Approximating continuous systems by timed automata

Abstract

In this work we develop a new technique for over-approximating (in the sense of timed trace inclusion) continuous dynamical systems by timed automata. This technique refines commonly-used discrete abstractions which are often too coarse to be useful. The essence of our technique is the partition of the state space into cubes and the allocation of a clock for each dimension. This allows us to get much better approximations of the behavior. We specialize this technique to multi-affine systems, a class of nonlinear systems of primary importance for the analysis of biochemical systems and demonstrate its applicability on an example taken from synthetic biology. © 2008 Springer-Verlag Berlin Heidelberg.