Discrete Event Dynamic Systems: An Overview

In this report we present an overview for the development of a theory for discrete event dynamic systems (DEDS). Dynamic systems are usually modeled by finite state automata with partially overservable events together with a mechanism for enabling and disabling a subset of state transitions. DEDS are attracting considerable interests, current applications are found in manufacturing systems, communications and air traffic systems, future applications will include robotics, computer vision and AI. We will discuss notions of modeling, stability issues, observability, feedback and invertibility. We will also discuss the perturbation analysis technique (PA) for analyzing and describing the behavior of DEDs

Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System

Output stabilizability of discrete event dynamic systems

Cover title. "Presented at the 1989 IEEE Conference on Decision and Control"--Cover.Includes bibliographical references (leaf 6).Research supported by the Air Force Office of Scientific Research. AFOSR-88-0032 Research supported by the Army Research Office. DAAL03-86-K-0171C.M. Özveren, A.S. Willsky

Evaluation of the mean cycle time in stochastic discrete event dynamic systems

We consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by second-order random matrices that are assumed to be independent and identically distributed. The problem of interest is to evaluate the mean growth rate of state vector, which is also referred to as the mean cycle time of the system, under various assumptions on the matrix entries. We give an overview of early results including a solution for systems determined by matrices with independent entries having a common exponential distribution. It is shown how to extend the result to the cases when the entries have different exponential distributions and when some of the entries are replaced by zero. Finally, the mean cycle time is calculated for systems with matrices that have one random entry, whereas the other entries in the matrices can be arbitrary nonnegative and zero constants. The random entry is always assumed to have exponential distribution except for one case of a matrix with zero row when the particular form of the matrix makes it possible to obtain a solution that does not rely on exponential distribution assumptions.Comment: The 6th International Conference on Queueing Theory and Network Applications (QTNA'11), Aug. 23-26, 2011, Seoul, Korea; ACM, New York, ISBN 978-1-4503-0758-

A formal description of discrete event dynamic systems including perturbation analysis

Simulation;operations research

Automatic generation of equations of motion for multibody system in discrete event simulation framework

AbstractIn this paper, the development of a simulation program that can automatically generate equations of motion for mutibody systems in the discrete event simulation framework is presented. The need to analyze the dynamic response of mechanical systems that are under event triggered conditions is increasing. General mechanical systems can be defined as multibody systems that are collections of interconnected rigid bodies, consistent with various types of joints that limit the relative motion of pairs of bodies. For complex multibody systems, a systematic approach is required to efficiently set up the mathematical models. Therefore, a dynamics kernel was developed to automatically generate the equations of motion for multibody systems based on multibody dynamics. The developed dynamics kernel also provides the numerical solver for the dynamic analysis of multibody systems. The general multibody dynamics kernel cannot deal with discontinuous state variables, event triggered conditions, and state triggered conditions, though. To enable it to deal with multibody systems in discontinuous environments, the multibody dynamics kernel was integrated into a discrete event simulation framework, which was developed based on the discrete event system specification (DEVS) formalism. DEVS formalism is a modular and hierarchical formalism for modeling and analyzing systems under event triggered conditions, which are described by discontinuous state variables. To verify the developed program, it was applied to an block-lifting and transport simulation, and dynamic analysis of the system is carried out

Analysis of non-linear discrete event dynamic systems in (min, +) algebra

Under the name discrete event dynamic systems are grouped some systems whose dynamic behaviour cannot be described by differential equations. This class of systems includes many industrial systems, for which we study the flow entities (material, resources). This paper deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGM). These models do not admit a linear representation in (min, +) algebra. This non-linearity is due to the presence of the weights on arcs. To mitigate this problem of non-linearity and to apply some basic results used to analysis the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model