Discrete Event Simulation of Hybrid Systems

This paper describes the quantization-based integration methods and extends their use to the simulation of hybrid systems. Using the fact that these methods approximate ordinary differential equations (ODEs) and differential algebraic equations (DAEs) by discrete event systems, it is shown how hybrid systems can be approximated by pure discrete event simulation models (within the DEVS formalism framework). In this way, the treatment and detection of events representing discontinuities---which constitute an important problem for classic ODE solvers---is notably simplified. It can be also seen that the main advantages of quantization-based methods (error control, reduction of computational costs, possibilities of parallelization, sparsity exploitation, etc.) are still verified in the presence of discontinuities. Finally, some examples which illustrate the use and the advantages of the methodology in hybrid systems are discussed.