Polynomial phase-portrait reachable set approximation for hybrid automata

Model transformation is to construct a computable automaton to over-approximate the original automaton. In this paper, the linear phase-portrait approximation is extended to the polynomial phase-portrait approximation, and the construction process of polynomial phase-portrait approximation is presented. To refine the coarse abstract model, the model can be gradually refined by increasing the order of polynomials or restricting errors. Finally, the effects of the two refinement approaches are compared by simulation.