{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:46:49Z","timestamp":1740124009173,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T00:00:00Z","timestamp":1453161600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T00:00:00Z","timestamp":1453161600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-0010085"],"award-info":[{"award-number":["CMMI-0010085"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-1069331"],"award-info":[{"award-number":["CMMI-1069331"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1007\/s10957-016-0868-3","type":"journal-article","created":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T19:41:48Z","timestamp":1453232508000},"page":"220-242","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Manifold-Following Approximate Solution of Completely Hypersensitive Optimal Control Problems"],"prefix":"10.1007","volume":"170","author":[{"given":"Erkut","family":"Aykutlug","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ufuk","family":"Topcu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth D.","family":"Mease","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,19]]},"reference":[{"key":"868_CR1","volume-title":"Applied Optimal Control: Optimization, Estimation, and Control","author":"AE Bryson","year":"1975","unstructured":"Bryson, A.E., Ho, Y.-C.: Applied Optimal Control: Optimization, Estimation, and Control. Taylor & Francis, New York, NY (1975). revised-printing"},{"key":"868_CR2","doi-asserted-by":"publisher","first-page":"3633","DOI":"10.1016\/S0005-1098(98)00161-7","volume":"35","author":"AV Rao","year":"1999","unstructured":"Rao, A.V., Mease, K.D.: Dichotomic basis approach to solving hyper-sensitive optimal control problems. Automatica 35, 3633\u20133642 (1999)","journal-title":"Automatica"},{"key":"868_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/(SICI)1099-1514(200001\/02)21:1<1::AID-OCA646>3.0.CO;2-V","volume":"21","author":"AV Rao","year":"2000","unstructured":"Rao, A.V., Mease, K.D.: Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems. Opt. Control Appl. Methods 21, 1\u201319 (2000)","journal-title":"Opt. Control Appl. Methods"},{"key":"868_CR4","unstructured":"Oberle, H.J., Grimm, W.: BNDSCO\u2014a program for the numerical solution of optimal controlproblems. Internal Report No. 515\u201389\/22, Institute for Flight SystemsDynamics, DLR, Oberpfaffenhofen, Germany (1989)"},{"key":"868_CR5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971231","volume-title":"Numerical Solution of Boundary Value Problems for Ordinary Differential Equations","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Mattheij, R.M., Russell, R.D.: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM Press, Philadelphia (1995)"},{"key":"868_CR6","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1109\/TAC.1972.1099976","volume":"17","author":"RR Wilde","year":"1972","unstructured":"Wilde, R.R., Kokotovic, P.K.: A dichotomy in linear control theory. IEEE Trans. Autom. Control 17, 382\u2013383 (1972)","journal-title":"IEEE Trans. Autom. Control"},{"key":"868_CR7","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/0005-1098(87)90008-2","volume":"23","author":"BO Anderson","year":"1972","unstructured":"Anderson, B.O., Kokotovic, P.K.: Optimal control problems over large time intervals. Automatica 23, 355\u2013363 (1972)","journal-title":"Automatica"},{"key":"868_CR8","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/BF00937170","volume":"29","author":"JH Chow","year":"1979","unstructured":"Chow, J.H.: A class of singularly perturbed nonlinear, fixed end-point control problems. J. Opt. Theory Appl. 29, 231\u2013251 (1979)","journal-title":"J. Opt. Theory Appl."},{"key":"868_CR9","volume-title":"Singular Perturbation Methods in Control: Analysis and Design","author":"PV Kokotovic","year":"1986","unstructured":"Kokotovic, P.V., Khalil, H.K., O\u2019Reilly, J.: Singular Perturbation Methods in Control: Analysis and Design. Academic Press, New York (1986)"},{"key":"868_CR10","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0022-0396(79)90152-9","volume":"31","author":"N Fenichel","year":"1979","unstructured":"Fenichel, N.: Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 53\u201398 (1979)","journal-title":"J. Differ. Equ."},{"key":"868_CR11","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/0022-0396(80)90001-7","volume":"38","author":"RJ Sacker","year":"1980","unstructured":"Sacker, R.J., Sell, G.R.: The spectrum of an invariant submanifold. J. Differ. Equ. 38, 135\u2013160 (1980)","journal-title":"J. Differ. Equ."