{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:09:20Z","timestamp":1761487760029},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>This article describes an algorithm for detecting the occurrence of events, which signify discontinuities in the first derivative of the state variables, while simulating a set of nonsmooth differential equations. Such combined-discrete continuous systems arise in many contexts and are often referred to as hybrid systems, switched systems, or nonsmooth systems. In all cases, the state events are triggered at simulated times which generate states corresponding to the zeros of some algebraic \u201cevent\u201d function. It has been noted that all existing simulators are prone to failure when these events occur in the neighborhood of model singularities---regions of the state space where the right-hand side of the differential equation is undefined. Such model singularities are often the impetus for using nonsmooth models in the first place. This failure occurs because existing algorithms blindly attempt to interpolate across singular regions, checking for possible events after the fact. The event detection algorithm described here overcomes this limitation using an approach inspired by feedback control theory. A carefully constructed extrapolation polynomial is used to select the integration step size by checking for potential future events, avoiding the need to evaluate the differential equation in potentially singular regions. It is shown that this alternate approach gives added functionality with little impact on the simulation efficiency.<\/jats:p>","DOI":"10.1145\/1189756.1189757","type":"journal-article","created":{"date-parts":[[2007,1,16]],"date-time":"2007-01-16T19:38:29Z","timestamp":1168976309000},"page":"1","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":39,"title":["A state event detection algorithm for numerically simulating hybrid systems with model singularities"],"prefix":"10.1145","volume":"17","author":[{"given":"Joel M.","family":"Esposito","sequence":"first","affiliation":[{"name":"US Naval Academy, Annapolis, Maryland, MD"}]},{"given":"Vijay","family":"Kumar","sequence":"additional","affiliation":[{"name":"University of Pennsylvania, Philadelphia, Pennsylvania, PA"}]}],"member":"320","published-online":{"date-parts":[[2007,1]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Ascher U. and Petzold L. 1998. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics Philadelphia PA.   Ascher U. and Petzold L. 1998. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics Philadelphia PA.","DOI":"10.1137\/1.9781611971392"},{"key":"e_1_2_1_2_1","volume-title":"Eds. Lecture Notes in Computer Science","volume":"2034","author":"Bahl V.","unstructured":"Bahl , V. and Linninger , A . 2001. Modeling of continuous--discrete processes. In Hybrid Systems: Computation and Control, M. D. Benedetto and A. Sangiovanni-Vincentelli , Eds. Lecture Notes in Computer Science , vol. 2034 . Springer Verlag, New York, 387--402. Bahl, V. and Linninger, A. 2001. Modeling of continuous--discrete processes. In Hybrid Systems: Computation and Control, M. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. Lecture Notes in Computer Science, vol. 2034. Springer Verlag, New York, 387--402."},{"key":"e_1_2_1_3_1","unstructured":"Benan K. Campbell S. and Petzold L. 1989. Numerical Solutions of Initial Value Problems. North Holland London England.  Benan K. Campbell S. and Petzold L. 1989. Numerical Solutions of Initial Value Problems. North Holland London England."},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/0378-4754(78)90068-X","article-title":"Efficient integration over discontinuities in ordinary differential equation simulations","author":"Carver M.","year":"1978","unstructured":"Carver , M. 1978 . Efficient integration over discontinuities in ordinary differential equation simulations . Math. Comput. Simul. XX , 190 -- 196 . Carver, M. 1978. Efficient integration over discontinuities in ordinary differential equation simulations. Math. Comput. Simul. XX, 190--196.","journal-title":"Math. Comput. Simul."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1029174.1029177"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/198429.198437"},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the 9th IMACS Conference on Simulation of Systems. 79--87","author":"Hay J.","unstructured":"Hay , J. and Griffin , A . 1979. Simulation of discontinuous dynamical systems . In Proceedings of the 9th IMACS Conference on Simulation of Systems. 79--87 . Hay, J. and Griffin, A. 1979. Simulation of discontinuous dynamical systems. In Proceedings of the 9th IMACS Conference on Simulation of Systems. 