Flowpipe approximation and clustering in space-time

Abstract

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.

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

“…Note that SpaceEx is a more general-purpose tool, while the approach here requires that all executions eventually reach the guard set. For SpaceEx, we used the space-time clustering analysis scenario [29], and, for each of the models, we tried to maximize the size of the initial set while ensuring the specification was not violated and the analysis time was less than 20 minutes. For the n = 11 model, using a flowpipe-tolerance parameter of 0.0005, in 541 seconds we could successfully analyze the system with up to 1.1% of the desired initial set size (1.2% violated the error specifi- Fig.…”

Conic Abstractions for Hybrid Systems

“…In the first, we have performed a scalability test using purely continuous systems given by random matrices of increasing size and for increasing precision of the analysis. In the second, we have considered the room heating benchmark and compared against SpaceEx under scenarios supp and stc and PHAVer [16,36,20].…”

Combining zonotopes and support functions for efficient reachability analysis of linear systems

“…The switched dynamics are such that overapproximation errors quickly accumulate and lead to diverging results. We use the support function implementation from [22] because it delivers higher precision than the simple algorithm from Sect. III.…”