{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T10:47:49Z","timestamp":1767869269269,"version":"3.49.0"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319734408","type":"print"},{"value":"9783319734415","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-73441-5_22","type":"book-chapter","created":{"date-parts":[[2018,1,2]],"date-time":"2018-01-02T10:42:23Z","timestamp":1514889743000},"page":"210-218","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Estimation of Star-Shaped Reachable Sets of Nonlinear Control Systems"],"prefix":"10.1007","author":[{"given":"Tatiana F.","family":"Filippova","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,1,3]]},"reference":[{"issue":"7","key":"22_CR1","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1016\/j.aml.2009.01.016","volume":"22","author":"NC Apreutesei","year":"2009","unstructured":"Apreutesei, N.C.: An optimal control problem for a prey-predator system with a general functional response. Appl. Math. Lett. 22(7), 1062\u20131065 (2009)","journal-title":"Appl. Math. Lett."},{"key":"22_CR2","doi-asserted-by":"crossref","unstructured":"August, E., Lu, J., Koeppl, H.: Trajectory enclosures for nonlinear systems with uncertain initial conditions and parameters. In: Proceedings of the 2012 American Control Conference, Fairmont Queen Elizabeth, Montr\u00e9al, Canada, pp. 1488\u20131493. June 2012","DOI":"10.1109\/ACC.2012.6314741"},{"key":"22_CR3","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1080\/10556780600604999","volume":"22","author":"R Baier","year":"2007","unstructured":"Baier, R., B\u00fcskens, C., Chahma, I.A., Gerdts, M.: Approximation of reachable sets by direct solution methods of optimal control problems. Optim. Methods Softw. 22, 433\u2013452 (2007)","journal-title":"Optim. Methods Softw."},{"key":"22_CR4","doi-asserted-by":"crossref","unstructured":"Boscain, U., Chambrion, T., Sigalotti, M.: On some open questions in bilinear quantum control. In: European Control Conference (ECC), Zurich, Switzerland, pp. 2080\u20132085. July 2013","DOI":"10.23919\/ECC.2013.6669238"},{"key":"22_CR5","doi-asserted-by":"crossref","unstructured":"Ceccarelli, N., Di Marco, M., Garulli, A., Giannitrapani, A.: A set theoretic approach to path planning for mobile robots. In: Proceedings of the 43rd IEEE Conference on Decision and Control, Atlantis, Bahamas, pp. 147\u2013152. December 2004","DOI":"10.1109\/CDC.2004.1428621"},{"key":"22_CR6","volume-title":"State Estimation for Dynamic Systems","author":"FL Chernousko","year":"1988","unstructured":"Chernousko, F.L.: State Estimation for Dynamic Systems. Nauka, Moscow (1988)"},{"issue":"2","key":"22_CR7","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1023\/B:JOTA.0000015683.35168.bf","volume":"120","author":"FL Chernousko","year":"2004","unstructured":"Chernousko, F.L., Ovseevich, A.I.: Properties of the optimal ellipsoids approximating the reachable sets of uncertain systems. J. Optim. Theory Appl. 120(2), 223\u2013246 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"22_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0121132","volume-title":"Quasidifferential Calculus","author":"VF Demyanov","year":"1986","unstructured":"Demyanov, V.F., Rubinov, A.M.: Quasidifferential Calculus. Optimization Software, New York (1986)"},{"issue":"2","key":"22_CR9","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1080\/13873950500068542","volume":"11","author":"TF Filippova","year":"2005","unstructured":"Filippova, T.F.: Set-valued solutions to impulsive differential inclusions. Math. Comput. Modell. Dyn. Syst. 11(2), 149\u2013158 (2005)","journal-title":"Math. Comput. Modell. Dyn. Syst."},{"issue":"Suppl. 2","key":"22_CR10","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1134\/S008154381006009X","volume":"269","author":"TF Filippova","year":"2010","unstructured":"Filippova, T.F.: Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control. Proc. Steklov Inst. Math. 269(Suppl. 