10.1007/978-3-319-96145-3_24
Kong, Hui
Hui
Kong0000-0002-3066-6941
Bartocci, Ezio
Ezio
Bartocci
Henzinger, Thomas A
Thomas A
Henzinger0000−0002−2985−7724
Reachable set over-approximation for nonlinear systems using piecewise barrier tubes
LNCS
Springer
2018
2018-12-11T11:44:51Z
2020-01-21T13:17:34Z
conference
https://research-explorer.app.ist.ac.at/record/142
https://research-explorer.app.ist.ac.at/record/142.json
5591566 bytes
application/pdf
We address the problem of analyzing the reachable set of a polynomial nonlinear continuous system by over-approximating the flowpipe of its dynamics. The common approach to tackle this problem is to perform a numerical integration over a given time horizon based on Taylor expansion and interval arithmetic. However, this method results to be very conservative when there is a large difference in speed between trajectories as time progresses. In this paper, we propose to use combinations of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse box which is big enough to contain the segment is constructed using sampled simulation and then in the box we compute by linear programming a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe. The benefit of using PBT is that (1) BT is independent of time and hence can avoid being stretched and deformed by time; and (2) a small number of BTs can form a tight over-approximation for the flowpipe, which means that the computation required to decide whether the BTs intersect the unsafe set can be reduced significantly. We implemented a prototype called PBTS in C++. Experiments on some benchmark systems show that our approach is effective.