Simulation of Zeno Hybrid Systems Using the Infinity Computer

This paper considers hybrid systems - dynamical systems that exhibit both continuous and discrete behavior, where interactions between the continuous and discrete dynamics occur when a pre-defined function becomes equal to zero. Thus, determination of zero-crossings plays a crucial role in the correct simulation of the system in this case. Correct determination of zero-crossings for a complex real-life system can require a lot of computational resources and, as a consequence, slow down the simulation significantly. This paper presents a new way to execute the simulation generating time observations of the hybrid system dynamically using numerical infinitesimals introduced by the Infinity Computer, allowing thus to determine zero-crossings correctly. The proposed method allows to automatically detect zero-crossings with any predefined accuracy and to analyze better the behavior of the system around the zero-crossings generating observations more densely, where it is necessary. Moreover, the search for zero-crossings is performed efficiently without re-evaluation of the whole system at any observation. To show the validity of the proposed method, an important real-life hybrid system has been studied and the simulation results have been compared with the standard method.