C. Abdallah, D. M. Dawson, P. Dorato, and M. Jamshidi, Survey of robust control for rigid robots, IEEE Control Systems, vol.11, issue.2, p.2430, 1991.

U. Ali and M. Egerstedt, Optimal control of switched dynamical systems under dwell time constraints, 53rd IEEE Conference on Decision and Control, CDC 2014, p.46734678, 2014.

E. L. Allgower and K. Georg, Numerical Continuation Methods : An Introduction, 1990.

G. Allaire and S. M. Kaber, Algèbre linéaire numérique. Mathématiques pour le 2e cycle. Ellipses, 2002.

D. O. Brian, J. B. Anderson, and . Moore, Linear optimal control, 1971.

P. Apkarian and D. Noll, Nonsmooth h ? synthesis, IEEE Transactions on Automatic Control, vol.51, issue.1, p.7186, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01868781

P. Apkarian, D. Noll, J. Thevenet, and H. Tuan, A Spectral Quadratic-SDP Method with Applications to Fixed-Order H 2 and H ? Synthesis, European Journal of Control, vol.10, issue.6, p.527538, 2004.

. Arianespace, Ariane 5 User's Manual, 2016.

A. A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint. Control theory and optimization, 2004.

M. S. Branicky, V. S. Borkar, and S. K. Mitter, A unied framework for hybrid control : model and optimal control theory, IEEE Transactions on Automatic Control, vol.43, issue.1, p.3145, 1998.

B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory. Mathématiques et Applications, 2003.

B. Bonnard and M. Chyba, Singular trajectories and their role in control theory, Mathématiques & Applications, vol.40

. Springer-verlag, , 2003.

O. Bonnefon, J. Coville, and G. Legendre, Concentration phenomenon in some non-local equation, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01212846

C. Sorin, R. A. Bengea, and . Decarlo, Optimal control of switching systems

, Automatica, vol.41, issue.1, p.1127, 2005.

F. J. Beutler, The operator theory of the pseudo-inverse. I. Bounded operators, J. Math. Anal. Appl, vol.10, p.451470, 1965.

F. J. Beutler, The operator theory of the pseudo-inverse. II. Unbounded operators with arbitrary range, J. Math. Anal. Appl, vol.10, p.471493, 1965.

B. Bonnard, L. Faubourg, G. Launay, and E. Trélat, Optimal Control with State Constraints and the Space Shuttle Re-entry Problem, Journal of Dynamical and Control Systems, vol.9, issue.2, p.155199, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00086315

B. Bonnard, L. Faubourg, and E. Trélat, Optimal control of the atmospheric arc of a space shuttle and numerical simulations with multiple-shooting method, Math. Models Methods Appl. Sci, vol.15, issue.1, p.109140, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00086338

B. Bonnard, L. Faubourg, and E. Trélat, Mécanique céleste et contrôle des véhicules spatiaux. Mathématiques et Applications, 2006.

S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics. Society for Industrial and Applied Mathematics, 1994.

A. E. Bryson and Y. C. Ho, Applied Optimal Control : Optimization, Estimation and Control, 1975.

R. Dr and . Bulirsch, Priv-Doz Dr Hans Josef Pesch, and Dipl Math Oskar von Stryk. Combining direct and indirect methods in optimal control : Range maximization of a hang glider, Optimal control, p.273288, 1993.

C. Carrère, Optimization of an in vitro chemotherapy to avoid resistant tumours, Journal of Theoretical Biology, vol.413, p.2433, 2017.

M. Costa, R. C. Boldrini, and . Bassanezi, Optimal chemical control of populations developing drug resistance, Mathematical Medicine and Biology, vol.9, issue.3, p.215226, 1992.

J. Caillau, O. Cots, and J. Gergaud, Dierential continuation for regular optimal control problems, Optimization Methods and Software, vol.27, issue.2, p.177196, 2012.

