Abstract

. For timed event graphs, linear models were obtained using dioid algebra. After describing backward equations which solve an optimal tracking problem and which introduce co-state variables, this paper presents preliminary results concerning the matrix of `ratios' (i.e. conventional differences) of co-states over states: this matrix sounds like a Riccati matrix, although a neat analogue to a Riccati equation has not been found yet. Keywords. Discrete event systems, timed event graphs, dioid algebra, residuation, co-state equations 1 INTRODUCTION In the last ten years, a new paradigm has emerged under the now classical name of `discrete event (dynamic) systems' (DEDS). Among the various aspects of these systems 1 , the scope is here performance evaluation. Hence the focus is on dates of occurrence of events, number of events occurred within a certain time interval, etc. It was shown that when synchronization is the basic phenomenon which drives the dynamics of such systems (thi...

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