This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) ...

Max-plus-linear (MPL) systems are a class of discrete event systems that can be described by models that are “linear” in the max-plus algebra. In this paper we focus on MPL systems such as they arise in the context of e.g. manufacturing systems, telecommunication networks, railway networks, and parallel computing. We derive a receding horizon control scheme for MPL systems that guarantees a pri...

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the max-plus algebra. In this paper we consider the stability of MPC for these max-plus linear (MPL) systems, and...

In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the...

We study the concept of systems synchronisation in Max-Plus algebra. show that problem synchronising linear is twofold. It can be stated terms controlled invariance, and coreachability. The invariance property a set for which suitable control exists, maintains trajectory set. recall some properties particular existence maximal invariant included into any given Beyond determination admissible se...

The topics of this paper are matrix factorizations and the minimal state space realization problem in the maxplus algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We present a heuristic algorithm to compute a factorization of a matrix in the max-plus algebra. Next we use this algorithm to determine the minimal system order (and to construct a mi...