Classification générique de synthèses temps minimales avec cible de codimension un et applications
Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 1, pp. 55-102.
@article{AIHPC_1997__14_1_55_0,
     author = {Bonnard, B. and Launay, G. and Pelletier, M.},
     title = {Classification g\'en\'erique de synth\`eses temps minimales avec cible de codimension un et applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {55--102},
     publisher = {Gauthier-Villars},
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     url = {http://archive.numdam.org/item/AIHPC_1997__14_1_55_0/}
}
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Bonnard, B.; Launay, G.; Pelletier, M. Classification générique de synthèses temps minimales avec cible de codimension un et applications. Annales de l'I.H.P. Analyse non linéaire, Volume 14 (1997) no. 1, pp. 55-102. http://archive.numdam.org/item/AIHPC_1997__14_1_55_0/

[1] V.I. Arnold, S.M. Goussein Zadé et A.N. Varchenko, Singularities of differentiable maps, Tome 1, Nauka, Moscou, 1981.

[2] R. Benedetti et J.J. Risler, Real algebraic and semi algebraic sets, Hermann, Paris, 1990. | MR | Zbl

[3] B. Bonnard et I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal, mathematicum, vol. 5, 1993, pp. 111-159. | MR | Zbl

[4] B. Bonnard et J. De Morant, Towards a geometric theory in the time minimal control of chemical batch reactors, SIAM J. on Control and Opt., vol. 33, n° 5, sept. 1995, pp. 1279-1311. | MR | Zbl

[5] B. Bonnard et M. Pelletier, Time minimal synthesis for planar systems in the neighborhood of a terminal manifold of codimension one, summary in J. of Mathematical systems, estimation and control, vol. 5, n° 3, 1995. | MR | Zbl

[6] B. Bonnard et M. Pelletier, Time minimal synthesis with target of codimension one under generic conditions, Pub. Banach Center, vol. 32, 1995. | Zbl

[7] I. Ekeland, Discontinuité des champs hamiltoniens et existence de solutions optimales en calcul des variations, Pub. IHES, n° 47, 1977, pp. 1-32. | Numdam | MR | Zbl

[8] M. Feinberg, Chemical reaction network structure and stability of complex isothermal reactions, Chemical Engineering Sciences, vol. 42, 10, 1987, pp. 2229-2268.

[9] H. Hermes, Lie algebras of vector fields and local approximation of attainable sets, SIAM J. on Control and Opt., vol. 16, 1978, pp. 715-727. | MR | Zbl

[10] C.G. Hill, An introduction to chemical engineering kinetics and reactor design, John Wiley, New York, 1977.

[11] W. Klingenberg, A course in differential geometry, Graduate texts in Mathematics, Springer Verlag, New York, 1978. | MR | Zbl

[12] F. Klok, Broken solutions of homogeneous variational problems, J. of Diff. Equ., vol. 55, 1984, pp. 101-134. | MR | Zbl

[13] S. Kobayashi, On conjugate and cut loci, in Studies in global geometry, vol. 4, S. S. Chern ed., Englewood Cliffs, Prentice Hall, NJ, 1967. | MR

[14] A.J. Krener, The higher-order maximal principle and its applications to singular extremals, SIAM J. on Control and Opt., vol. 15, 1977, pp. 256-293. | MR | Zbl

[15] I. Kupka, Geometric theory of extremals in optimal control problems, I. The fold and Maxwell cases, TAMS, vol. 299, 1973, pp. 225-243. | MR | Zbl

[16] G. Launay et M. Pelletier, Synthèse optimale avec cible de codimension un : le cas d'arrivée tangentielle, A paraître.

[17] E.B. Lee et L. Markus, Foundations of optimal control theory, John Wiley, New York, 1967. | MR | Zbl

[18] M. Pelletier, Contribution à l'étude de quelques singularités de systèmes non linéaires, Thèse, Université de Bourgogne, 1994.

[19] H. Poincaré, Sur les lignes géodésiques des surfaces convexes, TAMS, vol. 6, 1905, pp. 237-274. | JFM | MR

[20] L. Pontriaguine et al., Théorie mathématique des processus optimaux, ed. Mir., Moscou, 1974. | MR | Zbl

[21] H. Schättler, The local structure of time-optimal trajectories in dimension 3 under generic conditions, SIAM J. on Control and Opt., vol. 26, 1988, pp. 899-918. | MR | Zbl

[22] H.J. Sussmann, The structure of time-optimal trajectories for single-input systems in the plane : the C∞ non singular case, SIAM J. on Control and Opt., vol. 25, 1987, pp. 433-465. | MR

[23] H.J. Sussmann, Regular synthesis for time-optimal control for single-input real analytic systems in the plane, SIAM J. on Control and Opt., vol. 25, 1987, pp. 1145-1162. | MR | Zbl

[24] R.J. Walker, Algebraic curves, Princeton University Press, Princeton, 1951. | MR | Zbl