{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T22:57:34Z","timestamp":1781650654972,"version":"3.54.5"},"reference-count":35,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NCCR Automation","award":["51NF40_180545"],"award-info":[{"award-number":["51NF40_180545"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1109\/tac.2025.3545767","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:58:54Z","timestamp":1740491934000},"page":"5690-5704","source":"Crossref","is-referenced-by-count":4,"title":["BP-MPC: Optimizing the Closed-Loop Performance of MPC Using Backpropagation"],"prefix":"10.1109","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-2882-9128","authenticated-orcid":false,"given":"Riccardo","family":"Zuliani","sequence":"first","affiliation":[{"name":"Automatic Control Laboratory (IfA), ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8596-8739","authenticated-orcid":false,"given":"Efe C.","family":"Balta","sequence":"additional","affiliation":[{"name":"Inspire AG, Z&#x00FC;rich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6159-1962","authenticated-orcid":false,"given":"John","family":"Lygeros","sequence":"additional","affiliation":[{"name":"Automatic Control Laboratory (IfA), ETH Z&#x00FC;rich, Z&#x00FC;rich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(98)00073-9"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2033838"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/LCSYS.2020.2983384"},{"key":"ref4","first-page":"387","article-title":"Deterministic policy gradient algorithms","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Silver","year":"2014"},{"key":"ref5","first-page":"136","article-title":"OptNet: Differentiable optimization as a layer in neural networks","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Amos","year":"2017"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-87821-8"},{"key":"ref7","first-page":"8299","article-title":"Differentiable MPC for end-to-end planning and control","volume-title":"Proc. Annu. Conf. Neural Inf. Process. Syst.","author":"Amos","year":"2018"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.15607\/rss.2024.xx.003"},{"key":"ref9","article-title":"Robust differentiable predictive control with safety guarantees: A predictive safety filter approach","author":"Cortez","year":"2023"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2913768"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.3024161"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2020.12.1195"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-020-09706-y"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-020-01501-5"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-018-09409-5"},{"key":"ref16","first-page":"13537","article-title":"Nonsmooth implicit differentiation for machine-learning and optimization","volume-title":"Proc. Annu. Conf. Neural Inf. Process. Syst.","author":"Bolte","year":"2021"},{"key":"ref17","first-page":"361","article-title":"Learning convex optimization control policies","volume-title":"Proc. Learn. Dyn. Control","author":"Agrawal","year":"2020"},{"key":"ref18","first-page":"9562","article-title":"Differentiable convex optimization layers","volume-title":"Proc. Annu. Conf. Neural Inf. Process. Syst.","author":"Agrawal","year":"2019"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/22M1541630"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejcon.2025.101319"},{"key":"ref21","volume-title":"Introduction to O-Minimal Geometry","author":"Coste","year":"1999"},{"key":"ref22","article-title":"Nonsmooth implicit differentiation for machine learning and optimization","author":"Bolte","year":"2021"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2009.2017934"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974997"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5"},{"key":"ref26","volume-title":"An Introduction to Semialgebraic Geometry","author":"Coste","year":"2002"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2020.12.356"},{"key":"ref28","article-title":"Soft constraints and exact penalty functions in model predictive control","volume-title":"Proc. Control 2000 Conf.","author":"Kerrigan","year":"2000"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/0329054"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-018-0139-4"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2022.3176430"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2002.1025412"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2008.08.006"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-021-00208-8"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2012.11.009"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/9\/11143928\/10903987.pdf?arnumber=10903987","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T19:33:35Z","timestamp":1756755215000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10903987\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":35,"journal-issue":{"issue":"9"},"URL":"https:\/\/doi.org\/10.1109\/tac.2025.3545767","relation":{},"ISSN":["0018-9286","1558-2523","2334-3303"],"issn-type":[{"value":"0018-9286","type":"print"},{"value":"1558-2523","type":"electronic"},{"value":"2334-3303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}