On max-plus linear dynamical system theory: the regulation problem. (English) Zbl 1351.93090
Summary: A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus regulation problem”. In this context, we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems. The obtained controller is a simple linear static state feedback one and can be computed using efficient pseudo-polynomial algorithms. Simulation results will illustrate the applicability of the proposed methodology.
MSC:
| 93C65 | Discrete event control/observation systems |
| 15A80 | Max-plus and related algebras |
| 93B52 | Feedback control |
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