J. Caillau, B. Daoud, and J. Gergaud, Minimum fuel control of the planar circular restricted three-body problem, Celestial Mechanics and Dynamical Astronomy, vol.114, issue.1, p.137150, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00743098

A. Nalin and . Chaturvedi, Rigid-body attitude control using rotation matrices for continuous, singularity-free control laws, 2011.

M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat, Sparse stabilization and optimal control of the Cucker-Smale model, Math. Control Relat. Fields, vol.3, issue.4, p.447466, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00861910

J. B. Caillau, J. Gergaud, J. Noailles, ;. Chyba, T. Haberkorn et al., 3D Geosynchronous Transfer of a Satellite : Continuation on the Thrust, Journal of Optimization Theory and Applications, vol.118, issue.3, p.6273, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00540254

M. Chyba, T. Haberkorn, R. N. Smith, and S. K. Choi, Design and implementation of time ecient trajectories for autonomous underwater vehicles, Ocean Engineering, vol.35, issue.1, p.6376, 2008.

M. Cerf, T. Haberkorn, and E. Trélat, Continuation from a at to a round earth model in the coplanar orbit transfer problem, Optimal Control Applications and Methods, vol.33, issue.6, p.654675, 2012.

M. Chupin, T. Haberkorn, and E. Trélat, Low-Thrust Lyapunov to Lyapunov and Halo to Halo with L 2-Minimization, ESAIM : Mathematical Modelling and Numerical Analysis, vol.51, issue.3, p.965996, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01223738

F. H. Clarke, Optimization and Nonsmooth Analysis, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, 1990.

R. H. Chisholm, T. Lorenzi, and J. Clairambault, Cell population heterogeneity and evolution towards drug resistance in cancer : Biological and mathematical assessment, theoretical treatment optimisation, Biochimica et Biophysica Acta (BBA)-General Subjects, vol.1860, issue.11, p.26272645, 2016.

H. Rebecca, T. Chisholm, A. Lorenzi, and . Lorz, Eects of an advection term in nonlocal lotkavolterra equations, Communications in Mathematical Sciences, vol.14, issue.4, p.11811188, 2016.

J. Michel-coron, Global asymptotic stabilization for controllable systems without drift, Mathematics of Control, Signals and Systems, vol.5, issue.3, p.295312, 1992.

J. Coville, Convergence to equilibrium for positive solutions of some mutationselection model, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00855334

X. Cabré and J. Roquejore, The inuence of fractional diusion in sher-kpp equations, Communications in Mathematical Physics, vol.320, issue.3, p.679722, 2013.

. Odo-diekmann, A beginner's guide to adaptive dynamics, vol.63, p.4786, 2004.

C. Howard and D. , Orbital mechanics for engineering students, volume Elsevier aerospace engineering series, 2010.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, State-space solutions to standard h 2 and h ? control problems, IEEE Transactions on Automatic Control, vol.34, issue.8, p.831847, 1989.

O. Diekmann, P. Jabin, S. Mischler, and B. Perthame, The dynamics of adaptation : an illuminating example and a Hamilton-Jacobi approach, Theoretical Population Biology, vol.67, issue.4, p.257271, 2005.

A. V. Dmitruk and A. M. Kaganovich, The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control Letters, vol.57, issue.11, pp.964-970, 2008.

A. V. Dmitruk and A. M. Kaganovich, Maximum principle for optimal control problems with intermediate constraints, Computational Mathematics and Modeling, vol.22, issue.2, p.180215, 2011.

B. Novel and M. Lara, Control Theory for Engineers : A Primer. Environmental Science and Engineering / Environmental Engineering, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00964981

J. Doyle and G. Stein, Multivariable feedback design : Concepts for a classi

, cal/modern synthesis, IEEE Transactions on Automatic Control, vol.26, issue.1, p.416, 1981.

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL : A Modeling Language for Mathematical Programming, 1993.

R. Fourer, M. David, B. W. Gay, and . Kernighan, A modeling language for mathematical programming, vol.36, p.519554, 2002.

