.1016/j.automatica.2022.110665_b2 article-title: Randomized methods for design of uncertain systems: Sample complexity and sequential algorithms publication-title: Automatica doi: 10.1016/j.automatica.2014.11.004 – volume: 2 start-page: 543 issue: 3 year: 2018 ident: 10.1016/j.automatica.2022.110665_b16 article-title: Learning an approximate model predictive controller with guarantees publication-title: IEEE Control Systems Letters doi: 10.1109/LCSYS.2018.2843682 – volume: 47 start-page: 1974 issue: 12 year: 2002 ident: 10.1016/j.automatica.2022.110665_b3 article-title: Model predictive control based on linear programming — the explicit solution publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2002.805688 – volume: 59 start-page: 18 issue: 1 year: 2013 ident: 10.1016/j.automatica.2022.110665_b27 article-title: An accelerated dual gradient-projection algorithm for embedded linear model predictive control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2013.2275667 – volume: 3 start-page: 249 issue: 3 year: 2016 ident: 10.1016/j.automatica.2022.110665_b32 article-title: Operator splitting methods in control publication-title: Foundations and Trends in Systems and Control doi: 10.1561/2600000008 – start-page: 1 year: 2014 ident: 10.1016/j.automatica.2022.110665_b14 article-title: Structured nonconvex optimization of large-scale energy systems using PIPS-NLP – volume: 29 start-page: 2102 issue: 5 year: 2020 ident: 10.1016/j.automatica.2022.110665_b39 article-title: Near-optimal rapid MPC using neural networks: A primal-dual policy learning framework publication-title: IEEE Transactions on Control Systems Technology doi: 10.1109/TCST.2020.3024571 – volume: 125 start-page: 134 year: 2019 ident: 10.1016/j.automatica.2022.110665_b18 article-title: Graph-based modeling and simulation of complex systems publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2019.03.009 – volume: 31 start-page: 1443 issue: 10 year: 1995 ident: 10.1016/j.automatica.2022.110665_b26 article-title: A receding-horizon regulator for nonlinear systems and a neural approximation publication-title: Automatica doi: 10.1016/0005-1098(95)00044-W – volume: 53 start-page: 11319 issue: 2 year: 2020 ident: 10.1016/j.automatica.2022.110665_b11 article-title: Deep neural network approximation of nonlinear model predictive control publication-title: IFAC-PapersOnLine doi: 10.1016/j.ifacol.2020.12.538 – year: 2011 ident: 10.1016/j.automatica.2022.110665_b6 – volume: 145 year: 2021 ident: 10.1016/j.automatica.2022.110665_b7 article-title: Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2020.107174 – start-page: 651 year: 2011 ident: 10.1016/j.automatica.2022.110665_b35 article-title: Statistical learning theory: Models, concepts, and results – volume: 54 start-page: 2545 issue: 11 year: 2009 ident: 10.1016/j.automatica.2022.110665_b1 article-title: Randomized strategies for probabilistic solutions of uncertain feasibility and optimization problems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2009.2031207 – start-page: 237 year: 2006 ident: 10.1016/j.automatica.2022.110665_b29 article-title: Nonlinear model predictive control of a four tank system: An experimental stability study – volume: 92 start-page: 261 year: 2020 ident: 10.1016/j.automatica.2022.110665_b34 article-title: Accelerating nonlinear model predictive control through machine learning publication-title: Journal of Process Control doi: 10.1016/j.jprocont.2020.06.012 – volume: 64 start-page: 379 year: 2016 ident: 