A Quantitative Approach on Assume-Guarantee Contracts for Safety of Interconnected Systems

In this paper, the safety synthesis problem for a discrete-time system comprised by multiple interconnected systems is considered. Using compositional reasoning, a quantitative framework is applied to each of the subsystems. With this framework it has been possible to derive robust controlled invariant subsets for each of the subsystems with respect to the control invariant subsets of the other subsystems. These invariant subsets can be computed from a parameterized family of sets and they share a common safety controller. Contract-based design is utilized to built assume-guarantee contracts for all the subsystems, namely to assume that the other subsystems belong to their invariant sets and guarantee that the subsystem will belong to its invariant set. This circularity of the implications can be resolved by a fixed point algorithm which computes the parameters to guarantee that all the subsystems fulfill their contracts simultaneously. Then, the invariant set and the safety controller are given for the original system. To illustrate the effectiveness of the proposed approach, an application for the temperature regulation of adjacent rooms of a building is given as an example.