Institute of Information Theory and Automation

Controlled invariant modules over a ring or a semiring, with applications to control in manufacturing

Lecturer: J. J. Loiseau
Institute: Centre national de la recherche scientifique
Date and time: 04.12.2017 - 11:00
Room: 474
Department: Adaptive Systems (AS)

Details:

The concept of controlled invariance is fundamental for the control design of linear systems subject to strict constraints. We present here the extension of the method to max-plus linear systems, after a number of recent publications. We show that the controlled invariance is equivalent to invariance by static state feedback. At the contrary of the case of systems over a field, the feedback that makes invariant a given semimodule is not linear, in general. Anyway, it is computable using well-known methods for the solution of linear equation over the max-plus semiring. Another difference from the case of systems over a field is that the causality of the feedback must be verified, to permit its implementation. The causal controlled invariance can also be checked and we present algorithms. This opens the way to the computation of optimal solutions to many design problems in logistics and production management. We take from the literature the example of a cluster tool supervisor, and mention some other applications.
Institute of Information Theory and Automation