10.1016/j.automatica.2022.110665_b12 article-title: Clustering-based preconditioning for stochastic programs publication-title: Computational Optimization and Applications doi: 10.1007/s10589-015-9813-x – volume: 106 start-page: 25 issue: 1 year: 2006 ident: 10.1016/j.automatica.2022.110665_b36 article-title: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming publication-title: Mathematical Programming doi: 10.1007/s10107-004-0559-y – volume: 144 start-page: 107133 year: 2021 ident: 10.1016/j.automatica.2022.110665_b37 article-title: Reinforcement learning based optimal control of batch processes using Monte-Carlo deep deterministic policy gradient with phase segmentation publication-title: Computers & Chemical Engineering doi: 10.1016/j.compchemeng.2020.107133 – volume: 56 start-page: 2883 issue: 12 year: 2011 ident: 10.1016/j.automatica.2022.110665_b5 article-title: Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.2011.2141410 – volume: 47 start-page: 1279 issue: 7 year: 2011 ident: 10.1016/j.automatica.2022.110665_b9 article-title: Research on probabilistic methods for control system design publication-title: Automatica doi: 10.1016/j.automatica.2011.02.029 – volume: 63 start-page: 4834 issue: 19 year: 2008 ident: 10.1016/j.automatica.2022.110665_b38 article-title: Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems publication-title: Chemical Engineering Science doi: 10.1016/j.ces.2007.05.022 |
| SSID | ssj0004182 |
| Score | 2.539714 |
| Snippet | To facilitate the real-time implementation of nonlinear model predictive control (NMPC), this paper proposes a deep learning-based NMPC scheme, in which the... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 110665 |
| SubjectTerms | Deep neural networks Model predictive control Nonlinear systems Parallel computation Policy learning Stochastic optimization |
| Title | Using stochastic programming to train neural network approximation of nonlinear MPC laws |
| URI | https://dx.doi.org/10.1016/j.automatica.2022.110665 |
| Volume | 146 |
| WOSCitedRecordID | wos000878605100002&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-2836 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004182 issn: 0005-1098 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bS8MwFA66-aAP4hXnjTz4Nio23ZoWn8ZQVEQEJ8ynkqUNbmonrpP-fE9y0nZeQEWE0pZAljXn6-nX9JzvEHLgAklmqsUc4Lax09JnQdz2HAXPHqY_NHEpTbEJfnUV9Pvhta3ZOjHlBHiaBnkePv-rqaENjK1TZ39h7vJHoQHOweiwB7PD_keGxyAA4HTyXmgR5iIE68kkRo2xKERT61iCdVKMAkdp8Xz4VBLIFCU0tMrPdbf5KCz3LvRqp9nYaL0KI1eaY4R8uaZwaUIE7qZpBRqbeTbMq8auMMu0dyJ9EMPZ1QfGPkRylGkxVQwSulktb4rlpQ8T9KwB9xzgMv4714vLj5_cOK4ojHQQj72aQz24zlnwsbTEB5HsG8NFj7QYIX67nCd1xtsh-Ll65_ykf1HlyroBKsjbv2ijuzDm7-vxvqYsMzSkt0KW7fsD7aDdV8lckq6RpRlVyXXSNwigFQLoDAJoNqYGARQRQC0C6DsE0LGiJQIoIIBqBGyQ29OTXvfMsQU0HAmuOoPbgskYCCUcVcAUUGM-OGIDLoTrep6CJ5uIJfhsJeCtVgJtaYUqjLkcuF478duut0lqMFiyRaiuH8Jizw9icOCCJcKTXPqKJ4KHsLUahBdzFEmrLq-v5jEqwghHUTW7kZ7dCGe3Qdyy5zMqrPygz3FhhsgyRWSAESDo297bf-q9QxarG2GX1LKXabJHFuRrNpy87Fu4vQHcqZMA |
| linkProvider | Elsevier |
| 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=Using+stochastic+programming+to+train+neural+network+approximation+of+nonlinear+MPC+laws&rft.jtitle=Automatica+%28Oxford%29&rft.au=Li%2C+Yun&rft.au=Hua%2C+Kaixun&rft.au=Cao%2C+Yankai&rft.date=2022-12-01&rft.pub=Elsevier+Ltd&rft.issn=0005-1098&rft.eissn=1873-2836&rft.volume=146&rft_id=info:doi/10.1016%2Fj.automatica.2022.110665&rft.externalDocID=S0005109822005295 |
| 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 |