Behavioural assume-guarantee contracts for linear dynamical systems

Abstract

We present assume-guarantee contracts for continuous-time linear dynamical systems with inputs and outputs. These contracts are used to express specifications on the dynamic behaviour of a system. Contrary to existing approaches, we use simulation to compare the dynamic behaviour of two systems. This has the advantage of being supported by efficient numerical algorithms for verification as well as being related to the rich literature on (bi)simulation based techniques for verification and control, such as those based on (discrete) abstractions. Using simulation, we define contract implementation and a notion of contract refinement. We also define a notion of series composition for contracts, which allows us to reason about the series interconnection of systems on the basis of the contracts on its components. Together, the notions of refinement and composition allow contracts to be used for modular design and analysis of interconnected systems.

Series composition of simulation-based assume-guarantee contracts for linear dynamical systems

“…Contract-based design has proven to be an effective method for modular design and analysis of complex interconnected systems [1], [2], [3]. Motivated by this, we present assume-guarantee contracts for continuous-time linear dynamical systems with inputs and outputs in the spirit of [4], [5]. These contracts are defined as a pair of systems called assumptions and guarantees.…”

“…The assumptions capture the available information about the dynamic behaviour of the environment in which the system is supposed to operate, while the guarantees specify the desired dynamic behaviour of the system when interconnected with a compatible environment. In contrast to [4], [5], we formalize this with the notion of simulation, which is used to compare the dynamic behaviour of two systems.…”

“…The contracts in this paper draw inspiration from the contracts introduced in [4], [5]. The main difference with [4], [5], is that here we use simulation instead of inclusion of external behaviour as a means of comparing system behaviour.…”

“…The contracts in this paper draw inspiration from the contracts introduced in [4], [5]. The main difference with [4], [5], is that here we use simulation instead of inclusion of external behaviour as a means of comparing system behaviour. As mentioned before, this enables the use of efficient computational tools that are not available for the contracts in [4], [5].…”

“…The main difference with [4], [5], is that here we use simulation instead of inclusion of external behaviour as a means of comparing system behaviour. As mentioned before, this enables the use of efficient computational tools that are not available for the contracts in [4], [5]. Furthermore, as noticed in the theory of concurrent processes, simulation is more powerful than behavioural inclusion for nondeterministic systems, which will be used throughout this paper.…”