Decentralized Control of Product (max+)-automata using Coinduction

(Max,+)-automata are weighted automata over the (max,+) semiring. Deterministic (max,+)-automata are sequential models that need to be composed in order to model concurrent timed systems. In this paper, the synchronous product and the supervised product are defined by coinduction. Maximally permissive timed control then amounts to compute residuation of the supervised product that is defined by coinduction. It is proven by coinduction that the definition of maximally permissive timed control is correct. We apply this co-algebraic framework to decentralized control of product (max,+) automata.