Symplectic methods for optimization and control, Geometry of Feedback and Optimal Control, pp.19-78, 1998. ,
A Hamitonian approach to strong minima in optimal control, Proceedings of Symposia in Pure Mathematics, pp.11-22, 1998. ,
Strong Optimality for a Bang-Bang Trajectory, SIAM Journal on Control and Optimization, vol.41, issue.4, pp.991-1014, 2002. ,
DOI : 10.1137/S036301290138866X
Control Theory from the Geometric Viewpoint, Control Theory and Optimization, II, 2004. ,
DOI : 10.1007/978-3-662-06404-7
Mathematical Methods of Classical Mechanics, Graduate Texts in Marhematics, 1989. ,
Computational sensitivity analysis for state constrained optimal control problems, Annals of Operations Research, vol.101, issue.1/4, pp.75-99, 2001. ,
DOI : 10.1023/A:1010960221295
Lectures on the Calculus of Variations, 1968. ,
Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method, SIAM Journal on Control, vol.4, issue.2, pp.326-361, 1966. ,
DOI : 10.1137/0304027
Second order optimality conditions in the smooth case and applications in optimal control, ESAIM: Control, Optimisation and Calculus of Variations, vol.13, issue.2, pp.207-236, 2007. ,
DOI : 10.1051/cocv:2007012
URL : https://hal.archives-ouvertes.fr/hal-00086380
A High Order Test for Optimality of Bang???Bang Controls, SIAM Journal on Control and Optimization, vol.23, issue.1, pp.38-48, 1985. ,
DOI : 10.1137/0323004
Semiconcave Functions, Hamilton- Jacobi Equations, and Optimal Control, Progress in Nonlinear Differential Equations and their Applications, 2004. ,
Optimization ? Theory and Applications. Problems with Ordinary Differential Equations, Applications of Mathematics, vol.17, 1983. ,
The Relationship between the Maximum Principle and Dynamic Programming, SIAM Journal on Control and Optimization, vol.25, issue.5, pp.1291-1311, 1987. ,
DOI : 10.1137/0325071
Second-Order Optimality Conditions in Sets of ${\text{L}}^\infty $ Functions with Range in a Polyhedron, SIAM Journal on Control and Optimization, vol.33, issue.5, pp.1603-1635, 1995. ,
DOI : 10.1137/S036301299224031X
Applications of the theory of quadratic forms in Hilbert space to the calculus of variations, Pacific Journal of Mathematics, vol.1, issue.4, pp.525-582, 1951. ,
DOI : 10.2140/pjm.1951.1.525
Parametrized Families of Extremals and Singularities in Solutions to the Hamilton--Jacobi--Bellman Equation, SIAM Journal on Control and Optimization, vol.37, issue.5, pp.1346-1371, 1999. ,
DOI : 10.1137/S0363012997319139
The Structure of Small-Time Reachable Sets in Low Dimensions, SIAM Journal on Control and Optimization, vol.27, issue.1, pp.120-147, 1989. ,
DOI : 10.1137/0327008
Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy, Journal of Optimization Theory and Applications, vol.37, issue.3, pp.609-637, 2002. ,
DOI : 10.1023/A:1016027113579
Sensitivity analysis for parametric control problems with control-state constraints, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.253-283, 1996. ,
DOI : 10.1109/CDC.1994.410938
Sensitivity analysis for state constrained optimal control problems, Discrete Contin, Dynam. Systems, vol.4, pp.241-272, 1998. ,
Sensitivity analysis for optimal control problems subject to higher order state constraints, Optimization with data perturbations, II, Ann, Oper. Res, vol.101, pp.43-73, 2001. ,
First and second order sufficient optimality conditions in mathematical programming and optimal control, Mathematical Programming Study, vol.14, pp.163-177, 1981. ,
DOI : 10.1007/BFb0120927
Second order sufficient conditions and sensitivity analysis for the controlled Rayleigh problem, in Parametric Optimization and Related Topics, pp.245-259, 1997. ,
Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods, in On-line Optimization of Large Scale Systems, pp.17-55, 2001. ,
Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods, vol.191, issue.3, pp.26-129, 2005. ,
DOI : 10.1002/oca.756
Second Order Sufficient Conditions for Optimal Control Problems with Free Final Time: The Riccati Approach, SIAM Journal on Control and Optimization, vol.41, issue.2, pp.380-403, 2002. ,
DOI : 10.1137/S0363012900377419
Second order optimality conditions for bang-bang control problems, Control and Cybernetics, vol.32, issue.3, pp.555-584, 2003. ,
Second Order Sufficient Conditions for Time-Optimal Bang-Bang Control, SIAM Journal on Control and Optimization, vol.42, issue.6, pp.2239-2263, 2004. ,
DOI : 10.1137/S0363012902402578
Second-order sufficient conditions for control problems with mixed control-state constraints, Journal of Optimization Theory and Applications, vol.32, issue.3, pp.649-667, 1995. ,
DOI : 10.1007/BF02192163
Calculus of Variations and Optimal Control, Transl. Math. Monogr, vol.180, 1998. ,
Sufficient conditions for relative minima of broken extremals in optimal control theory, Journal of Mathematical Analysis and Applications, vol.269, issue.1, pp.98-128, 2002. ,
DOI : 10.1016/S0022-247X(02)00008-2
Second order conditions for broken extremal In: Calculus of Variations and Optimal Control, pp.198-216, 1998. ,
Equivalence of second order optimality conditions for bang-bang control problems. Part 1: main results, Control and Cybernetics, vol.34, issue.3, pp.927-949, 2005. ,
Equivalence of second order optimality conditions for bang-bang control problems. Part 2: Proofs, variational derivatives and representations, Control and Cybernetics, vol.36, pp.555-584 ,
Transformation of quadratic forms to perfect squares for broken extremal, Set-Valued Anal, pp.209-232, 2002. ,
State-local optimality of a bang???bang trajectory: a Hamiltonian approach, Systems & Control Letters, vol.53, issue.3-4, pp.269-279, 2004. ,
DOI : 10.1016/j.sysconle.2004.05.005
The Mathematical Theory of Optimal Processes, 1962. ,
Morse-Sard type results in sub-Riemannian geometry, Mathematische Annalen, vol.6, issue.1, pp.145-159, 2005. ,
DOI : 10.1007/s00208-004-0622-2
URL : https://hal.archives-ouvertes.fr/hal-00086340
On the stabilization problem for nonholonomic distributions, Journal of the European Mathematical Society, vol.11, issue.2, pp.223-255, 2009. ,
DOI : 10.4171/JEMS/148
URL : https://hal.archives-ouvertes.fr/hal-00105488
The index of second variation of a control system, English transl. in: Math. USSR Sbornik, vol.113, issue.41, pp.464-486, 1980. ,
First- and Second-Order Sufficient Optimality Conditions for Bang-Bang Controls, SIAM Journal on Control and Optimization, vol.35, issue.1, pp.315-440, 1997. ,
DOI : 10.1137/S0363012993246191
Smooth Regularization of Bang-Bang Optimal Control Problems, IEEE -Transactions on Automatic Control, 2009. ,
DOI : 10.1109/TAC.2010.2047742
URL : https://hal.archives-ouvertes.fr/hal-00414680
Regularity properties of the minimum-time map, Nonlinear synthesis, Progr. Systems Control Theory, vol.9, pp.270-282, 1989. ,
Envelopes, conjugate points and optimal bangbang extremals, Proc. 1985 Paris Conf. on Nonlinear Systems, 1987. ,
DOI : 10.1007/978-94-009-4706-1_17
Regular synthesis and sufficient conditions for optimality, SIAM J. Control Optim, vol.39, issue.2, pp.359-410, 2000. ,
OnL1-minimization in optimal control and applications to robotics, Optimal Control Applications and Methods, vol.4, issue.6, pp.301-321, 2006. ,
DOI : 10.1002/oca.781
The Riccati Equation for Optimal Control Problems with Mixed State-Control Constraints: Necessity and Sufficiency, SIAM Journal on Control and Optimization, vol.32, issue.5, pp.1297-1321, 1994. ,
DOI : 10.1137/S0363012992233640