Stochastic Assume-Guarantee Contracts for Cyber-Physical System Design.

We present an assume-guarantee contract framework for cyber-physical system design under probabilistic requirements. Given a stochastic linear system and a set of requirements captured by bounded Stochastic Signal Temporal Logic (StSTL) contracts, we propose algorithms to check contract compatibility, consistency, and refinement, and generate a sequence of control inputs that satisfies a contract. We leverage encodings of the verification and control synthesis tasks into mixed integer optimization problems, and conservative approximations of probabilistic constraints that produce sound and tractable problem formulations. We illustrate the effectiveness of our approach on three case studies, including the design of controllers for aircraft power distribution networks.