2), 95\u2013102 (2010)","journal-title":"Proc. Steklov Inst. Math."},{"key":"22_CR11","unstructured":"Filippova, T.F.: Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty. In: Discrete and Continuous Dynamical Systems, Supplement 2011, Dynamical Systems, Differential Equations and Applications, vol. 1. pp. 410\u2013419, Springfield, American Institute of Mathematical Sciences (2011)"},{"key":"22_CR12","unstructured":"Filippova, T.F.: State estimation for uncertain systems with arbitrary quadratic nonlinearity. In: Proceedings of the PHYSCON 2015, Istanbul, Turkey, August 1922, pp. 1\u20136 (2015)"},{"key":"22_CR13","doi-asserted-by":"crossref","unstructured":"Filippova, T.F.: Estimates of reachable sets of impulsive control problems with special nonlinearity. In: Proceedings of the AIP Conference, vol. 1773, p. 100004, 1\u20138 (2016)","DOI":"10.1063\/1.4964998"},{"key":"22_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/978-3-540-78827-0_36","volume-title":"Large-Scale Scientific Computing","author":"TF Filippova","year":"2008","unstructured":"Filippova, T.F., Berezina, E.V.: On state estimation approaches for uncertain dynamical systems with quadratic nonlinearity: theory and computer simulations. In: Lirkov, I., Margenov, S., Wa\u015bniewski, J. (eds.) LSSC 2007. LNCS, vol. 4818, pp. 326\u2013333. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78827-0_36"},{"key":"22_CR15","unstructured":"Filippova, T.F., Lisin, D.V.: On the estimation of trajectory tubes of differential inclusions. Proc. Steklov Inst. Math. Probl. Control Dyn. Syst. Suppl. 2, pp. S28\u2013S37 (2000)"},{"key":"22_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/978-3-642-29843-1_13","volume-title":"Large-Scale Scientific Computing","author":"TF Filippova","year":"2012","unstructured":"Filippova, T.F., Matviychuk, O.G.: Reachable sets of impulsive control system with cone constraint on the control and their estimates. In: Lirkov, I., Margenov, S., Wa\u015bniewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 123\u2013130. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29843-1_13"},{"issue":"1","key":"22_CR17","doi-asserted-by":"crossref","first-page":"45","DOI":"10.15826\/umj.2015.1.004","volume":"1","author":"TF Filippova","year":"2015","unstructured":"Filippova, T.F., Matviychuk, O.G.: Estimates of reachable sets of control systems with bilinearquadratic nonlinearities. Ural Math. J. 1(1), 45\u201354 (2015)","journal-title":"Ural Math. J."},{"key":"22_CR18","doi-asserted-by":"crossref","unstructured":"Gusev, M.I.: Application of penalty function method to computation of reachable sets for control systems with state constraints. In: Proceedings of the AIP Conference, vol. 1773 p. 050003, 1\u20138 (2016)","DOI":"10.1063\/1.4964973"},{"key":"22_CR19","volume-title":"Control and Observation Under Conditions of Uncertainty","author":"AB Kurzhanski","year":"1977","unstructured":"Kurzhanski, A.B.: Control and Observation Under Conditions of Uncertainty. Nauka, Moscow (1977)"},{"key":"22_CR20","volume-title":"Set-valued Analysis and Differential Inclusions: Progress in Systems and Control Theory","year":"1990","unstructured":"Kurzhanski, A.B., Veliov, V.M. (eds.): Set-valued Analysis and Differential Inclusions: Progress in Systems and Control Theory, vol. 16. Birkh\u00e4user, Boston (1990)"},{"key":"22_CR21","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/978-1-4612-0349-0_4","volume-title":"Advances in Nonlinear Dynamics and Control: A Report from Russia. Progress in Systems and Control Theory","author":"AB Kurzhanski","year":"1993","unstructured":"Kurzhanski, A.B., Filippova, T.F.: On the theory of trajectory tubes \u2013 a mathematical formalism