{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T03:48:26Z","timestamp":1772941706609,"version":"3.50.1"},"reference-count":46,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Control"],"published-print":{"date-parts":[[2010,1]]},"DOI":"10.3166\/ejc.16.609-623","type":"journal-article","created":{"date-parts":[[2011,2,8]],"date-time":"2011-02-08T16:16:50Z","timestamp":1297181810000},"page":"609-623","source":"Crossref","is-referenced-by-count":4,"title":["Reachability Analysis of Stochastic Hybrid Systems: A Biodiesel Production System"],"prefix":"10.1016","volume":"16","author":[{"given":"Derek","family":"Riley","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kasandra","family":"Riley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xenofon","family":"Koutsoukos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.3166\/ejc.16.609-623_bib0005","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/978-3-540-71493-4_4","article-title":"Computational approaches to reachability analysis of stochastic hybrid systems","volume":"4416","author":"Abate","year":"2007","journal-title":"Hybrid Syst Comput Control, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0010","first-page":"4018","article-title":"An approximate dynamic programming approach to probabilistic reachability for stochastic hybrid systems","author":"Abate","year":"2008","journal-title":"In IEEE Conf Dec Control"},{"issue":"11","key":"10.3166\/ejc.16.609-623_bib0015","doi-asserted-by":"crossref","first-page":"2724","DOI":"10.1016\/j.automatica.2008.03.027","article-title":"Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems","volume":"44","author":"Abate","year":"2008","journal-title":"Automatica"},{"key":"10.3166\/ejc.16.609-623_bib0020","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1002\/jctb.1392","article-title":"The effect of substrate concentrations on the production of biodiesel by lipase-catalysed transesterification of vegetable oils","volume":"81","author":"Al-Zuhair","year":"2006","journal-title":"J Chem Tech Biotech"},{"key":"10.3166\/ejc.16.609-623_bib0025","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/3-540-45351-2_6","article-title":"Hybrid modeling and simulation of biomolecular networks","volume":"2034","author":"Alur","year":"2001","journal-title":"Hybrid Syst Comput Control, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0030","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/11730637_7","article-title":"Reachability analysis for controlled discrete time stochastic hybrid systems","volume":"3927","author":"Amin","year":"2006","journal-title":"Hybrid Syst Comput Control, LNCS"},{"issue":"3\u20134","key":"10.3166\/ejc.16.609-623_bib0035","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1089\/10665270360688011","article-title":"Stochastic roadmap simulation: An efficient representation and algorithm for analyzing molecular motion","volume":"10","author":"Apaydin","year":"2003","journal-title":"J Comp Biol"},{"key":"10.3166\/ejc.16.609-623_bib0040","article-title":"An alternative to Gillespie's algorithm for simulating chemical reactions","author":"Barbuti","year":"2005","journal-title":"Comp Meth Sys Biol"},{"key":"10.3166\/ejc.16.609-623_bib0045","first-page":"309","article-title":"Structured modeling of concurrent stochastic hybrid systems","volume":"3253","author":"Bernadskiy","year":"2004","journal-title":"FORMATS, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0050","article-title":"Parallel and Distributed Computation: Numerical Methods","author":"Bertsekas","year":"1989","journal-title":"Prentice-Hall"},{"key":"10.3166\/ejc.16.609-623_bib0055","first-page":"3182","article-title":"Probabilistic reachability analysis for large scale stochastic hybrid systems","author":"Blom","year":"2007","journal-title":"IEEE Conf Decision Control"},{"key":"10.3166\/ejc.16.609-623_bib0060","unstructured":"Blom H, Lygeros J, Everdij M, Loizou S, Kyriakopoulos K. Stochastic Hybrid Systems: Theory and Safety Critical Applications. Lecture Notes in Control and Informations Sciences."