SUMMARY Max-plus-linear (MPL) systems are a class of nonlinear systems that can be described by models that are " linear " in the max-plus algebra. We provide here solutions to three types of finite-horizon min-max control problems for uncertain MPL systems, depending on the nature of the control input over which we optimize: open-loop input sequences, disturbances feedback policies, and state ...

In this contribution, we reconsider the notion of determinism for max-plus automata by including quantitative aspect in its definition. A determinization procedure adapted to so-called weight-determinism is proposed. The motivation generalize results based on automata.

Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machine-scheduling, information technology and...

We establish the following max-plus analogue of Minkowski’s theorem. Any point of a compact max-plus convex subset of (R∪{−∞})n can be written as the max-plus convex combination of at most n + 1 of the extreme points of this subset. We establish related results for closed max-plus convex cones and closed unbounded max-plus convex sets. In particular, we show that a closed max-plus convex set ca...