Compositional construction of bounded error over-approximations of acyclic interconnected continuous dynamical systems

Abstract

We consider the problem of bounded time safety verification of interconnections of input-output continuous dynamical systems. We present a compositional framework for computing bounded error approximations of the complete system from those of the components. The main crux of our approach consists of capturing the input-output signal behaviors of a component using an abstraction predicate that represents the input-output sample behaviors corresponding to the signal behaviors. We define a semantics for the abstraction predicate that captures an over-approximation of the input-output signal behaviors of a component. Next, we define how to compose abstraction predicates of components to obtain an abstraction predicate for the composed system. We instantiate our compositional abstraction construction framework for linear dynamical systems by providing concrete methods for constructing the input-output abstraction predicates for the individual systems.