Verification of Co-simulation Algorithms Subject to Algebraic Loops and Adaptive Steps

Simulation-based analyses of cyber-physical systems are increasingly vital. Co-simulation is one such technique that enables the coupling of specialized simulation tools through an orchestration algorithm. The orchestrator dictates how each simulation tool should simulate its corresponding subsystem. Obtaining correct simulation results requires an implementation-aware orchestration algorithm tailored to the specific scenario, without the orchestrator knowing each simulation tool's implementation. Such an algorithm should stabilize algebraic loops, perform time step negotiation, and adhere to each simulation tool's implementation. This paper describes an approach and implementation to prove that a given orchestration algorithm respects all contracts related to the simulation units' implementation. The approach has been applied to an industrial case study and other complex scenarios. The tool and results are available online.