},{"key":"868_CR12","volume-title":"Lyapunov Exponents and Smooth Ergodic Theory","author":"L Barreira","year":"2002","unstructured":"Barreira, L., Pesin, Ya B.: Lyapunov Exponents and Smooth Ergodic Theory. American Mathematical Society, Providence (2002)"},{"key":"868_CR13","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1080\/00207179208934253","volume":"55","author":"AM Lyapunov","year":"1992","unstructured":"Lyapunov, A.M.: The general problem of stability of motion. Int. J. Control 55, 531\u2013773 (1992)","journal-title":"Int. J. Control"},{"issue":"1","key":"868_CR14","doi-asserted-by":"publisher","first-page":"318","DOI":"10.2514\/2.5049","volume":"26","author":"KD Mease","year":"2003","unstructured":"Mease, K.D., Bharadwaj, S., Iravanchy, S.: Timescale analysis for nonlinear dynamical systems. J. Guid. Control Dyn. 26(1), 318\u2013330 (2003)","journal-title":"J. Guid. Control Dyn."},{"key":"868_CR15","unstructured":"Mease, K.D., Topcu, U., Aykutlug, E., Maggia, M.: Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces. Commun. Nonlinear Sci. Numer. Simul. 36, 148\u2013174 (2016)"},{"issue":"4","key":"868_CR16","doi-asserted-by":"publisher","first-page":"1467","DOI":"10.1175\/2007JAS2419.1","volume":"65","author":"CM Danforth","year":"2008","unstructured":"Danforth, C.M., Kalnay, E.: Using singular value decomposition to parametrize state-dependent model errors. J. Atmos. Sci. 65(4), 1467\u20131478 (2008)","journal-title":"J. Atmos. Sci."},{"key":"868_CR17","doi-asserted-by":"publisher","first-page":"144102","DOI":"10.1103\/PhysRevLett.96.144102","volume":"96","author":"CM Danforth","year":"2006","unstructured":"Danforth, C.M., Yorke, J.A.: Making forecasts for chaotic physical processes. Phys. Rev. Lett. 96, 144102 (2006)","journal-title":"Phys. Rev. Lett."},{"issue":"15","key":"868_CR18","doi-asserted-by":"publisher","first-page":"2129","DOI":"10.1175\/1520-0469(1996)053<2129:FTIOLS>2.0.CO;2","volume":"53","author":"DL Hartmann","year":"1996","unstructured":"Hartmann, D.L., Buizza, R., Palmer, T.N.: Finite-time instabilities of lower-stratospheric flow. J. Atmos. Sci. 53(15), 2129\u20132143 (1996)","journal-title":"J. Atmos. Sci."},{"key":"868_CR19","volume-title":"Atmospheric Modeling, Data Assimilation and Predictability","author":"E Kalnay","year":"2003","unstructured":"Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, Cambridge (2003)"},{"key":"868_CR20","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1016\/S0167-2789(00)00199-8","volume":"149","author":"G Haller","year":"2001","unstructured":"Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248\u2013277 (2001)","journal-title":"Phys. D"},{"key":"868_CR21","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1016\/j.physd.2010.11.010","volume":"240","author":"G Haller","year":"2011","unstructured":"Haller, G.: A variational theory of hyperbolic Lagrangian coherent structures. Phys. D 240, 574\u2013598 (2011)","journal-title":"Phys. D"},{"key":"868_CR22","doi-asserted-by":"publisher","first-page":"065404","DOI":"10.1063\/1.2740025","volume":"48","author":"F Lekien","year":"2007","unstructured":"Lekien, F., Shadden, S.C., Marsden, J.E.: Lagrangian coherent structures in n-dimensional systems. J. Math. Phys. 48, 065404 (2007)","journal-title":"J. Math. Phys."},{"key":"868_CR23","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/j.physd.2005.10.007","volume":"212","author":"SC Shadden","year":"2005","unstructured":"Shadden, S.C., Lekien, F., Marsden, J.E.: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Phys. D 212, 271\u2013304 (2005)","journal-title":"Phys. D"},{"key":"868_CR24","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1111\/j.1600-0870.2007.00234.x","volume":"59A","author":"CL Wolfe","year":"2007","unstructured":"Wolfe, C.L., Samelson, R.M.: An efficient method for recovering Lyapunov vectors from singular vectors. Tellus 59A, 355\u2013366 (2007)","journal-title":"Tellus"},{"key":"868_CR25","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/j.physleta.2005.05.054","volume":"342","author":"A Adrover","year":"2005","unstructured":"Adrover, A., Creta, F., Giona, M., Valorani, M.: Biorthogonalization, geometric invariant properties and rate-based estimate of Lyapunov spectra. Phys. Lett. A 342, 421\u2013429 (2005)","journal-title":"Phys. Lett. A"},{"key":"868_CR26","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.physd.2005.05.021","volume":"213","author":"A Adrover","year":"2006","unstructured":"Adrover, A., Creta, F., Valorani, M., Vitacolonna, V.: Natural tangent dynamics with recurrent biorthonormalizations: a geometric computational approach to dynamical systems exhibiting slow manifolds and periodic\/chaotic