The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX cross-references are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The

The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1

In this paper a brief overview of hybrid control systems is given and an introduction to several approaches in hybrid systems research with an extended list of references is presented. Emphasis is put on Petri net approaches to hybrid control.

. We address the problem of designing a distributed, hybrid factory given a description of an assembly process and a palette of controllers for basic assembly operations. In particular, we present a method that, starting with a product assembly graph (PAG), allows us to "compile " a factory description, consisting of a geometry and a hybrid, dynamical system representing the motions of robots on that geometry. This method is based on a formalism, which we have described in previous work, that allows us to manage the details of low level, continuous control of robot actuation and high level, logical control of various couplings of robot behaviors. The factory description is intended to be an aid in the design of an actual factory, if not directly implementable itself. 1 Introduction Large distributed networks of robots and computers form the basis of modern manufacturing systems. These systems should be rapidly reconfigurable, to adjust to design changes in the products they...

Abstract. Fluidification is a common relaxation technique used to deal in a more friendly way with large discrete event dynamic systems. In Petri nets, fluidification leads to continuous Petri nets systems in which the firing amounts are not restricted to be integers. For these systems reachability can be interpreted in several ways. The concepts of reachability and lim-reachability were considered in [7]. They stand for those markings that can be reached with a finite and an infinite firing sequence respectively. This paper introduces a third concept, the δ-reachability. A marking is δ-reachable if the system can get arbitrarily close to it with a finite firing sequence. A full characterization, mainly based on the state equation, is provided for all three concepts for general nets. Under the condition that every transition is fireable at least once, it holds that the state equation does not have spurious solutions if δ-reachability is considered. Furthermore, the differences among the three concepts are in the border points of the spaces they define. For mutual lim-reachability and δ-reachability among markings, i.e., reversibility, a necessary and sufficient condition is provided in terms of liveness. 1

. The paper describes the challenges of modeling embedded hybrid control systems at a higher abstraction level. It discusses the problems of modeling such systems and suggests the use of hybrid Petri nets. Modeling an exemplary embedded control system with a special hybrid Petri net class using an objectoriented modeling and simulation tool shows the potential of hybrid Petri nets. Key Words. Embedded Control Systems, Hybrid Petri Nets 1.

It has repeatedly been argued that the semi-cubical complexes , which derive directly from the higher-dimensional automata, are as general a model for concurrency as one may ever need. In fact, most (but not all) classical examples of interacting concurrent processes have an adequate semi-cubical description. I believe this is only due to the fact that most classical examples are built around the notion of discrete event, or action, which makes the transition from the example's idea to higher-dimensional automata, to semi-cubical complexes, very natural. But it is not dicult to provide realistic examples of concurrency not based on such discrete events, which leads to local po-spaces with no \cubi cation". Although the concept of local po-space is very general and admits many pathologies, the examples of concurrency I have in mind are well-behaved and not a pathology at all, so the generality of the local po-spaces is for them a large overkill. Still, they do not t into the semi-cubical strait jacket. This report puts forward the notion of po-manifold, a subcategory of the local po-spaces slightly bigger than the semi-cubical complexes. A po-manifold is locally homeomorphic to a block, which is an extremely nice global po-space. The local homeomorphisms satisfy a simple consistency condition. This means the pomanifolds are \locally nice" even though they may be too smooth to admit a cubi- cation.

We consider two generalizations of the duality between transition systems and Petri nets. In the first, transitions are replaced by paths, that is partial functions from a fixed set \Delta to states. This allows to model continuous and/or hybrid systems when \Delta represents durations.

: The paper describes the challenges of modelling hybrid embedded systems. It discusses the problems of modelling such systems and suggests the use of hybrid Petri nets. The potential of hybrid Petri nets is shown by modelling an exemplary embedded mechatronic system with a special hybrid Petri net class using a special modelling tool. Keywords: Modelling, Embedded systems, Mechatronic systems, Hybrid Petri nets 1. INTRODUCTION The design of complex embedded systems makes high demands on the design process due to the close combination of hardware and software components. These demands rise rapidly, if the system includes components of different time and signal concepts. Such systems are called heterogeneous or hybrid systems. The special characteristic of mechatronic systems in comparison to classical systems originates from their higher heterogeneity and complexity. Even the simplest mechatronic system consists of subsystems of different physical natures. Modern electric drive sy...

Abstract- CPNs has been a useful tool not only to approximate a discrete system but also to model a continuous process. In this paper, CPNs are augmented with maximal and minimal jiring speeds, and Interval speed CPNs (ICPNs) is defined. The enabling and firing of transitions of lCPNs are discussed, and the enabling of continuous transitions is classified into three levels: 0-level, I-level and 2-level. Some rules to calculate the instantaneous firing speeds are also developed. In addition, illustrative examples are presented.