Behavioural assume-guarantee contracts for linear dynamical systems

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.

Compositional Synthesis of Signal Temporal Logic Tasks via Assume-Guarantee Contracts

“…To tackle this complexity issue, different compositional approaches have been proposed for the analysis and control of interconnected systems. The two most commonly used approaches are based on input-output properties (e.g., small-gain or dissipativity properties) [5]- [7] and assume-guarantee contracts [6]- [14]. Both types of compositional approaches allow one to tackle large-scale complex systems in a divide and conquer manner, which considers a system as an interconnection of smaller subsystems, and breaks down complex large design or verification problems into sub-problems of manageable sizes.…”