},{"key":"10.3166\/ejc.16.609-623_bib0065","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1007\/978-3-540-24743-2_16","article-title":"Extended stochastic hybrid systems and their reachability problem","volume":"2993","author":"Bujorianu","year":"2004","journal-title":"Hybrid Syst Comput Control, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0070","first-page":"1872","article-title":"General stochastic hybrid systems: Modeling and optimal control","author":"Bujorianu","year":"2004","journal-title":"In 43rd IEEE Conf Dec Control"},{"key":"10.3166\/ejc.16.609-623_bib0075","first-page":"5180","article-title":"Parameter identification for stochastic hybrid models of biological interaction networks","author":"Cinquemani","year":"2007","journal-title":"In Proc IEEE Conf Dec Control"},{"issue":"12","key":"10.3166\/ejc.16.609-623_bib0080","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1007\/s11746-000-0198-y","article-title":"Kinetics of palm oil transesterification in a batch reactor","volume":"77","author":"Darnoko","year":"2000","journal-title":"J AmOil Chemists\u2019 Soc"},{"issue":"1","key":"10.3166\/ejc.16.609-623_bib0085","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1089\/10665270252833208","article-title":"Modeling and simulation of genetic regulatory systems: a literature review","volume":"9","author":"de Jong","year":"2002","journal-title":"J Comp Biol"},{"key":"10.3166\/ejc.16.609-623_bib0090","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1016\/j.energy.2006.06.019","article-title":"Effect of incompletely converted soybean oil on biodiesel quality","volume":"32","author":"Fernando","year":"2007","journal-title":"Energy"},{"key":"10.3166\/ejc.16.609-623_bib0095","article-title":"Controlled Markov Processes and Viscosity Solutions","author":"Fleming","year":"1993"},{"key":"10.3166\/ejc.16.609-623_bib0100","unstructured":"Garvels M. The splitting method in rare event simulation. PhD thesis, University of Twente, the Netherlands, 1997."},{"key":"10.3166\/ejc.16.609-623_bib0105","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1049\/sb:20045019","article-title":"Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-notch protein signalling","volume":"1","author":"Ghosh","year":"2004","journal-title":"Sys Biol"},{"key":"10.3166\/ejc.16.609-623_bib0110","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"Gillespie","year":"1976","journal-title":"J Comp Phys"},{"issue":"4","key":"10.3166\/ejc.16.609-623_bib0115","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1287\/opre.47.4.585","article-title":"Multilevel splitting for estimating rare event probabilities","volume":"47","author":"Glasserman","year":"1999","journal-title":"Oper Res"},{"key":"10.3166\/ejc.16.609-623_bib0120","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/978-3-540-71493-4_21","article-title":"Learning cycle-linear hybrid automata for excitable cells","volume":"4416","author":"Grosu","year":"2007","journal-title":"Hybrid Syst Comput Control, LNCS"},{"issue":"2","key":"10.3166\/ejc.16.609-623_bib0125","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1049\/iet-syb:20060035","article-title":"Analysis of lactose metabolism in E. coli using reachability analysis of hybrid systems","volume":"1","author":"Halasz","year":"2007","journal-title":"IET Syst Biol"},{"key":"10.3166\/ejc.16.609-623_bib0130","doi-asserted-by":"crossref","first-page":"6959","DOI":"10.1063\/1.1505860","article-title":"Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics","volume":"117","author":"Haseltine","year":"2002","journal-title":"J Chem Phys"},{"key":"10.3166\/ejc.16.609-623_bib0135","first-page":"669","article-title":"Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems","volume":"15","author":"Hespanha","year":"2005","journal-title":"Int J Robust Cont, Special Issue on Control at Small Scales"},{"key":"10.3166\/ejc.16.609-623_bib0140","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/978-3-540-24743-2_28","article-title":"Modeling subtilin production in Bacillus subtilis using stochastic hybrid systems","volume":"2993","author":"Hu","year":"2004","journal-title":"Hybrid Syst Comput Control, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0145","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/11730637_29","article-title":"Computational methods for reachability analysis of stochastic hybrid systems","volume":"3927","author":"Koutsoukos","year":"2006","journal-title":"Hybrid Syst Comput Control, LNCS"},{"issue":"2","key":"10.3166\/ejc.16.609-623_bib0150","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1109\/TSMCA.2007.914777","article-title":"Computational methods for verification of stochastic hybrid systems","volume":"38","author":"Koutsoukos","year":"2008","journal-title":"IEEE Trans Syst, Man Cybern, Part A"},{"key":"10.3166\/ejc.16.609-623_bib0155","article-title":"Sequential Monte Carlo simulation of rare event probability in stochastic hybrid systems","author":"Krystul","year":"2005","journal-title":"16th IFAC World