A. T. Fuller, Study of an Optimum Non-linear Control System, Journal of Electronics and Control, vol.15, issue.1, p.6371, 1963.

P. Gahinet and P. Apkarian, A linear matrix inequality approach to h ? control, International Journal of Robust and Nonlinear Control, vol.4, issue.4, p.421448, 1994.

P. Gahinet, A convex parametrization of h ? suboptimal controllers, Proceedings of the 31st IEEE Conference on Decision and Control, vol.1, p.937942, 1992.

J. Ge, P. M. Frank, and C. Lin, Robust H ? state feedback control for linear systems with state delay and parameter uncertainty, Automatica, vol.32, issue.8, pp.1183-1185, 1996.

J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem, ESAIM : COCV, vol.12, issue.2, p.294310, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00367592

J. Greene, O. Lavi, D. Michael-m-gottesman, and . Levy, The impact of cell density and mutations in a model of multidrug resistance in solid tumors, Bulletin of mathematical biology, vol.76, issue.3, p.627653, 2014.

M. Garavello and B. Piccoli, Hybrid necessary principle, vol.43, p.18671887, 2005.

M. Garavello and B. Piccoli, Hybrid Necessary Principle, SIAM Journal on Control and Optimization, vol.43, issue.5, p.18671887, 2005.

G. H. Golub and C. F. Van-loan, Matrix computations. Johns Hopkins Studies in the Mathematical Sciences, 2013.

T. Haberkorn, P. Martinon, and G. J. , Low Thrust Minimum-Fuel Orbital Transfer : A Homotopic Approach, Journal of Guidance, Control, and Dynamics, vol.27, issue.6, p.10461060, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00271161

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Dierential Equations I : Nonsti Problems, Springer Series in Computational Mathematics, 2008.

K. C. Koh and H. S. Cho, A smooth path tracking algorithm for wheeled mobile robots with dynamic constraints, J. Intell. Robotics Syst, vol.24, issue.4, p.367385, 1999.

H. K. Khalil, Nonlinear systems, 1992.

H. Kwakernaak and R. Sivan, Linear optimal control systems, 1972.

J. Arthur, H. Krener, and . Schättler, The structure of small-time reachable sets in low dimensions, SIAM J. Control Optim, vol.27, issue.1, p.120147, 1989.

M. Kimmel and A. ‘wierniak, Control theory approach to cancer chemotherapy : Beneting from phase dependence and overcoming drug resistance, Tutorials in Mathematical Biosciences III, vol.1872, p.185221, 2006.

M. Krstic and P. Tsiotras, Inverse optimal stabilization of a rigid spacecraft, IEEE Transactions on Automatic Control, vol.44, issue.5, p.10421049, 1999.

I. Kupka, Geometric theory of extremals in optimal control problems. I. The fold and Maxwell case, Trans. Amer. Math. Soc, vol.299, issue.1, p.225243, 1987.

T. Lorenzi, H. Rebecca, L. Chisholm, B. Desvillettes, and . Hughes, Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to uctuating environments, Journal of theoretical biology, vol.386, p.166176, 2015.

F. Lin, Robust Control Design : An Optimal Control Approach, 2007.

A. Lorz, T. Lorenzi, and J. Clairambault, Eects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors, 2013.

A. Lorz, T. Lorenzi, and J. Clairambault, Modeling the eects of space structure and combination therapies on phenotypic heterogeneity and drug resistance in solid tumors, Bulletin of mathematical biology, vol.77, issue.1, p.122, 2015.

A. Lorz, T. Lorenzi, M. E. Hochberg, J. Clairambault, and B. Perthame, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies, ESAIM : Mathematical Modelling and Numerical Analysis, vol.47, issue.02, p.377399, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00714274

H. Li, X. Li, and J. Yong, Optimal Control Theory for Innite Dimensional Systems, chapter 4-Necessary conditions for optimal control, Systems & control : foundations & applications. Birkhäuser, 1995.

