Characterization of the Darboux point for particular classes of problems
dc.contributor.author | Powers, William Francis | en_US |
dc.contributor.author | Mereau, P. M. | en_US |
dc.date.accessioned | 2006-09-11T15:48:09Z | |
dc.date.available | 2006-09-11T15:48:09Z | |
dc.date.issued | 1977-08 | en_US |
dc.identifier.citation | Mereau, P. M.; Powers, W. F.; (1977). "Characterization of the Darboux point for particular classes of problems." Journal of Optimization Theory and Applications 22(4): 537-562. <http://hdl.handle.net/2027.42/45212> | en_US |
dc.identifier.issn | 0022-3239 | en_US |
dc.identifier.issn | 1573-2878 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/45212 | |
dc.description.abstract | A minimal sufficient condition for global optimality involving the Darboux point, analogous to the minimal sufficient condition of local optimality involving the conjugate point, is presented. The Darboux point is then characterized for optimal control problems with linear dynamics, cost functionals with a general terminal state term and an integrand quadratic in the state and control, and general terminal conditions. The Darboux point is shown to be the supremum of a sequence of conjugate points. If the terminal state term is quadratic, along with a scalar quadratic boundary condition, then the Darboux point is also the time at which the Riccati matrix becomes unbounded, giving a characterization of the unboundedness of the Riccati matrix at points which are not in general conjugate points. | en_US |
dc.format.extent | 1125489 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers-Plenum Publishers; Plenum Publishing Corporation ; Springer Science+Business Media | en_US |
dc.subject.other | Optimal Control | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Applications of Mathematics | en_US |
dc.subject.other | Optimization | en_US |
dc.subject.other | Calculus of Variations and Optimal Control | en_US |
dc.subject.other | Engineering, General | en_US |
dc.subject.other | Calculus of Variations | en_US |
dc.subject.other | Global Sufficient Conditions | en_US |
dc.subject.other | Darboux Point | en_US |
dc.subject.other | Conjugate Point | en_US |
dc.subject.other | Optimization | en_US |
dc.subject.other | Operation Research/Decision Theory | en_US |
dc.subject.other | Theory of Computation | en_US |
dc.title | Characterization of the Darboux point for particular classes of problems | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationother | ADERSA/GERBIOS, Velizy, France | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/45212/1/10957_2004_Article_BF01268173.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01268173 | en_US |
dc.identifier.source | Journal of Optimization Theory and Applications | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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