Predicting Events for the Simulation of Hybrid Systems

The quality of the numeric simulation of hybrid systems highly depends on the capability of the simulator to detect discrete events during continuous evolutions. Due to the interaction of discrete and continuous dynamics, failures to detect such events may have catastrophic impacts on the global simulation. Current methods employ numeric algorithms/solvers for the underlying systems of differential equations, and therefore inherently suffer from the accumulation of numeric inaccuracies. In this paper, we propose a method for simulation of hybrid systems that is based on a combination of symbolic and numeric computations, which allows one to predict discrete events without accumulating numeric inaccuracies during the continuous evolution. Our method is applicable for a wide range of hybrid systems like the subclass of linear hybrid automata.