Contracts as specifications for dynamical systems in driving variable form

TL;DR

This paper extends assume/guarantee contract theory to continuous-time control systems, offering a formal and flexible way to specify, verify, and compare control specifications for complex engineering systems.

Contribution

It introduces a novel contract framework for continuous-time systems, expanding the applicability of contract theory beyond discrete systems and enabling richer specifications.

Findings

Contracts can be verified for implementation correctness

Framework supports comparison of different contracts

Illustrated with a vehicle following system example

Abstract

This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations of control specifications, providing an alternative to specifications in terms of dissipativity properties or set-invariance. The framework has the potential to capture a richer class of specifications more suitable for complex engineering systems. The proposed contracts are supported by results that enable the verification of contract implementation and the comparison of contracts. These results are illustrated by an example of a vehicle following system.