Optimal Control of a Class of Timed Discrete Event Systems with Shared Resources, An Approach Based on the Hadamard Product of Series in Dioids

The topic of this paper is modeling and control of timed discrete event systems in a dioid framework if systems operate under the restriction of shared resources. The behavior of such systems can be elegantly modeled using the Hadamard product of series in dioids. Using residuation of the Hadamard product, it is possible to compute optimal control, where optimality is in the sense of a lexicographical order reflecting the chosen prioritization of subsystems. The paper concludes with an example, illustrating the efficiency of the proposed method.