Computing flow pipe of embedded hybrid systems using deep group preserving scheme

In this paper, we propose a novel methodology of numerical approximation to analyze flow of a nonlinear embedded hybrid system. For proving that all trajectories of a hybrid system do not enter an unsafe region, many classic numerical approaches such as Euler, Runge–Kutta methods for ordinary differential equations (ODEs) are applied, whereas, there exist several defects, including so-called spurious solutions and ghost fixed points. Moreover, to approximate the proper solution as much as possible, step size selection becomes especially important. In comparison, integrating group preserving scheme (GPS) which calculates true circumstance getting rid of spurious solutions and ghost fixed points, with neural network model which reduces numerical errors, deep GPS (DGPS) eliminates aforementioned adverse factors and gains better numerical approximation using a large time step size. The experimental results show that the proposed method makes safety verification for an embedded hybrid system well.