{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:11Z","timestamp":1787322971412,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>In this paper, a form of open local accessibility for nonlinear control systems is introduced called the continuous fountain condition. Subject to the conditions that (i) the states of a system are continuous fountains and (ii) one of various recurrence conditions holds, it is established that the system state space is (globally) controllable. It is shown that these controllability results imply the controllability of certain subsets of the state space of Hamiltonian control systems called energy slices. The relations between the notion of a fountain and (i) local accessibility and (ii) the full Lie algebra rank condition for control affine systems are investigated. Finally, the results in this paper are shown to have application to hierarchical hybrid control theory in that they give conditions for a finite analytic partition to satisfy the so-called in-block controllability property; this is illustrated with a linear mass-spring system example.<\/jats:p>","DOI":"10.1137\/s0363012999361950","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1532-1553","source":"Crossref","is-referenced-by-count":8,"title":["On the Global Controllability of Nonlinear Systems: Fountains, Recurrence, and Applications to Hamiltonian Systems"],"prefix":"10.1137","volume":"41","author":[{"given":"Peter E.","family":"Caines","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ekaterina S.","family":"Lemch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","first-page":"535","volume":"292","author":"Bonnard Bernard","year":"1981","journal-title":"C. 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Caines,\n                      Hybrid partition machines with disturbances\n                      , in Proceedings of the AAAI 1999 Spring Symposium Series on Hybrid Systems and AI: Modeling Analysis and Control of Discrete and Continuous Systems, AAAI Technical Report SS\u201099\u201005, Stanford University, Stanford, CA, 1999, pp. 109\u2013117."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1109\/9.362852"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0308042"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0312001"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1109\/9.769375"},{"key":"R22","unstructured":"V. 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