Control Theory from the Geometric Viewpoint, Encyclopaedia of Mathematical Sciences, vol.87, 2004412. ,
Global asymptotic stability for a class of nonlinear chemical equations, SIAM J. Appl. Math, vol.5, issue.68, pp.1464-1476, 2008. ,
Sufficient conditions for optimality and the justification of the dynamic programming method, SIAM J. Control Optim, vol.4, pp.326-361, 1966. ,
Feedback equivalence for nonlinear systems and the time optimal control problem, SIAM J. Control Optim, vol.29, issue.6, pp.1300-1321, 1991. ,
Second order optimality conditions in the smooth case and applications in optimal control, ESAIM Control Optim. Calc. Var, vol.13, pp.207-236, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00086380
Singular trajectories and their role in control theory, Mathématiques & Applications, vol.40, 2003357. ,
Towards a geometric theory in the time minimal control of chemical batch reactors, SIAM J. Contr. Opt, vol.33, pp.1279-1311, 1995. ,
Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal, Forum Math, vol.5, issue.2, pp.111-159, 1993. ,
Time minimal control of batch reactors, ESAIM: Control, Optimisation and Calculus of Variations, vol.3, pp.407-467, 1998. ,
Classification générique de synthèses temps minimales avec cible de codimension un et applications, Annales de l'I.H.P. Analyse non linéaire 14 no, pp.55-102, 1997. ,
Time minimal synthesis for planar systems in the neighborhood of a terminal manifold of codimension one, J. of Mathematical Systems, Estimation and Control, vol.5, issue.3, pp.379-381, 1995. ,
, Optimal Control with Applications in Space and Quantum Dynamics, vol.5, 2012298.
, Optimal Syntheses for Control Systems on 2-D Manifolds, Mathématiques et Applications, vol.43, p.262, 2004.
Existence of Regular Syntheses for General Problems, J. Diff. Equations, vol.38, pp.317-343, 1980. ,
, Contrôle optimal géométrique : méthodes homotopiques et applications, Phd thesis, 2012.
Discontinuité des champs hamiltoniens et existence des solutions optimales en calcul des variations, Inst. HautesÉtudes Sci. Publ. Math, vol.47, pp.5-32, 1977. ,
On chemical kinetics of a certain class, Rational Mech. Anal, vol.46, issue.1, 1972. ,
Study of an optimum non linear system, J. Electronics Control, vol.15, pp.63-71, 1963. ,
Geometric control theory, Cambridge Studies in Advanced Mathematics, vol.52, 1997492. ,
General mass action kinetics, Arch. Ration. Mech. Anal, vol.47, issue.1, pp.81-116, 1972. ,
The high order maximal principle and its application to singular extremals, SIAM Journal on Control and Optimization, vol.15, issue.2, pp.256-293, 1977. ,
Geometric theory of extremals in optimal control problems. I. The fold and Maxwell case, Trans. Amer. Math. Soc, vol.299, issue.1, pp.225-243, 1987. ,
The ubiquity of Fuller's phenomenon, Nonlinear controllability and optimal control, pp.313-350, 1990. ,
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two, J. Dynam. Control Systems, vol.3, issue.2, pp.165-203, 1997. ,
Singular controls and chattering arcs in optimal control problems arising in biomedicine, Control & Cybernetics, vol.38, pp.1501-1523, 2009. ,
Singularities of smooth functions and maps, London Mathematical Society Lecture Note Series, vol.58, p.256, 1982. ,
Kinetic proofreading in T-cell receptor signal transduction Proc, Natl. Acad. Sci. USA, vol.92, pp.5042-5046, 1995. ,
, The mathematical theory of optimal processes, 1964.
, Geometric optimal control. Theory, methods and examples, Interdisciplinary Applied Mathematics, vol.38, 2012640.
Sontag Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction, IEEE Trans. Automat. Contr, vol.46, issue.7, pp.1028-1047, 2001. ,
Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, Nonlinear Controllability and Optimal Control, pp.1-20, 1990. ,
, Reaction kinetics: exercises, programs and theorems, 2018469.