E. B. Lee and L. Markus, Foundations of optimal control theory, chapter 4-The maximal principle and the existence of optimal controllers for nonlinear processes. SIAM series in applied mathematics, 1967.

E. B. Lee and L. Markus, Foundations of optimal control theory. SIAM series in applied mathematics, 1967.

H. Leman, S. Meleard, and S. Mirrahimi, Inuence of a spatial structure on the long time behavior of a competitive lotka-volterra type system, vol.20, p.2014

U. Ledzewicz and H. Schättler, Drug resistance in cancer chemotherapy as an optimal control problem, Discrete and Continuous Dynamical Systems Series B, vol.6, issue.1, p.129, 2006.

U. Ledzewicz and H. Schättler, On optimal chemotherapy for heterogeneous tumors, Journal of Biological Systems, vol.22, issue.02, p.177197, 2014.

L. Qiang and W. Bong, Robust time-optimal control of uncertain exible spacecraft, Journal of Guidance, Control, and Dynamics, vol.15, issue.3, p.597604, 1992.

X. Li and J. Yong, Optimal control theory for innite dimensional systems, 2012.

H. Maurer, C. Büskens, J. R. Kim, and C. Y. Kaya, Optimization methods for the verication of second order sucient conditions for bangbang controls, Optimal Control Applications and Methods, vol.26, issue.3, p.129156, 2005.

D. Mcfarlane and K. Glover, A loop-shaping design procedure using h innity synthesis, IEEE Transactions on Automatic Control, vol.37, issue.6, p.759769, 1992.

H. Maurer and N. P. Osmolovskii, Second Order Sucient Conditions for Time-Optimal Bang-Bang Control, SIAM Journal on Control and Optimization, vol.42, issue.6, p.22392263, 2004.
DOI : 10.1137/s0363012902402578

R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited, Systems & Control Letters, vol.18, issue.2, p.9398, 1992.

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The mathematical theory of optimal processes. Translated from the Russian by K. N. Bibliographie Trirogo, 1962.

C. Pouchol, J. Clairambault, A. Lorz, and E. Trélat, Asymptotic analysis and optimal control of an integro-dierential system modelling healthy and cancer cells exposed to chemotherapy, Journal de Mathématiques Pures et Appliquées, 2017.

B. Perthame, Transport equations in biology, 2006.

H. Pesch, A practical guide to the solution of real-life optimal control problems, Control and cybernetics, vol.23, issue.1, 1994.

B. Piccoli, Necessary conditions for hybrid optimization, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), vol.1, p.410415, 1999.

H. Poincaré, Sur le probleme des trois corps et les équations de la dynamique, Acta Mathematica. F. & G. Beijer, p.1890

C. Pouchol and E. Trélat, Global stability with selection in integrodierential lotka-volterra systems modelling trait-structured populations, 2017.

M. S. Shaikh and P. E. Caines, Optimality zone algorithms for hybrid systems computation and control : From exponential to linear complexity, Proceedings of the 44th IEEE Conference on Decision and Control, p.14031408, 2005.

M. S. Shaikh and P. E. Caines, On the hybrid optimal control problem : Theory and algorithms, IEEE Transactions on Automatic Control, vol.52, issue.9, p.15871603, 2007.

H. Schättler, On the local structure of time-optimal bang-bang trajectories in R 3, SIAM J. Control Optim, vol.26, issue.1, p.186204, 1988.

J. Héctor, V. Sussmann, and . Jurdjevic, Controllability of nonlinear systems, Journal of Dierential Equations, vol.12, issue.1, p.95116, 1972.

H. Schättler and U. Ledzewicz, Optimal Control for Mathematical Models of Cancer Therapies, 2015.

C. J. Silva and E. Trélat, Smooth Regularization of Bang-Bang Optimal Control Problems, IEEE Trans. Automat. Contr, vol.55, issue.11, p.24882499, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00414680

C. Silva and E. Trélat, Smooth regularization of bang-bang optimal control problems, IEEE Trans. Automat. Control, vol.55, issue.11, p.24882499, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00414680

J. Héctor and . Sussmann, A nonsmooth hybrid maximum principle, p.325354, 1999.

H. J. Sussmann, Set-valued dierentials and the hybrid maximum principle

, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), vol.1, p.558563, 2000.

