{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T20:49:48Z","timestamp":1767991788082,"version":"3.49.0"},"reference-count":42,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"12","license":[{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ECCS-1309569"],"award-info":[{"award-number":["ECCS-1309569"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CNS-1552838"],"award-info":[{"award-number":["CNS-1552838"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Automat. Contr."],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1109\/tac.2018.2804760","type":"journal-article","created":{"date-parts":[[2018,2,9]],"date-time":"2018-02-09T19:32:28Z","timestamp":1518204748000},"page":"4250-4263","source":"Crossref","is-referenced-by-count":12,"title":["A Unified Stochastic Hybrid System Approach to Aggregate Modeling of Responsive Loads"],"prefix":"10.1109","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1078-887X","authenticated-orcid":false,"given":"Lin","family":"Zhao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7511-2870","authenticated-orcid":false,"given":"Wei","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06400-9","author":"revuz","year":"1999","journal-title":"Continuous Martingales and Brownian Motion"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809781"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2014.7039766"},{"key":"ref32","author":"lee","year":"2013","journal-title":"Introduction to Smooth Manifolds"},{"key":"ref31","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14394-6","author":"\u00f8ksendal","year":"2003","journal-title":"Stochastic Differential Equations"},{"key":"ref30","author":"hanson","year":"2004","journal-title":"Applied stochastic processes and control for Jump Diffusions Modeling analysis and computation"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532546"},{"key":"ref36","author":"karatzas","year":"1991","journal-title":"Brownian Motion and Stochastic Calculus"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791253"},{"key":"ref34","year":"0","journal-title":"GridLAB-D Residential Module User's Guide"},{"key":"ref10","article-title":"Modeling heterogeneous populations of thermostatically controlled loads using diffusion-advection PDEs","author":"moura","year":"2013","journal-title":"Proc ASME Dyn Syst Control Conf"},{"key":"ref40","author":"driver","year":"2002","journal-title":"Surfaces Surface Integrals and Integration by Parts"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2014.915083"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1115\/DSCC2014-6022"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2015.2457428"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2015.7403144"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2016.2614830"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4483-2"},{"key":"ref17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-2795-6","author":"bujorianu","year":"2012","journal-title":"Stochastic reachability analysis of hybrid systems"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/3-540-46430-1_16","article-title":"Towards a theory of stochastic hybrid systems","volume":"1790","author":"hu","year":"2000","journal-title":"Lecture Notes in Computer Science"},{"key":"ref19","first-page":"319","article-title":"Stochastic hybrid processes with hybrid jumps","author":"blom","year":"2003","journal-title":"Analysis and design of hybrid system"},{"key":"ref28","author":"evans","year":"2010","journal-title":"Partial Differential Equations"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2013.2266121"},{"key":"ref27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-1605-1","author":"schuss","year":"2010","journal-title":"Theory and Applications of Stochastic Processes An Analytical Approach"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2012.2204074"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2015.2432057"},{"key":"ref29","author":"duchateau","year":"1986","journal-title":"Schaums Outline of Theory and Problems of Partial Differential Equations"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2014.2335158"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1104071"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2015.2432060"},{"key":"ref2","first-page":"1963","article-title":"Modeling and control of aggregated heterogeneous thermostatically controlled loads for ancillary services","author":"koch","year":"2011","journal-title":"Proc 17th Power Syst Comput Conf"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2012.2204261"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2008.12.012"},{"key":"ref20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-1105-6","author":"yin","year":"2010","journal-title":"Hybrid Switching Diffusions Properties and Applications"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.01.112"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/11587392_1"},{"key":"ref42","author":"billingsley","year":"1995","journal-title":"Probability and Measure (Wiley Series in Probability and Mathematical Statistics)"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.24033\/asens.1222"},{"key":"ref41","author":"shorack","year":"1986","journal-title":"Empirical Processes with Applications to Statistics"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2009.07.008"},{"key":"ref26","article-title":"Equivalent thermal parameters for an occupied gas-heated house","volume":"91","author":"wilson","year":"1985","journal-title":"ASHRAE Trans"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1979-0542886-X"}],"container-title":["IEEE Transactions on Automatic Control"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielaam\/9\/8556145\/8288646-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/9\/8556145\/08288646.pdf?arnumber=8288646","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T22:53:28Z","timestamp":1693522408000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8288646\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":42,"journal-issue":{"issue":"12"},"URL":"https:\/\/doi.org\/10.1109\/tac.2018.2804760","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":[[2018,12]]}}}