{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:28:16Z","timestamp":1762522096081,"version":"3.41.0"},"reference-count":45,"publisher":"Association for Computing Machinery (ACM)","issue":"5s","license":[{"start":{"date-parts":[[2017,10,10]],"date-time":"2017-10-10T00:00:00Z","timestamp":1507593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100006602","name":"Air Force Research Laboratory","doi-asserted-by":"publisher","award":["FA8750-15-1-0105"],"award-info":[{"award-number":["FA8750-15-1-0105"]}],"id":[{"id":"10.13039\/100006602","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-15-1-0258"],"award-info":[{"award-number":["FA9550-15-1-0258"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Embed. Comput. Syst."],"published-print":{"date-parts":[[2017,10,31]]},"abstract":"<jats:p>In this article we study ways of constructing meaningful operational models of piecewise-smooth systems (PWS). The systems we consider are described by polynomial vector fields defined on non-overlapping semi-algebraic sets, which form a partition of the state space. Our approach is to give meaning to motion in systems of this type by automatically synthesizing operational models in the form of hybrid automata (HA). Despite appearances, it is in practice often difficult to arrive at satisfactory HA models of PWS. The different ways of building operational models that we explore in our approach can be thought of as defining different semantics for the underlying PWS. These differences have a number of interesting nuances related to phenomena such as chattering, non-determinism, so-called mythical modes and sliding behaviour.<\/jats:p>","DOI":"10.1145\/3126506","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T12:52:50Z","timestamp":1507812770000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Operational Models for Piecewise-Smooth Systems"],"prefix":"10.1145","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5849-7991","authenticated-orcid":false,"given":"Andrew","family":"Sogokon","sequence":"first","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4941-6632","authenticated-orcid":false,"given":"Khalil","family":"Ghorbal","sequence":"additional","affiliation":[{"name":"INRIA, Rennes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8021-9923","authenticated-orcid":false,"given":"Taylor T.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Vanderbilt University, Nashville, TN, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,10,10]]},"reference":[{"volume-title":"Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems. In Hybrid Systems (Lecture Notes in Computer Science), Robert L","year":"1992","author":"Alur Rajeev","key":"e_1_2_1_1_1"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2005.1582237"},{"volume-title":"Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics) (2 ed.)","author":"Basu Saugata","key":"e_1_2_1_3_1"},{"volume-title":"Johnson","year":"1998","author":"Caviness Bob F.","key":"e_1_2_1_4_1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39799-8_18"},{"volume-title":"Quantifier elimination for real closed fields by cylindrical algebraic decompostion","series-title":"Lecture Notes in Computer Science","author":"Collins George E.","key":"e_1_2_1_6_1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/038"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2008.919306"},{"volume-title":"An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"Cox David","key":"e_1_2_1_9_1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(88)80004-X"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/5.871305"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/646880.710464"},{"volume-title":"An Introduction to Hybrid Automata, Numerical Simulation and Reachability Analysis","author":"Frehse Goran","key":"e_1_2_1_13_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-658-09994-7_3"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/2032305.2032335"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21401-6_36"},{"volume-title":"TACAS 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5-13, 2014. Proceedings. 279--294","year":"2014","author":"Ghorbal Khalil","key":"e_1_2_1_16_1"},{"volume-title":"Systems 8 Structures 47","year":"2017","author":"Ghorbal Khalil","key":"e_1_2_1_17_1"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2008.931718"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(79)90056-1"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/1005068"},{"volume-title":"Ordinary Differential Equations","author":"Hartman Philip","key":"e_1_2_1_21_1","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719222"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.5555\/788018.788803"},{"volume-title":"On the regularization of Zeno hybrid automata. Systems 8 Control Letters 38, 3","year":"1999","author":"Johansson Karl H.","key":"e_1_2_1_23_1"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-46681-0_15"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2038642.2038659"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1999.831255"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.806650"},{"key":"e_1_2_1_28_1","doi-asserted-by":"crossref","unstructured":"Bhubaneswar Mishra. 1993. Algorithmic Algebra. Springer.   Bhubaneswar Mishra. 1993. Algorithmic Algebra. Springer.","DOI":"10.1007\/978-1-4612-4344-1"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.5555\/1030818.1030903"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0016-0032(96)00126-3"},{"volume-title":"Proceedings of the Fifteenth National Conference on Artificial Intelligence and Tenth Innovative Applications of Artificial Intelligence Conference, AAAI 98","year":"1998","author":"Mosterman Pieter J.","key":"e_1_2_1_31_1"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2010.495189"},{"volume-title":"Annales de l\u2019institut Fourier","author":"Novikov Dmitri","key":"e_1_2_1_33_1"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10817-008-9103-8"},{"volume-title":"Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics","author":"Platzer Andr\u00e9","key":"e_1_2_1_35_1"},{"volume-title":"Teel","year":"2008","author":"Sanfelice Ricardo G.","key":"e_1_2_1_36_1"},{"volume-title":"A new decision method for elementary algebra. Annals of Mathematics","year":"1954","author":"Seidenberg Abraham","key":"e_1_2_1_37_1"},{"volume-title":"A decision method for elementary algebra and geometry. Bull. Amer. Math. Soc. 59","year":"1951","author":"Tarski Alfred","key":"e_1_2_1_38_1"},{"key":"e_1_2_1_39_1","volume-title":"Graduate Studies in Mathematics","volume":"140","author":"Teschl Gerald","year":"2012"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10703-007-0044-3"},{"volume-title":"Sliding Modes in Control and Optimization","author":"Utkin Vadim I.","key":"e_1_2_1_41_1"},{"volume-title":"Van Der Schaft and Hans Schumacher","year":"2000","author":"Arjan","key":"e_1_2_1_42_1"},{"volume-title":"An Improved HHL Prover: An Interactive Theorem Prover for Hybrid Systems","author":"Wang Shuling","key":"e_1_2_1_43_1"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1966.1098336"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(96)00036-2"}],"container-title":["ACM Transactions on Embedded Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3126506","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3126506","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3126506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T19:05:01Z","timestamp":1750273501000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3126506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,10]]},"references-count":45,"journal-issue":{"issue":"5s","published-print":{"date-parts":[[2017,10,31]]}},"alternative-id":["10.1145\/3126506"],"URL":"https:\/\/doi.org\/10.1145\/3126506","relation":{},"ISSN":["1539-9087","1558-3465"],"issn-type":[{"type":"print","value":"1539-9087"},{"type":"electronic","value":"1558-3465"}],"subject":[],"published":{"date-parts":[[2017,10,10]]},"assertion":[{"value":"2017-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-10-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}