Under-approximate flowpipes for non-linear continuous systems

Xin Chen Rwth, Sriram Sankaranarayanan, Erika Abraham
2014 2014 Formal Methods in Computer-Aided Design (FMCAD)  
We propose an approach for computing under-as well as over-approximations for the reachable sets of continuous systems which are defined by non-linear Ordinary Differential Equations (ODEs). Given a compact and connected initial set of states, described by a system of polynomial inequalities, we compute under-approximations of the set of states reachable over time. Our approach is based on a simple yet elegant technique to obtain an accurate Taylor model over-approximation for a backward
more » ... r a backward flowmap based on well-known techniques to over-approximate the forward map. Next, we show that this over-approximation can be used to yield both over-and underapproximations for the forward reachable sets. Based on the result, we are able to conclude "may" as well as "must" reachability to prove properties or conclude the existence of counterexamples. A prototype of the approach is implemented and its performance is evaluated over a reasonable number of benchmarks.
doi:10.1109/fmcad.2014.6987596 dblp:conf/fmcad/RwthSA14 fatcat:x45nwtjbuze7tgzk73du4fgp3a