G. Cohen

Bio: G. Cohen is an academic researcher from Mines ParisTech. The author has contributed to research in topics: Linear system & Petri net. The author has an hindex of 17, co-authored 25 publications receiving 3755 citations. Previous affiliations of G. Cohen include French Institute for Research in Computer Science and Automation.

Synchronization and Linearity: An Algebra for Discrete Event Systems

Abstract: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing

Abstract: A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e., involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized; the case of a flowshop-like production process is analyzed in detail.

Algebraic tools for the performance evaluation of discrete event systems

Abstract: It is shown that a certain class of Petri nets called event graphs can be represented as linear time-invariant finite-dimensional systems using some particular algebras. This sets the ground on which a theory of these systems can be developed in a manner which is very analogous to that of conventional linear system theory. Some preliminary basic developments in that direction are shown. Several ways in which one can consider event graphs as linear systems are described. These correspond to approaches in the time domain, in the event domain, and in a two-dimensional domain. In each of these approaches, a different algebra has to be used for models to remain linear, but the common feature of these algebras is that they all fall into the axiomatic definition of 'dioids'. A unified presentation of basic algebraic results on dioids is provided. >

Introduction to Discrete Event Systems

Abstract: Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

Controlled Markov processes and viscosity solutions

Abstract: This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. The authors approach stochastic control problems by the method of dynamic programming. The text provides an introduction to dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. A new Chapter X gives an introduction to the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets. Chapter VI of the First Edition has been completely rewritten, to emphasize the relationships between logarithmic transformations and risk sensitivity. A new Chapter XI gives a concise introduction to two-controller, zero-sum differential games. Also covered are controlled Markov diffusions and viscosity solutions of Hamilton-Jacobi-Bellman equations. The authors have tried, through illustrative examples and selective material, to connect stochastic control theory with other mathematical areas (e.g. large deviations theory) and with applications to engineering, physics, management, and finance. In this Second Edition, new material on applications to mathematical finance has been added. Concise introductions to risk-sensitive control theory, nonlinear H-infinity control and differential games are also included.

The control of discrete event systems

Abstract: A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

Network Calculus: A Theory of Deterministic Queuing Systems for the Internet

Abstract: Network Calculus.- Application of Network Calculus to the Internet.- Basic Min-plus and Max-plus Calculus.- Min-plus and Max-plus System Theory.- Optimal Multimedia Smoothing.- FIFO Systems and Aggregate Scheduling.- Adaptive and Packet Scale Rate Guarantees.- Time Varying Shapers.- Systems with Losses.