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 Ricc...

Interval weighted automata are introduced as automata with weights in a product dioid (idempotent semiring). They constitute an extension of (max,+) automata since they enable us to model temporal constraints (instead of exact durations) for transitions. Their synchronous composition, that coincides with the synchronous product of underlying (one clock) timed automata, results in multi-event in...

This paper deals with the model-reference control of timed event graphs using the dioid algebra and the residuation theory. It proposes a control structure based on a precompensator and a feedback controller to improve the controlled system performance. It is shown that this approach always leads to an optimal behavior of the closed-loop system. An example is given to illustrate the proposed ap...

Interval weighted automata are introduced as automata with weights in a product dioid (idempotent semiring). They constitute an extension of (max,+) automata since they enable us to model temporal constraints (instead of exact durations) for transitions. Their synchronous composition, which coincides with the synchronous product of underlying (one clock) timed automata, results in multi-event i...

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximu...

In previous work we have shown how (max,+)-algebra can be used to model cyclically operated high-throughput screening systems. In this paper the system is modeled in a two-dimensional dioid M ax in [[γ, δ]]. A controller is determined using residuation theory. The resulting control guarantees just-in-time operation of the plant. A small example is used to demonstrate the approach to model and c...