Approximate Simulation Relations for Hybrid Systems

Abstract

Approximate simulation relations have been introduced as a powerful tool for the approximation of discrete and continuous systems. Approximation of purely discrete systems has traditionally been based on language inclusion and equivalence with notions such as simulation or bisimulation relations. These concepts have been useful for simplifying problems such as safety verification or controller synthesis. When dealing with continuous and hybrid systems, typically observed over the real numbers with possibly noisy observations, the usual notions based on ezact language inclusion is quite restrictive and not robust. The notion of language approximation is much more adequate in this context. It proposes a framework for system approximation based on approximate versions of simulation relations. Instead of requiring that the observations of a system and its approximation are and remain equal, one requires that they are and remain arbitrarily close.