Supervisory Control of (max,+) automata: Timing aspects

(max,+) automata, an important class of both timed automata and weighted automata, are used as a model of a class of timed discrete event systems and their supervisory control is developped. The concept of supervised product is introduced to control (max,+) automata and its properties are studied. Decomposition of morphism matrix of the controlled system based on the tensor dioid algebra is proposed and the supervisory control of (max,+) automata is studied using residuation theory of formal power series. Finally we discuss the synchronous composition of (max,+) automata that yields a more general class of timed automata: product interval automata.