Safety Properties of Hybrid System Product Lines

Hybrid systems are an important class of Cyber-physical systems. Hybrid systems are characterized by a combination of discrete and continuous dynamics. Over the last two decades, research has focused on formal techniques and tools for proving properties of hybrid systems, these techniques have matured to the point where they are ready for industrial application. An advantage of the existing formal techniques is their ability to prove safety properties over a range of model parameters and thus allow for results to be generalized to an entire product line. However, a critical barrier to industrial adoption of formal techniques is their integration with widely adopted industrial standards. This paper identifies "parameterized hybrid systems" as an extension of the existing notion of a hybrid system and provides a formal definition based on foundational theory from the domain of software product line engineering. Using this definition, an engineering procedure is proposed to aid in proving properties over many choices of system parameters for a product line. The proposed engineering procedure is discussed in the context of several widely adopted industrial standards (ISO 26262, DO-178C, and EN 50128) which contain gaps regarding the use of formal methods for proving safety of parameterized systems.