Contents I Introduction
Hybrid systems are dynamic systems with the processes of continuous variables and discrete events existing and exchanging informatione.g. digital embedded system. One of the primary problems of hybrid systems is to determine the reachable set, but the accurate computation of reachable sets is confined to some simple hybrid systems, such as timed hybrid automata and rectangular automata. For general hybrid systems, the accurate computation of reachable set is not decidable, even not computable [1]. Based on this problem, many methods have been proposed to determine the approximate reachable set and to derive the system's properties [2]–[3] [4] [5]. In the field of safety validation, the decision of the over-approximation to the reachable set can deduce the safety of the system. Model transformation is to construct a computable approximate hybrid automaton, whose reachable set over-approximates the original hybrid automaton. Thomos. A. Henzinger proposed the concept of phase-portrait approximation and constructed linear phase-portrait approximation automaton in which the reachable set over-approximates the original hybrid system in [6]. In [7], polynomial automata are constructed based on Taylor formula. This approach is not phase-portrait, and there are some limits to improve the approximate accuracy just by increasing the power series of polynomials. So the linear phase-portrait approximation is extended to polynomial phase-portrait approximation and the construction approach of polynomial phase-portrait approximation automata is proposed in this paper.
