Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems

Michaël Di Loreto (1) , Stéphane Gaubert (2, 3) , Ricardo Katz (4) , Jean-Jacques Loiseau (5)

1 AMPERE - Ampère
2 MAXPLUS - Max-plus algebras and mathematics of decision
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
5 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.

Mots clés: conditioned invariance; controlled invariance; duality; geometric control; dynamic observer; max-plus algebra; discrete event systems; tropical semiring

Domaines: Energie électrique

Michaël Di Loreto, Stéphane Gaubert, Ricardo Katz, Jean-Jacques Loiseau. Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems. SIAM Journal on Control and Optimization, 2010, 48 (8), pp.5606-5628. ⟨10.1137/090747191⟩. ⟨hal-00562586⟩