Stochastic hybrid systems (SHSs) are a modelling framework for a cyber-physical system (CPS), used to simulate, validate, and verify safety critical controllers under uncertainty. Popular simulation tools can miss detecting discontinuities when simulating SHS, thereby producing incorrect outputs during simulation. We propose a novel adaptive step size simulation/integration technique for a subset of SHS—stochastic differential equations (SDEs) with discontinuous drift and diffusion coefficients. Each integration step, of the Euler-Maruyama numerical solution of the SDEs, is made dependent upon the values of the continuous variables inducing the discontinuity. This in turn guarantees convergence of the system trajectory towards the discontinuity without missing it. A thorough analysis and extensive benchmarking of the proposed integration technique shows the efficacy of the approach when simulating complex SHSs.

随机混合系统（SHS）是网络物理系统（CPS）的建模框架，用于在不确定性下模拟，验证和验证安全关键控制器。流行的仿真工具在仿真SHS时可能会漏检不连续性，从而在仿真过程中产生不正确的输出。我们为SHS的子集-具有不连续漂移和扩散系数的随机微分方程（SDE）提出了一种新颖的自适应步长仿真/集成技术。SDE的Euler-Maruyama数值解的每个积分步骤都取决于引起不连续性的连续变量的值。反过来，这保证了系统轨迹向不连续点收敛，而不会丢失它。