T. Singh and S. R. Vadali, Robust time-optimal control-Frequency domain approach, Journal of Guidance, Control, and Dynamics, vol.17, issue.2, p.346353, 1994.

E. Trélat, Some Properties of the Value Function and Its Level Sets for Ane Control Systems with Quadratic Cost, Journal of Dynamical and Control Systems, vol.6, issue.4, p.511541, 2000.

E. Trélat, Contrôle optimal, Contrôle Optimal. Mathématiques Concrètes

P. Vuibert, Théorie & applications, 2005.

E. Trélat, Contrôle optimal. Mathématiques Concrètes

P. Vuibert, Théorie & applications, 2005.

E. Trélat, Optimal control and applications to aerospace : Some results and challenges, Journal of Optimization Theory and Applications, vol.154, issue.3, p.713758, 2012.

H. Tan, S. Shu, and F. Lin, An optimal control approach to robust tracking of linear systems, International Journal of Control, vol.82, issue.3, p.525540, 2009.

O. Stryk and R. Bulirsch, Direct and indirect methods for trajectory optimization, Annals of Operations Research, vol.37, issue.1, p.357373, 1992.

Y. Wardi, Optimal control of switched-mode dynamical systems. {IFAC} Proceedings Volumes, vol.45, 2012.

A. Wächter, T. Lorenz, and . Biegler, On the implementation of an interior-point lter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, vol.106, issue.1, p.2557, 2006.

A. Wächter, . Lorenz, and . Biegler, On the implementation of an interior-point lter line-search algorithm for large-scale nonlinear programming. Mathematical programming, vol.106, p.2557, 2006.

T. Windeknecht, Optimal stabilization of rigid body attitude, Journal of Mathematical Analysis and Applications, vol.6, issue.2, p.325335, 1963.

W. Bong, S. Ravi, and L. Qiang, Robust time-optimal control of uncertain structural dynamic systems, Journal of Guidance, Control, and Dynamics, vol.16, issue.5, p.980983, 1993.

X. Xu and P. J. Antsaklis, Optimal control of switched systems : new results and open problems, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), vol.4, p.26832687, 2000.

L. Xie, E. De-souza, and C. , Robust h inn ; control for linear systems with norm-bounded time-varying uncertainty, IEEE Transactions on Automatic Control, vol.37, issue.8, p.11881191, 1992.

S. Xu, P. Shi, Y. Chu, and Y. Zou, Robust stochastic stabilization and control of uncertain neutral stochastic time-delay systems, Journal of Mathematical Analysis and Applications, vol.314, issue.1, p.116, 2006.

K. H. You and E. B. Lee, Robust, near time-optimal control of nonlinear second order systems with model uncertainty, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162), p.232236, 2000.

F. Zhu and P. J. Antsaklis, Optimal control of hybrid switched systems : A brief survey, Discrete Event Dynamic Systems, vol.25, issue.3, p.345364, 2015.

G. Zames, Feedback and optimal sensitivity : Model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Transactions on Automatic Control, vol.26, issue.2, p.301320, 1981.
DOI : 10.1109/tac.1981.1102603

K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Feher/Prentice Hall Digital an, 1996.

J. Zhu, E. Trélat, and M. Cerf, Minimum time control of the rocket attitude reorientation associated with orbit dynamics, SIAM J. Control Optim, vol.54, issue.1, p.391422, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01170274

J. Zhu, E. Trélat, and M. Cerf, Planar tilting maneuver of a spacecraft : singular arcs in the minimum time problem and chattering, Discrete and Continuous Dynamical Systems-Series B, vol.16, issue.4, p.13471388, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01145876