Control of Linear Min-plus Systems under Temporal Constraints

Abstract

Abstract-We consider a class of controlled timed event graphs subject to strict temporal constraints. Such a graph is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a system of difference equations that are linear in the Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the min-plus algebra. Then, a method for the synthesis of a control law ensuring the respect of constraints is described. We give explicit formulas characterizing a control law, which, if two conditions are satisfied, ensures the validity of the temporal constraints. It is a causal state feedback, involving delays. The method is illustrated on an example.

Max-Plus Control Design for Temporal Constraints Meeting in Timed Event Graphs

“…The presented approach in the Max-Plus algebra resembles to the one in the Min-Plus algebra already developed in [4]. We point out that the conditions obtained in Max-Plus algebra are simpler than that obtained in the Min-Plus case.…”

“…A first attempt to control TEG under strict temporal constraints has been presented in [4]. This initial approach was developed in the Min-Plus algebra, under the assumption that all delays of the considered graph are integers.…”

Analysis of P-time Event Graphs in (Max,+) and (Min,+) Algebras

“…We denote by M max the maximal number of initial tokens (of initial marking) in one place. We recall from [2] a simplification based on the behavioral equivalence of P-time event graphs given by replacing every place containing m ≥ 2 tokens by place with 1 token and the same timing and upstream sequence of m − 1 transitions and places with timing [0, 0]. This leads to the event graphs, where the initial marking is bounded by 1.…”

Control of discrete event systems with respect to strict duration: Supervision of an industrial manufacturing plant

“…The supervision is aimed at guaranteeing the respect of temporal constraints without impacting significantly the dynamic behaviour of the system. Similar problems of 1 meeting time constraints have been recently addressed via different approaches [27,21,3,26,20]. We propose solutions based on a constrained (max, +) state equation for the TEG model of the DES.…”