Cyber-Physical Systems with Dynamic Structure: Towards Modeling and Verification of Inductive Invariants

Cyber-physical systems achieve sophisticated system behavior exploring the tight interconnection of physical coupling present in classical engineering systems and information technology based coupling. A particular challenging case are systems where these cyber-physical systems are formed ad hoc according to the specific local topology, the available networking capabilities, and the goals and constraints of the subsystems captured by the information processing part. In this paper we present a formalism that permits to model the sketched class of cyber-physical systems. The ad hoc formation of tightly coupled subsystems of arbitrary size are specified using a UML-based graph transformation system approach. Differential equations are employed to define the resulting tightly coupled behavior. Together, both form hybrid graph transformation systems where the graph transformation rules define the discrete steps where the topology or modes may change, while the differential equations capture the continuous behavior in between such discrete changes. In addition, we demonstrate that automated analysis techniques known for timed graph transformation systems for inductive invariants can be extended to also cover the hybrid case for an expressive case of hybrid models where the formed tightly coupled subsystems are restricted to smaller local networks.