Behavioural assume-guarantee contracts for linear dynamical systems

TL;DR

This paper introduces a behavioural framework for specifying, implementing, and refining assume-guarantee contracts in continuous-time linear dynamical systems, aiding the design of complex engineering systems.

Contribution

It formalizes contracts for linear systems, characterizes implementation and refinement, and provides necessary conditions for implementation existence, with practical illustration.

Findings

Characterization of contract implementation

Necessary conditions for implementation existence

Contract refinement and conjunction analysis

Abstract

Motivated by the growing requirements on the operation of complex engineering systems, we present contracts as specifications for continuous-time linear dynamical systems with inputs and outputs. A contract is defined as a pair of assumptions and guarantees, both characterized in a behavioural framework. The assumptions encapsulate the available information about the dynamic behaviour of the environment in which the system is supposed to operate, while the guarantees express the desired dynamic behaviour of the system when interconnected with relevant environments. In addition to defining contracts, we characterize contract implementation, and we find necessary conditions for the existence of an implementation. We also characterize contract refinement, which is used to characterize contract conjunction in two special cases. These concepts are then illustrated by an example of a vehicle following system.