M. A. Informationstechnik and T. München, Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars, pp.91-20100715, 2010.

M. Althoff and B. H. Krogh, Zonotope bundles for the efficient computation of reachable sets, IEEE Conference on Decision and Control and European Control Conference, pp.6814-6821, 2011.
DOI : 10.1109/CDC.2011.6160872

M. Assellaou, O. Bokanowski, A. Désilles, and H. Zidani, Value function and optimal trajectories for a maximum running cost control problem with state constraints. Application to an abort landing problem, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01484190

J. Aubin, A. M. Bayen, and P. Saint-pierre, Viability theory. New directions, in Systems & Control: Foundations & Applications, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00636570

J. Aubin and A. Cellina, Differential Inclusions, volume 264 of Grundlehren der mathematischen Wissenschaften, 1984.

R. Baier, M. Gerdts, and I. Xausa, Approximation of reachable sets using optimal control algorithms, Numerical Algebra, Control and Optimization, vol.3, issue.3, pp.519-548, 2013.
DOI : 10.3934/naco.2013.3.519
URL : https://hal.archives-ouvertes.fr/inria-00637880

M. Bardi and I. Capuzzo-dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Systems & Control: Foundations & Applications, With appendices by Maurizio Falcone and Pierpaolo Soravia, 1997.
DOI : 10.1007/978-0-8176-4755-1

E. N. Barron and H. Ishii, The Bellman equation for minimizing the maximum cost, Nonlinear Analysis: Theory, Methods & Applications, vol.13, issue.9, pp.1067-1090, 1989.
DOI : 10.1016/0362-546X(89)90096-5

O. Bokanowski, A. Désilles, H. Zidani, and J. Zhao, User's guide for the ROC- HJ solver: Reachability, Optimal Control, and Hamilton-Jacobi equations, 2017.

O. Bokanowski, N. Forcadel, and H. Zidani, Reachability and Minimal Times for State Constrained Nonlinear Problems without Any Controllability Assumption, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4292-4316, 2010.
DOI : 10.1137/090762075
URL : https://hal.archives-ouvertes.fr/hal-00395589

O. Bokanowski and H. Zidani, MINIMAL TIME PROBLEMS WITH MOVING TARGETS AND OBSTACLES, Proceedings of the 18th IFAC World Congress, pp.2589-2593, 2011.
DOI : 10.3182/20110828-6-IT-1002.02261
URL : https://hal.archives-ouvertes.fr/inria-00629166

M. G. Crandall and P. Lions, Two approximations of solutions of Hamilton-Jacobi equations, Mathematics of Computation, vol.43, issue.167, pp.1-19, 1984.
DOI : 10.1090/S0025-5718-1984-0744921-8

A. Désilles, H. Zidani, and E. Crück, Collision analysis for an UAV, AIAA Guidance, Navigation, and Control Conference, pp.13-16, 2012.
DOI : 10.1007/BF01204182

M. Falcone, Numerical solution of dynamic programming equations, Optimal Control and Viscosity Solutions of Hamilton- Jacobi-Bellman Equations, Systems & Control: Foundations & Applications, pp.471-504, 1997.

M. Falcone and R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations, Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.133, 2014.
DOI : 10.1137/1.9781611973051
URL : https://hal.archives-ouvertes.fr/hal-00916055

P. Fayolle, A. Pasko, and B. Schmitt, SARDF: Signed Approximate Real Distance Functions in Heterogeneous Objects Modeling, Lecture Notes in Comput. Sci, vol.4889, pp.118-141, 2008.
DOI : 10.1007/978-3-540-68443-5_5

M. Gerdts, Solving mixed-integer optimal control problems by branch&bound: a case study from automobile test-driving with gear shift, Optimal Control Applications and Methods, vol.83, issue.1, pp.1-18, 2005.
DOI : 10.1007/978-3-642-86470-4

M. Gerdts, A variable time transformation method for mixed-integer optimal control problems, Optimal Control Applications and Methods, vol.83, issue.3, pp.169-182, 2006.
DOI : 10.1007/978-3-642-80684-1

M. Gerdts, User's Guide for OCPID-DAE1 ? Optimal Control and Parameter Identification with Differential-Algebraic Equations of Index 1, 2013.

M. Gerdts and I. Xausa, Avoidance trajectories using reachable sets and parametric sensitivity analysis Revised Selected Papers, System Modeling and Optimization. 25th IFIP TC 7 Conference on System Modeling and Optimization, pp.12-16, 2011.
DOI : 10.1007/978-3-642-36062-6_49

E. G. Gilbert, D. W. Johnson, S. Sathiya, and . Keerthi, A fast procedure for computing the distance between complex objects in three-dimensional space, IEEE Journal on Robotics and Automation, vol.4, issue.2, pp.193-203, 1988.
DOI : 10.1109/56.2083

J. C. Hart, Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer, pp.527-545, 1996.

R. Kianfar, P. Falcone, and J. Fredriksson, Reachability analysis of cooperative adaptive cruise controller, 2012 15th International IEEE Conference on Intelligent Transportation Systems, pp.1537-1542, 2012.
DOI : 10.1109/ITSC.2012.6338839

C. and L. Guernic, Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics, École Doctorale Mathématiques, Sciences et Technologies de l'Information, p.422569, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00422569

I. M. Mitchell, A. M. Bayen, and C. J. Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, vol.50, issue.7, pp.50947-957, 2005.
DOI : 10.1109/TAC.2005.851439

J. Nilsson, J. Fredriksson, and A. C. Ödblom, Verification of collision avoidance systems using reachability analysis in Cape Tow, Proceedings of the 19th IFAC World Congress, pp.10676-10681, 2014.

S. Osher and C. Shu, High-Order Essentially Nonoscillatory Schemes for Hamilton???Jacobi Equations, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.907-922, 1991.
DOI : 10.1137/0728049

J. D. Rowland and R. B. Vinter, Construction of optimal feedback controls, Systems & Control Letters, vol.16, issue.5, pp.357-367, 1991.
DOI : 10.1016/0167-6911(91)90057-L

C. Shu, Survey on discontinuous Galerkin methods for Hamilton-Jacobi equations, Recent Advances in Scientific Computing and Applications, pp.323-330
DOI : 10.1090/conm/586/11653

P. Soravia, Nonlinear H? control Bardi and I. Capuzzo-Dolcetta, editors, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems & Control: Foundations & Applications, in Appendix B, pp.505-531, 1997.

I. Xausa, Verification of Collision Avoidance Systems using Optimal Control and Sensitivity Analysis, 2015.

I. Xausa, R. Baier, M. Gerdts, M. Gonter, and C. Wegwerth, Avoidance trajectories for driver assistance systems via solvers for optimal control problems, Proceedings on the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012), 2012.
URL : https://hal.archives-ouvertes.fr/hal-00712878