We show that max-plus polyhedra are usable as a data structure in reachability analysis of timed automata. Drawing inspiration from the extensive work that has been done on difference bound matrices, as well as previous work on max-plus polyhedra in other areas, we develop the algorithms needed to perform forward and backward reachability analysis using maxplus polyhedra. To show that the appro...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract Systems in which the operations min, max and addition appear simultaneously are called min-max-plus systems. Such systems, which are extensions of timed discrete event systems (which on their turn are based on the max-plus algebra, i.e. on the operations max and addition only), have been studied...

The dynamics analysis for linear systems described by state-space representations in max-plus algebra is addressed within the context of the software facilities offered by the Petri Net Toolbox (PN Toolbox) running under MATLAB. By developing this toolbox, the application field of the MATLAB environment (extremely popular among control engineers) is considerably enlarged towards covering event ...

The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact mat...

In this paper, Hybrid Petri Nets are proposed as a modelling methodology to control production in a large class of manufacturing processes. A hybrid Petri net (HPN) is a combination of a ‘classical’ Petri net and a continuous Petri net, the ‘fluid’ version of a timed Petri net. The two parts of an HPN can affect each other. In the particular model proposed, the discrete part of the HPN ‘regulat...

The max-plus (or tropical) algebra is obtained by replacing the addition by the maximisation (or the minimisation) and the multiplication by the addition. It arises in the dynamic programming approach to deterministic optimal control. In particular , the evolution semigroup of a first order Hamilton-Jacobi equation is linear in the max-plus sense if the Hamiltonian is convex in the adjoint vari...

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Se...

The classical algorithms to align two biological sequences (Needleman and Wunsch and Smith and Waterman algorithms) can be seen as a sequence of elementary operations in (max;+) algebra: each line (viewed as a vector) of the dynamic programming table of the alignment algorithms can be deduced by a (max;+) multiplication of the previous line by a matrix. Taking into account the properties of the...