Classification générique de synthèses temps minimales avec cible de codimension un et applications

 Access to full text

 Full (PDF)

1. [1] V.I. Arnold, S.M. Goussein Zadé et A.N. Varchenko, Singularities of differentiable maps, Tome 1, Nauka, Moscou, 1981. Zbl1297.32001
2. [2] R. Benedetti et J.J. Risler, Real algebraic and semi algebraic sets, Hermann, Paris, 1990. Zbl0694.14006MR1070358
3. [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. Zbl0779.49025MR1205250
4. [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. Zbl0882.49024MR1348110
5. [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. Zbl0852.49014MR1651819
6. [6] B. Bonnard et M. Pelletier, Time minimal synthesis with target of codimension one under generic conditions, Pub. Banach Center, vol. 32, 1995. Zbl0971.49009
7. [7] I. Ekeland, Discontinuité des champs hamiltoniens et existence de solutions optimales en calcul des variations, Pub. IHES, n° 47, 1977, pp. 1-32. Zbl0447.49015MR493584
8. [8] M. Feinberg, Chemical reaction network structure and stability of complex isothermal reactions, Chemical Engineering Sciences, vol. 42, 10, 1987, pp. 2229-2268. 
9. [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. Zbl0388.49025MR493664
10. [10] C.G. Hill, An introduction to chemical engineering kinetics and reactor design, John Wiley, New York, 1977. 
11. [11] W. Klingenberg, A course in differential geometry, Graduate texts in Mathematics, Springer Verlag, New York, 1978. Zbl0366.53001MR474045
12. [12] F. Klok, Broken solutions of homogeneous variational problems, J. of Diff. Equ., vol. 55, 1984, pp. 101-134. Zbl0507.58022MR759829
13. [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. MR212737
14. [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. Zbl0354.49008MR433288
15. [15] I. Kupka, Geometric theory of extremals in optimal control problems, I. The fold and Maxwell cases, TAMS, vol. 299, 1973, pp. 225-243. Zbl0606.49016MR869409
16. [16] G. Launay et M. Pelletier, Synthèse optimale avec cible de codimension un : le cas d'arrivée tangentielle, A paraître. 
17. [17] E.B. Lee et L. Markus, Foundations of optimal control theory, John Wiley, New York, 1967. Zbl0159.13201MR220537
18. [18] M. Pelletier, Contribution à l'étude de quelques singularités de systèmes non linéaires, Thèse, Université de Bourgogne, 1994. 
19. [19] H. Poincaré, Sur les lignes géodésiques des surfaces convexes, TAMS, vol. 6, 1905, pp. 237-274. MR1500710JFM36.0669.01
20. [20] L. Pontriaguine et al., Théorie mathématique des processus optimaux, ed. Mir., Moscou, 1974. Zbl0289.49002MR358482
21. [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. Zbl0656.49007MR948651
22. [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. MR877071
23. [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. Zbl0701.93035MR905037
24. [24] R.J. Walker, Algebraic curves, Princeton University Press, Princeton, 1951. Zbl0039.37701MR33083

1. B. Bonnard, G. Launay, Time minimal control of batch reactors