Set-Theoretic Methods in Control, 2007. ,
DOI : 10.1007/978-3-319-17933-9
Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015. ,
DOI : 10.1109/IROS.2015.7353861
Positive invariant sets for fault tolerant multisensor control schemes, International Journal of Control, vol.40, issue.12, pp.2622-2640, 2010. ,
DOI : 10.1016/j.automatica.2004.01.014
URL : https://hal.archives-ouvertes.fr/hal-00293927
Low-Complexity Polytopic Invariant Sets for Linear Systems Subject to Norm-Bounded Uncertainty, IEEE Transactions on Automatic Control, vol.60, issue.5, pp.1416-1421, 2015. ,
DOI : 10.1109/TAC.2014.2352692
Invariant approximations of the minimal robust positively Invariant set, IEEE Transactions on Automatic Control, vol.50, issue.3, pp.406-410, 2005. ,
DOI : 10.1109/TAC.2005.843854
Robust control design with guaranteed state ultimate bound, Proceedings of the 3rd International Conference on Integrated Modeling and Analysis in Applied Control and Automation, 2007. ,
DOI : 10.1016/j.automatica.2007.10.022
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.4448
Invariant approximations of robustly positively invariant sets for constrained linear discrete-time systems subject to bounded disturbances, 2004. ,
A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality, Journal of Global Optimization, vol.39, issue.3, pp.395-407, 2009. ,
DOI : 10.1007/s10898-008-9334-6
Nonlinear Systems, Third Edition, 2002. ,
Applied nonlinear control, Englewood Cliffs (N.J, 1991. ,
The Lorenz Attractor Exists Comptes Rendus de l, Académie des Sciences, vol.328, issue.12, pp.1197-1202, 1999. ,
DOI : 10.1016/s0764-4442(99)80439-x
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.9324
Tinkerbell Is Chaotic, SIAM Journal on Applied Dynamical Systems, vol.10, issue.4, pp.1480-1501, 2011. ,
DOI : 10.1137/100819011
URL : https://hal.archives-ouvertes.fr/hal-00835176
Rigorously computed orbits of dynamical systems without the wrapping effect, Computing, vol.66, issue.Suppl, pp.47-67, 1998. ,
DOI : 10.1007/BF02684450
Cr-lohner algorithm, Schedae Informaticae, vol.20, pp.9-46, 2011. ,
Methods and Applications of Interval Analysis, 1979. ,
DOI : 10.1137/1.9781611970906
Validated explicit and implicit runge-kutta methods, Reliable Computing, vol.22, p.79, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01243053
Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY, The Journal of Logic and Algebraic Programming, vol.64, issue.1, pp.135-154, 2005. ,
DOI : 10.1016/j.jlap.2004.07.008
URL : https://hal.archives-ouvertes.fr/inria-00071850
The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems, Electronic Notes in Theoretical Computer Science, vol.223, issue.223, pp.87-102, 2008. ,
DOI : 10.1016/j.entcs.2008.12.033
Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques, Nonlinear Analysis: Hybrid Systems, vol.5, issue.2, pp.149-162, 2011. ,
DOI : 10.1016/j.nahs.2010.05.010
URL : https://hal.archives-ouvertes.fr/hal-00611996
Inner approximated reachability analysis, Proceedings of the 17th international conference on Hybrid systems: computation and control, HSCC '14, pp.163-172, 2014. ,
DOI : 10.1145/2562059.2562113
URL : https://hal.archives-ouvertes.fr/hal-01073731
Capture basin approximation using interval analysis, International Journal of Adaptive Control and Signal Processing, vol.49, issue.2-3, pp.264-272, 2011. ,
DOI : 10.1002/acs.1195
URL : https://hal.archives-ouvertes.fr/hal-00593261
Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4377-4394, 2010. ,
DOI : 10.1137/090749955
An Interval Approach for Stability Analysis: Application to Sailboat Robotics, IEEE Transactions on Robotics, vol.29, issue.1, 2012. ,
DOI : 10.1109/TRO.2012.2217794
URL : https://hal.archives-ouvertes.fr/hal-00738788
Invariance for ordinary differential equations, Mathematical Systems Theory, vol.7, issue.2, pp.353-372, 1967. ,
DOI : 10.1007/BF01695169
Combined Path-following and Obstacle Avoidance Control of a Wheeled Robot, The International Journal of Robotics Research, vol.26, issue.4, pp.361-375, 2007. ,
DOI : 10.1177/0278364907076790
URL : https://hal.archives-ouvertes.fr/lirmm-00127995
Linear Differential Game with Two Pursuers and One Evader, Advances in Dynamic Games, pp.209-226, 2011. ,
Computation of parametric barrier functions for dynamical systems using interval analysis, 53rd IEEE Conference on Decision and Control, pp.753-758, 2014. ,
DOI : 10.1109/CDC.2014.7039472
URL : https://hal.archives-ouvertes.fr/hal-01073673
Consistency techniques in ordinary differential equations Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus, Proceedings of the Fourth International Conference on Principles and Practice of Constraint Programming , ser. Lecture Notes in Computer Science, 1965. ,
Consistency in networks of relations, Consistency in networks of relations, pp.99-118, 1977. ,
DOI : 10.1016/0004-3702(77)90007-8
Static Analysis of Numerical Algorithms, Proceedings of SAS 06, pp.18-34, 2006. ,
DOI : 10.1007/11823230_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.403.8199
A Contractor Based on Convex Interval Taylor, Proc. of CPAIOR, pp.1-16, 2012. ,
DOI : 10.1007/978-3-642-29828-8_1
URL : https://hal.archives-ouvertes.fr/hal-00733848
Set-membership state estimation with fleeting data, Automatica, vol.48, issue.2, pp.381-387, 2012. ,
DOI : 10.1016/j.automatica.2011.11.004
URL : https://hal.archives-ouvertes.fr/hal-00670459
Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00845131
Localization Confidence Domains via Set Inversion on Short-Term Trajectory, IEEE Transactions on Robotics, vol.29, issue.5, 2013. ,
DOI : 10.1109/TRO.2013.2262776
URL : https://hal.archives-ouvertes.fr/hal-00877443
Contractor programming, Artificial Intelligence, vol.173, issue.11, pp.1079-1100, 2009. ,
DOI : 10.1016/j.artint.2009.03.002
URL : https://hal.archives-ouvertes.fr/hal-00428957
Abstract interpretation, Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '77, pp.238-252, 1977. ,
DOI : 10.1145/512950.512973
URL : https://hal.archives-ouvertes.fr/inria-00528590
Constructive Interval Disjunction, Proc. CP, Constraint Programming, pp.635-650, 2007. ,
DOI : 10.1007/978-3-540-74970-7_45
URL : https://hal.archives-ouvertes.fr/hal-00486726
On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis, Reliable Computing, vol.26, issue.6, pp.409-421, 2007. ,
DOI : 10.1007/s11155-007-9042-9
URL : https://hal.archives-ouvertes.fr/hal-00859290
Approximation of the viability kernel, Applied Mathematics & Optimization, vol.14, issue.3, 1994. ,
DOI : 10.1007/BF01204182
Outer approximation of attractors using an interval quantization, Reliable Computing, vol.19, pp.261-273, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00989626
A lattice-theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics, vol.5, issue.2, pp.285-309, 1955. ,
DOI : 10.2140/pjm.1955.5.285
URL : http://projecteuclid.org/download/pdf_1/euclid.pjm/1103044538
Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999. ,
DOI : 10.1016/S0096-3003(98)10083-8