Safety verification of finite real-time nonlinear hybrid systems using enhanced group preserving scheme

Abstract

In recent years, finite realtime nonlinear hybrid systems(FRNHS) have been widely used in the fields of biology, chemical control, embedded systems, etc. Its safety verification becomes more and more important. Compared with traditional hybrid systems, the safety verification of FRNHS is decidable, but the computational accuracy of its reach set demands higher. Group preserving scheme(GPS) achieves better accuracy and stabilization than traditional numerical algorithms due to its inherent properties in Minkowski space. This paper creatively applies GPS into the safety verification of FRNHS. Based on Euler method and GPS, we put forward the corresponding enhanced algorithms, which make the numerical computational accuracy higher. Through the experiment, the errors introduced by four various numerical computation methods are compared. The experimental results indicate that the proposed enhanced GPS in this paper has higher accuracy and can effectively make safety verification for FRNHS within the $$\epsilon \text {-}$$∈-error approximation.