congress"},{"key":"10.3166\/ejc.16.609-623_bib0160","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0007-6","article-title":"Numerical Methods for Stochastic Control Problems in Continuous Time","author":"Kushner","year":"2001"},{"key":"10.3166\/ejc.16.609-623_bib0165","first-page":"1666","article-title":"Simulation and verification for computational modeling of signaling pathways","author":"Kwiatkowska","year":"2006","journal-title":"In Proc Winter Simulation Conf"},{"key":"10.3166\/ejc.16.609-623_bib0170","first-page":"137","article-title":"Splitting for rare-event simulation","author":"L\u2019Ecuyer","year":"2006","journal-title":"Winter Simulation Conf"},{"issue":"6","key":"10.3166\/ejc.16.609-623_bib0175","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.automatica.2004.01.012","article-title":"On reachability and minimum cost optimal control","volume":"40","author":"Lygeros","year":"2004","journal-title":"Automatica"},{"issue":"7","key":"10.3166\/ejc.16.609-623_bib0180","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1109\/TAC.2005.851439","article-title":"A time-dependent Hamilton- Jacobi formulation of reachable sets for continuous dynamic games","volume":"50","author":"Mitchell","year":"2005","journal-title":"IEEE Trans Autom Control"},{"key":"10.3166\/ejc.16.609-623_bib0185","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1007\/978-3-540-31954-2_31","article-title":"A toolbox of Hamilton-Jacobi solvers for analysis of nondeterministic continuous and hybrid systems","volume":"3414","author":"Mitchell","year":"2005","journal-title":"Hybrid Syst Comput Control, LNCS"},{"issue":"11","key":"10.3166\/ejc.16.609-623_bib0190","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1007\/s11746-997-0254-2","article-title":"Kinetics of transesterification of soybean oil","volume":"74","author":"Noureddini","year":"1997","journal-title":"J Am Oil Chemists\u2019 Soc"},{"key":"10.3166\/ejc.16.609-623_bib0195","article-title":"Probabilistic aircraft conflict detection","author":"Prandini","year":"2005","journal-title":"In HYBRIDGE"},{"key":"10.3166\/ejc.16.609-623_bib0200","series-title":"Winter Simulation Conf","article-title":"Simulation of stochastic hybrid systems with switching and reflecting boundaries","author":"Riley","year":"2008"},{"issue":"3","key":"10.3166\/ejc.16.609-623_bib0205","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1049\/iet-syb.2008.0101","article-title":"Modeling and analysis of the sugar cataract development process using stochastic hybrid systems","volume":"3","author":"Riley","year":"2009","journal-title":"IET: Syst Biol"},{"key":"10.3166\/ejc.16.609-623_bib0210","doi-asserted-by":"crossref","DOI":"10.1002\/9780470230381","article-title":"Simulation and the Monte Carlo Method","author":"Rubinstein","year":"2007"},{"key":"10.3166\/ejc.16.609-623_bib0215","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1063\/1.1835951","article-title":"Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions","volume":"122","author":"Salis","year":"2005","journal-title":"J Chem Phys"},{"key":"10.3166\/ejc.16.609-623_bib0220","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/3-540-49372-7_20","article-title":"Parallel object oriented Monte Carlo simulations","volume":"1505","author":"Troyer","year":"1998","journal-title":"Comput Object Oriented Parallel Environ, LNCS"},{"key":"10.3166\/ejc.16.609-623_bib0225","doi-asserted-by":"crossref","first-page":"4151","DOI":"10.1109\/IEMBS.2006.259294","article-title":"Hybrid automata as a unifying framework for modeling cardiac cells","author":"Ye","year":"2006","journal-title":"In Conf Proc IEEE Eng Med Biol Soc"},{"key":"10.3166\/ejc.16.609-623_bib0230","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0960-8524(03)00040-3","article-title":"Biodiesel production from waste cooking oil: 1 process design and technological assessment","volume":"89","author":"Zhang","year":"2003","journal-title":"Bioresource Technol"}],"container-title":["European Journal of Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358010706907?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0947358010706907?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T12:02:26Z","timestamp":1559995346000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0947358010706907"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":46,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["S0947358010706907"],"URL":"https:\/\/doi.org\/10.3166\/ejc.16.609-623","relation":{},"ISSN":["0947-3580"],"issn-type":[{"value":"0947-3580","type":"print"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}