Invariant Sets for Assume-Guarantee Contracts

International audienceContract theory is a powerful tool to reason on systems that are interacting with an external environment, possibly made of other systems. Formally, a contract is usually given by assumptions and guarantees, which specify the expected behavior of the system (the guarantees) in a certain context (the assumptions). In this work, we present a verification framework for discrete-time dynamical systems with assume-guarantee contracts. We first introduce a class of assume-guarantee contracts with their satisfaction semantics parameterized by a time-horizon over which assumptions are evaluated. We then show that the problem of verifying whether such contracts are satisfied is equivalent to show the existence of a positive invariant set for an auxiliary system. This allows us to leverage the extensive literature on invariant set computation. A simple illustrative example is provided to show the effectiveness of our approach