for uncertain dynamics, viability and control. In: Kurzhanski, A.B. (ed.) Advances in Nonlinear Dynamics and Control: A Report from Russia. Progress in Systems and Control Theory, vol. 17, pp. 122\u2013188. Birkh\u00e4user, Boston (1993). https:\/\/doi.org\/10.1007\/978-1-4612-0349-0_4"},{"key":"22_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0277-6","volume-title":"Ellipsoidal Calculus for Estimation and Control","author":"AB Kurzhanski","year":"1997","unstructured":"Kurzhanski, A.B., Valyi, I.: Ellipsoidal Calculus for Estimation and Control. Birkh\u00e4user, Boston (1997)"},{"key":"22_CR23","series-title":"Systems & Control, Foundations & Applications","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-10277-1","volume-title":"Dynamics and Control of Trajectory Tubes: Theory and Computation","author":"AB Kurzhanski","year":"2014","unstructured":"Kurzhanski, A.B., Varaiya, P.: Dynamics and Control of Trajectory Tubes: Theory and Computation. Systems & Control, Foundations & Applications, vol. 85. Basel, Birkh\u00e4user (2014)"},{"key":"22_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/978-3-642-12535-5_34","volume-title":"Large-Scale Scientific Computing","author":"MI Krastanov","year":"2010","unstructured":"Krastanov, M.I., Veliov, V.M.: High-order approximations to nonholonomic affine control systems. In: Lirkov, I., Margenov, S., Wa\u015bniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 294\u2013301. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-12535-5_34"},{"issue":"3","key":"22_CR25","first-page":"96","volume":"5","author":"OG Matviychuk","year":"2016","unstructured":"Matviychuk, O.G.: Ellipsoidal estimates of reachable sets of impulsive control systems with bilinear uncertainty. Cybern. Phys. 5(3), 96\u2013104 (2016)","journal-title":"Cybern. Phys."},{"key":"22_CR26","doi-asserted-by":"crossref","unstructured":"Matviychuk, O.G.: Internal ellipsoidal estimates for bilinear systems under uncertainty. In: Proceedings of the AIP Conference, vol. 1789, p. 060008, 1\u20138 (2016)","DOI":"10.1063\/1.4968500"},{"issue":"1","key":"22_CR27","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1134\/S1064562412040114","volume":"86","author":"SS Mazurenko","year":"2012","unstructured":"Mazurenko, S.S.: A differential equation for the gauge function of the star-shaped attainability set of a differential inclusion. Doklady Math. 86(1), 476\u2013479 (2012)","journal-title":"Doklady Math."},{"key":"22_CR28","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.automatica.2004.02.014","volume":"40","author":"BT Polyak","year":"2004","unstructured":"Polyak, B.T., Nazin, S.A., Durieu, C., Walter, E.: Ellipsoidal parameter or state estimation under model uncertainty. Automatica 40, 1171\u20131179 (2004)","journal-title":"Automatica"},{"key":"22_CR29","volume-title":"Uncertain Dynamical Systems","author":"FC Schweppe","year":"1973","unstructured":"Schweppe, F.C.: Uncertain Dynamical Systems. Prentice-Hall, Englewood Cliffs (1973)"},{"issue":"2","key":"22_CR30","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1137\/0729026","volume":"29","author":"V Veliov","year":"1992","unstructured":"Veliov, V.: Second-order discrete approximation to linear differential inclusions. SIAM J. Numer. Anal. 29(2), 439\u2013451 (1992)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Lecture Notes in Computer Science","Large-Scale Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-73441-5_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,8]],"date-time":"2019-10-08T22:46:21Z","timestamp":1570574781000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-73441-5_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319734408","9783319734415"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-73441-5_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]}}}