Composition of Behavioural Assume–Guarantee Contracts

The growing complexity of modern engineering systems necessitates a method for design and analysis that is inherently modular. Methods based on using contracts for system design have successfully tackled this issue for a variety of system classes, but mostly in the context of discrete software systems. Motivated by this, we present assume–guarantee contracts for continuous linear dynamical systems with inputs and outputs. Such contracts serve as system specifications through two aspects. The assumptions specify the dynamic behavior of the environment of the system, which provides inputs for it, whereas, the guarantees specify the desired dynamic behavior of the output of the system when interconnected with a relevant environment. This is formalized by utilizing the behavioral approach to system theory. We define and characterize notions of contract implementation and contract refinement, where the latter is used to compare contracts. We also define and characterize two notions of contract composition that allow one to reason about two types of system interconnections: series and feedback. The properties of refinement and composition allow contracts to be used for modular design and analysis.