limit sets. Phys. D 213, 121\u2013146 (2006)","journal-title":"Phys. D"},{"issue":"3","key":"868_CR27","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1137\/080741999","volume":"8","author":"J Guckenhheimer","year":"2009","unstructured":"Guckenhheimer, J., Kuehn, C.: Computing slow manifolds of saddle type. SIAM J. Appl. Dyn. Syst. 8(3), 854\u2013879 (2009)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"868_CR28","doi-asserted-by":"publisher","first-page":"046107","DOI":"10.1063\/1.4826655","volume":"23","author":"HM Osinga","year":"2013","unstructured":"Osinga, H.M., Tsaneva-Atanasova, K.T.: Geometric analysis of transient bursts. Chaos 23, 046107 (2013)","journal-title":"Chaos"},{"key":"868_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and Stochastic Optimal Control","author":"WH Fleming","year":"1975","unstructured":"Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)"},{"issue":"1","key":"868_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2558904","volume":"41","author":"MA Patterson","year":"2014","unstructured":"Patterson, M.A., Rao, A.V.: GPOPS-II: a MATLAB software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math. Softw. 41(1), 1\u201337 (2014)","journal-title":"ACM Trans. Math. Softw."},{"key":"868_CR31","volume-title":"Ordinary Differential Equations","author":"VI Arnol\u2019d","year":"1992","unstructured":"Arnol\u2019d, V.I.: Ordinary Differential Equations. Springer, Berlin (1992)"},{"key":"868_CR32","volume-title":"Control and Dynamic Systems","author":"HJ Kelly","year":"1973","unstructured":"Kelly, H.J.: Aircraft maneuver optimization by reduced-order approximations. In: Leondes, C.T. (ed.) Control and Dynamic Systems. Academic Press, New York (1973)"},{"key":"868_CR33","doi-asserted-by":"crossref","unstructured":"Aykutlug, E., Maggia, M., Mease, K.D.: Solving partially hyper-sensitive optimal control problems using manifold structure. In: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Nonlinear Control Systems, vol. 9, Part 1, pp. 187\u2013192. Toulouse, France. International Federation of Automatic Control (2013)","DOI":"10.3182\/20130904-3-FR-2041.00190"},{"issue":"5","key":"868_CR34","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1137\/S0036142901392304","volume":"40","author":"L Dieci","year":"2002","unstructured":"Dieci, L., Van Vleck, E.S.: Lyapunov spectral intervals: theory and computation. J. Numer. Anal. 40(5), 516\u2013542 (2002)","journal-title":"J. Numer. Anal."},{"issue":"3","key":"868_CR35","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0167-2789(87)90034-0","volume":"27","author":"I Goldhirsch","year":"1987","unstructured":"Goldhirsch, I., Sulem, P.L., Orszag, S.A.: Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method. Phys. D 27(3), 311\u2013337 (1987)","journal-title":"Phys. D"},{"key":"868_CR36","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"issue":"11","key":"868_CR37","doi-asserted-by":"publisher","first-page":"1759","DOI":"10.1016\/S0960-0779(98)00233-1","volume":"10","author":"R Doerner","year":"1999","unstructured":"Doerner, R., Hubinger, B., Martienssen, W., Grossmann, S., Thomae, S.: Stable manifolds and predictability of dynamical systems. Chaos Solitons Fractals 10(11), 1759\u20131782 (1999)","journal-title":"Chaos Solitons Fractals"},{"key":"868_CR38","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1017\/S002211209100040X","volume":"233","author":"JA Vastano","year":"1991","unstructured":"Vastano, J.A., Moser, R.D.: Short-time Lyapunov exponent analysis and the transition to chaos in Taylor\u2013Couette flow. J. Fluid Mech. 233, 83\u2013118 (1991)","journal-title":"J. Fluid Mech."},{"key":"868_CR39","doi-asserted-by":"crossref","unstructured":"Topcu, U., Mease, K.D.: Using Lyapunov vectors and dichotomy to solve hyper-sensitive optimal control problems. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA (2006)","DOI":"10.1109\/CDC.2006.376966"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0868-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-0868-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0868-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0868-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T13:28:26Z","timestamp":1589722106000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-0868-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,19]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["868"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-0868-3","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2016,1,19]]},"assertion":[{"value":"23 April 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}