Error bounds based stochastic approximations and simulations of hybrid dynamical systems

Abstract

This paper introduces, develops and discusses an integration-inspired methodology for the simulation and analysis of deterministic hybrid dynamical systems. When simulating hybrid systems, and thus unavoidably introducing some numerical error, a progressive tracking of this error can be exploited to discern the properties of the system, i.e., it can be used to introduce a stochastic approximation of the original hybrid system, the simulation of which would give a more complete representation of the possible trajectories of the system. Moreover, the error can be controlled to check and even guarantee (in certain special cases) the robustness of simulated hybrid trajectories.