The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Ellipsoidal Techniques for Reachability Under State Constraints
SIAM Journal on Control and Optimization
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
A dynamic algorithm for approximate flow computations
Proceedings of the 14th international conference on Hybrid systems: computation and control
SpaceEx: scalable verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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In this paper, we present an approximation of the set of reachable states, called flowpipe, for a continuous system with affine dynamics. Our approach is based on a representation we call flowpipe sampling, which consists of a set of continuous, interval-valued functions over time. A flowpipe sampling attributes to each time point a polyhedral enclosure of the set of states reachable at that time point, and is capable of representing a nonconvex enclosure of a nonconvex flowpipe. The use of flowpipe samplings allows us to represent and approximate the nonconvex flowpipe efficiently. In particular, we can measure the error incurred by the initial approximation and by further processing such as simplification and convexification. A flowpipe sampling can be efficiently translated into a set of convex polyhedra in a way that minimizes the number of convex sets for a given error bound. When applying flowpipe approximation for the reachability of hybrid systems, a reduction in the number of convex sets spawned by each image computation can lead to drastic performance improvements.