Contract-based design for computation and verification of a closed-loop hybrid system

Contract-based design is an approach where the design process is seen as a successive assembly of components where a component is represented in terms of assumptions about its environment and guarantees about its behavior. In the composition, if assumptions of each component are contained in guarantees offered by the others, then the composition is well formed. In this paper, we focus on contract-based design and the use of Heterogeneous Rich Component models for embedded controllers where the plant, sensors and actuators are described by hybrid systems. We assume that the components are assembled in a feedback configuration. The problem is to show that this composition satisfies requirements using the assumptions-guarantees of the plant, sensors, actuators and controller. To do so, we give rules on how to compose assumptions and promises for components in cascade and feedback configurations. We then apply these rules to expose the actual calculation involved on a test case, a water-level control problem. We also show how to check that the requirements on the closed-loop configuration are satisfied, i.e, that they are contained in the promises of this configuration using a formal verification tool (Ariadne) for hybrid systems.