On the Generation of Timed Discrete Approximations for Continuous Systems

Abstract

In this contribution we present two procedures to systematically derive timed discrete approximations from continuous models. Both methods are based on a rectangular state space partition and aim at mapping continuous dynamic behaviours described by ODE-systems with switched inputs onto timed state transition systems: In the first approach the transitions between the discrete states are determined by analysing the flow between rectangular cells of the state space. The second one uses numerical integration of the ODE-system between partitions of the boundaries of the cells. The application of both approaches is illustrated by a chemical process example. The paper discusses completeness and consistency properties of the approximation mappings as well as issues of accuracy and computational effort.