79--87."},{"key":"e_1_2_1_11_1","volume-title":"Nonlinear Control Systems","author":"Isidori A.","unstructured":"Isidori , A. 1995. Nonlinear Control Systems . Springer-Verlog , London, England . Isidori, A. 1995. Nonlinear Control Systems. Springer-Verlog, London, England."},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0098-1354(84)90001-2","article-title":"A simulator for batch and semi-continuous processes","volume":"8","author":"Joglekar G.","year":"1984","unstructured":"Joglekar , G. and Reklaitis , G. 1984 . A simulator for batch and semi-continuous processes . Computers in Chemical Engineering 8 , 6, 315 -- 327 . Joglekar, G. and Reklaitis, G. 1984. A simulator for batch and semi-continuous processes. Computers in Chemical Engineering 8, 6, 315--327.","journal-title":"Computers in Chemical Engineering"},{"key":"e_1_2_1_13_1","unstructured":"Kelton W. Sadowski R. and Sturrock D. T. 2004. Simulation with Arena 3rd ed. McGraw Hill Boston MA.   Kelton W. Sadowski R. and Sturrock D. T. 2004. Simulation with Arena 3rd ed. McGraw Hill Boston MA."},{"key":"e_1_2_1_14_1","volume-title":"Hybrid Systems: Computation and Control","author":"Mosterman P.","unstructured":"Mosterman , P. 1999. An overview of hybrid simulation phenomena and their support by simulation packages . In Hybrid Systems: Computation and Control , F. Vaandrager and J. H. van Schuppen, Eds. Lecture Notes in Computer Science, vol. 1569 . Springer-Verlag , New York, 163--177. Mosterman, P. 1999. An overview of hybrid simulation phenomena and their support by simulation packages. In Hybrid Systems: Computation and Control, F. Vaandrager and J. H. van Schuppen, Eds. Lecture Notes in Computer Science, vol. 1569. Springer-Verlag, New York, 163--177."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/232807.232809"},{"key":"e_1_2_1_16_1","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/0098-1354(91)85016-N","article-title":"Algorithms for the location of discontinuities in dynamic simulation problems","volume":"15","author":"Prestin A.","year":"1991","unstructured":"Prestin , A. and Berzine , M. 1991 . Algorithms for the location of discontinuities in dynamic simulation problems . Comput. Chem. Eng. 15 , 10, 701 -- 713 . Prestin, A. and Berzine, M. 1991. Algorithms for the location of discontinuities in dynamic simulation problems. Comput. Chem. Eng. 15, 10, 701--713.","journal-title":"Comput. Chem. Eng."},{"key":"e_1_2_1_17_1","volume-title":"Simulation with Visual SLAM and AweSim","author":"Pritsker A.","unstructured":"Pritsker , A. and O'Reilly , J. 1999. Simulation with Visual SLAM and AweSim , 2 nd ed. Wiley , New York . Pritsker, A. and O'Reilly, J. 1999. Simulation with Visual SLAM and AweSim, 2nd ed. Wiley, New York.","edition":"2"},{"key":"e_1_2_1_18_1","series-title":"Lecture Notes in Computer Science","volume-title":"Results and Trends in Theoretical Computer Science","author":"Ruohonen K.","unstructured":"Ruohonen , K. 1994. Event detection for ODEs and nonrecuirsive heirarchies . In Results and Trends in Theoretical Computer Science . Lecture Notes in Computer Science , vol. 812 . Springer-Verlag , New York , 358--371. Ruohonen, K. 1994. Event detection for ODEs and nonrecuirsive heirarchies. In Results and Trends in Theoretical Computer Science. Lecture Notes in Computer Science, vol. 812. Springer-Verlag, New York, 358--371."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/103147.103149"},{"key":"e_1_2_1_20_1","volume-title":"Eds","author":"Tomlin C.","year":"2002","unstructured":"Tomlin , C. and Greenstreet , M. , Eds . 2002 . In Proceedings of the 5th International Workshop, Hybrid Systems : Computation and Control. (Palo Alto, CA.). Lecture Notes in Computer Science, vol. 2289 . Springer-Verlag , New York. Tomlin, C. and Greenstreet, M., Eds. 2002. In Proceedings of the 5th International Workshop, Hybrid Systems: Computation and Control. (Palo Alto, CA.). Lecture Notes in Computer Science, vol. 2289. Springer-Verlag, New York."}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1189756.1189757","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T19:48:17Z","timestamp":1672256897000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1189756.1189757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1145\/1189756.1189757"],"URL":"https:\/\/doi.org\/10.1145\/1189756.1189757","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"value":"1049-3301","type":"print"},{"value":"1558-1195","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]},"assertion":[{"value":"2007-01-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}