Fast multi-core co-simulation of Cyber-Physical Systems: Application to internal combustion engines

The design process of complex Cyber-Physical Systems often relies on co-simulations of the system, involving the interaction of several simulated models of sub-systems. However, reaching real-time simulations is currently prevented by prohibitive CPU times using the single-threaded existing simulation tools. This paper investigates the problem of the efficient parallel co-simulation of hybrid dynamical systems. It introduces a finely-grained co-simulation method enabling numerical integration speed-ups. It is obtained using a partition across the model into loosely coupled sub-systems with sparse communication between modules. The proposed scheme leads to schedule a large number of operations with a wide range of execution times. A suitable off-line scheduling algorithm, based on the input/output dynamics of the models, is proposed to minimize the simulation errors induced by the parallel execution. This scheme is finally tested using the phenomenological model of a combustion engine issued from the Functional Mockup Interface framework. Compared with the sequential case, it shows significant speed-ups while keeping the numerical integration accuracy under control.