%0 Journal Article %T Computing an Inner and an Outer Approximation of the Viability Kernel %+ Lab-STICC_ENSTAB_CID_IHSEV %+ Pôle STIC_OSM %+ Lab-STICC_ENSTAB_CID_PRASYS %A Monnet, Dominique %A Ninin, Jordan %A Jaulin, Luc %< avec comité de lecture %@ 1385-3139 %J Reliable Computing %I Springer Verlag %V 22 %8 2016-08-29 %D 2016 %K interval analysis %K viability kernel %Z Computer Science [cs]/Operations Research [cs.RO] %Z Mathematics [math]/Optimization and Control [math.OC]Journal articles %X The viability kernel corresponds to the set of all state vectors of a controlled dynamic system that are viable, i.e., such that there exists an input such that the system will not enter inside a forbidden zone. In this paper, we propose a method which computes an inner and an outer approximation of the viability kernel in a guaranteed way. Our method is based on interval analysis and uses the notions of V-viability and capture basin. We illustrate our approach on the car on the hill problem. A software package has been developed to solve any 2D-problem. %G English %2 https://hal.science/hal-01366752/document %2 https://hal.science/hal-01366752/file/Viability_Kernel_FINAL.pdf %L hal-01366752 %U https://hal.science/hal-01366752 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ INSMI %~ ENIB %~ LAB-STICC_ENIB %~ LAB-STICC %~ TDS-MACS %~ INSTITUTS-TELECOM