Series of abstractions for hybrid automata

Abstract

We present a technique based on the use of the quantifier elimination decision procedure for real closed fields and simple theorem proving to construct a series of successively finer qualitative abstractions of hybrid automata. The resulting abstractions are always discrete transition systems which can then be used by any traditional analysis tool. The constructed abstractions are conservative and can be used to establish safety properties of the original system. Our technique works on linear and non-linear polynomial hybrid systems, that is, the guards on discrete transitions and the continuous flows in all modes can be specified using arbitrary polynomial expressions over the continuous variables. We have a prototype tool in the SAL environment [13] which is built over the theorem prover PVS [19]. The technique promises to scale well to large and complex hybrid systems.