ON THE CALCULATION OF THE TRANSFER FUNCTION OF TIMED EVENT PETRI NETS
JAN KOMENDA, A. EL MOUDNI, N. ZERHO · Cybernetics & Systems · 1997
In this paper, a method for the calculation of the transfer function of timed event graphs is developed. The transfer function has the form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. It is very important in the investigation of the problem of controllability of a system, because it provides us with the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid,which seems to be difficult for matrices of large dimensions. For this reason, we propose another approach using only the max-plus modeling of a system, that is, the dater's description. We have considered the multivariable case with several input and output transitions. We can obtain the transfer function as the output corresponding to a special control. This control follows from the dater's description of the zero and identity elements of this dioid. To illustrate this approach we give two examples. The purpose of the first one is to compare different approaches to this problem; the second one may serve as an application. We use our approach to determine the transfer function of a manufacturing system.