Duality between invariant spaces for max-plus linear discrete event systems

Michaël Di Loreto (1) , Stephane Gaubert (2) , Ricardo Katz (3) , Jean-Jacques Loiseau (4)

1 AMPERE - Ampère
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
4 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.

Domains: Optimization and Control [math.OC]

Michaël Di Loreto, Stephane Gaubert, Ricardo Katz, Jean-Jacques Loiseau. Duality between invariant spaces for max-plus linear discrete event systems. 2009. ⟨hal-00411243⟩