Control of nonautonomous discrete event systems using dioid algebra

In this article, finite nonautonomous discrete event systems are studied in the dioid of formal series. If such a system can be described by a timed event Petri net, a max algebra model of the system can be written. Furthermore, the input-output relation of the nonautonomous system appears in the dioid of formal series. The greatest subsolution of a system of linear equations in the dioid of formal series is found. This subsolution can be used to calculate the latest admissible input of the nonautonomous discrete event system, such that the output of the system is achieved. The application of the theory to an assembly line is given.