{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T21:53:45Z","timestamp":1725573225490},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540319948"},{"type":"electronic","value":"9783540319955"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11666806_29","type":"book-chapter","created":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T03:09:49Z","timestamp":1139972989000},"page":"263-270","source":"Crossref","is-referenced-by-count":2,"title":["Approximations with Error Estimates for Optimal Control Problems for Linear Systems"],"prefix":"10.1007","author":[{"given":"Vladimir M.","family":"Veliov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"4","key":"29_CR1","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1137\/S036301290138866X","volume":"41","author":"A.A. Agrachev","year":"2002","unstructured":"Agrachev, A.A., Stefani, G., Zezza, P.: Strong optimality for a bang-bang trajectory. SIAM J. Control Optim.\u00a041(4), 991\u20131014 (2002)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"29_CR2","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1006\/jmaa.1993.1363","volume":"179","author":"B.D. Doitchinov","year":"1993","unstructured":"Doitchinov, B.D., Veliov, V.M.: Parametrisations of integrals of set-valued mappings and applications. J. of Math. Anal. and Appl.\u00a0179(2), 483\u2013499 (1993)","journal-title":"J. of Math. Anal. and Appl."},{"issue":"1","key":"29_CR3","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1137\/S0036142999351765","volume":"38","author":"A.L. Dontchev","year":"2000","unstructured":"Dontchev, A.L., Hager, W.W., Veliov, V.M.: Second-order Runge-Kutta approximations in control constrained optimal control. SIAM J. Numerical Anal.\u00a038(1), 202\u2013226 (2000)","journal-title":"SIAM J. Numerical Anal."},{"issue":"6","key":"29_CR4","doi-asserted-by":"publisher","first-page":"1843","DOI":"10.1137\/S0363012901399271","volume":"41","author":"U. Felgenhauer","year":"2003","unstructured":"Felgenhauer, U.: On stability of bang-bang type controls. SIAM J. Control Optim.\u00a041(6), 1843\u20131867 (2003)","journal-title":"SIAM J. Control Optim."},{"key":"29_CR5","unstructured":"Felgenhauer, U.: On the optimality of optimal bang-bang controls for linear and semilinear systems. Control & Cybernetics (to appear)"},{"key":"29_CR6","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/BF02684347","volume":"58","author":"R. Ferretti","year":"1997","unstructured":"Ferretti, R.: High-order approximations of linear control systems via Runge-Kutta schemes. Computing\u00a058, 351\u2013364 (1997)","journal-title":"Computing"},{"key":"29_CR7","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1023\/A:1026099606815","volume":"26","author":"O. Kostyukova","year":"2003","unstructured":"Kostyukova, O., Kostina, E.: Analysis of properties of the solutions to parametric time-optimal problems. Computational Optimization and Applications\u00a026, 285\u2013326 (2003)","journal-title":"Computational Optimization and Applications"},{"issue":"6","key":"29_CR8","doi-asserted-by":"publisher","first-page":"2239","DOI":"10.1137\/S0363012902402578","volume":"42","author":"H. Maurer","year":"2004","unstructured":"Maurer, H., Osmolovskii, N.: Second order sufficient conditions for time-optimal bang-bang control. SIAM J. Control Optim.\u00a042(6), 2239\u20132263 (2004)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"29_CR9","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/S0022-247X(02)00008-2","volume":"269","author":"J. Noble","year":"2002","unstructured":"Noble, J., Sch\u00e4ttler, H.: Sufficient conditions for relative minima of broken extremals in optimal control theory. J. Math. Anal. Appl.\u00a0269(1), 98\u2013128 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"29_CR10","first-page":"198","volume-title":"Calculus of variations and optimal control (Haifa, 1998)","author":"N.P. Osmolovskii","year":"2000","unstructured":"Osmolovskii, N.P.: Second-order conditions for broken extremal. In: Calculus of variations and optimal control (Haifa, 1998), vol.\u00a0411, pp. 198\u2013216. Chapman & Hall\/CRC Res. Notes Math., Boca Raton (2000)"},{"key":"29_CR11","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/B978-0-12-059650-8.50052-1","volume-title":"International Conference on Differential Equations (Calif., 1974)","author":"A. Pli\u015b","year":"1975","unstructured":"Pli\u015b, A.: Accessible sets in control theory. In: International Conference on Differential Equations (Calif., 1974), pp. 646\u2013650. Academic Press, London (1975)"},{"issue":"2","key":"29_CR12","doi-asserted-by":"crossref","first-page":"103","DOI":"10.4213\/sm111","volume":"187","author":"E. Polovinkin","year":"1996","unstructured":"Polovinkin, E.: Strongly convex analysis. Mat. Sb.\u00a0187(2), 103\u2013130 (1996); translation in Sb. Math.\u00a0187(2), 259\u2013286 (1996)","journal-title":"Mat. Sb."},{"key":"29_CR13","volume-title":"The mathematical theory of optimal processes.","author":"L.S. Pontryagin","year":"1962","unstructured":"Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The mathematical theory of optimal processes. John Wiley & Sons, Chichester (1962)"},{"key":"29_CR14","doi-asserted-by":"publisher","first-page":"1235","DOI":"10.1137\/S0363012994267352","volume":"34","author":"A. Schwartz","year":"1996","unstructured":"Schwartz, A., Polak, E.: Consistent approximations for optimal control problems based on Runge-Kutta integration. SIAM J. Control Optim.\u00a034, 1235\u20131269 (1996)","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"29_CR15","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/BF00940201","volume":"54","author":"V.M. Veliov","year":"1987","unstructured":"Veliov, V.M.: On the convexity of integrals of multivalued mappings: applications in control theory. J. Optim. Theory Appl.\u00a054(3), 541\u2013563 (1987)","journal-title":"J. Optim. Theory Appl."},{"key":"29_CR16","unstructured":"Veliov, V.M.: Approximations to Differential Inclusions by Discrete Inclusions. In: WP\u201389\u2013017, IIASA, Laxenburg, Austria (1989)"},{"key":"29_CR17","unstructured":"Veliov, V.M.: Error analysis of discrete approximations to bang-bang optimal control problems: the linear case. Control & Cybernetics (to appear)"}],"container-title":["Lecture Notes in Computer Science","Large-Scale Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11666806_29.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T07:13:11Z","timestamp":1619507591000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11666806_29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540319948","9783540319955"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/11666806_29","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2006]]}}}