Algebraic Characteristics and Structure Decomposition for “Linear” Discrete Event Dynamic Systems

ALGEBRAIC CHARACTERISTICS AND STRUCTURE DECOMPOSITION FOR “LINEAR” DISCRETE EVENT DYNAMIC SYSTEMS

Discrete event dynamic systems (DEDS), are systems, which change state over time, based on current state and state transition rules. Each state is separated from its neighbour by a step rather than a continuum of infinitesimal states. This continuum in DEDS needs a representation between 0 and 1. The application of fuzzy logic in defining and modelling the DEDS is suggested as a possible solution because the nature of DEDS may be asynchronous, distributed, parallel, non-deterministic and/or stochastic. This results in the generalisation of crisp finite automata into fuzzy automata for a DEDS. In this paper, a DEDS in the form of hopper feed system is considered. The system is reformulated using state vectors and event transition matrices and is extended to fuzzy vectors and matrices. An algorithm is proposed for the final control action to be implemented using a programmable logic controller (PLC).

ABSTRACTIn this paper, the static output feedback stabilisation of discrete event dynamic systems (DEDSs) is investigated via the semi-tensor product (STP) of matrices. Firstly, the dynamics of DEDSs modelled by deterministic Moore-type finite automata are converted into an matrix expression in the STP frame. Secondly, necessary and sufficient conditions for the existence of a static output feedback control pattern, stabilising the controlled discrete event dynamic systems to some equilibrium point, are given, and constructive algorithms to seek the static output feedback control pattern including an effective specific solution algorithm and an analytic solution algorithm are proposed. Thirdly, the equilibrium-based static output feedback stabilisation of DEDSs is extended to the set-based static output feedback stabilisation and necessary and sufficient conditions and constructive algorithms to seek the corresponding control pattern are provided. Finally, some examples are presented to illustrate the effectiveness of the proposed approach.

Discrete event dynamic systems (DEDS) are prevalent in many areas of engineering, like manufacturing, maintenance, distributed computing, etc. Activities or discrete events in DEDS are generally large in numbers, highly parallel, distributed, and highly intertwined. Modeling DEDS systems are further complicated by the fact that the decisions to be made from the model may incorporate inference engines that uses advanced statistical analysis on massive data and may also include fuzzy decisions. This paper talks about development of a new tool for modeling and simulation of DEDS that can satisfy the characteristics mentioned above; the new tool is called General purpose Petri net Simulator (GPenSIM). This paper further presents a recent extension to the new tool, which is the real-time simulation capability.

Discrete Event Dynamic System (DEDS) is a dynamic system in which unexpected events take place at irregular intervals. Such systems can describe many different real phenomena occurring in transport networks, technological processes and computer systems and also in examples of design systems presented in this article. This article describes methods to support managing the design of IT infrastructure as a DEDS dealing with the allocation of human resources, the synchronisation of tasks and risk management. These methods are based on the max-plus system modelling theory , while the example uses a schedule of managing the design, implementation and deployment of software which helps monitor and control complex technological processes. The proposed solution can be used in both standard and agile & lean management principles promoted in recent years.

THE SUPERVISORY CONTROL PROBLEM SOLVED VIA PETRI NETS

Because the classical control theory does not give satisfactory results in the DEDS (discrete event dynamic systems) control systems synthesis, especially in analytical terms, and because such systems are very important in human life-e.g. flexible manufacturing systems (FMS), transport systems, communications systems, etc.-another approaches are wanted. The main aim of this paper is to point out a simple approach leading to a very simple dealing with the FMS (as a kind of the DEDS) modelling and intelligent control problems solving. On that way imbedding some results of applied artificial intelligence, especially the rule-based knowledge representation and simple form of automatic reasoning, is used.

Rule-based Composable Modelling of Industrial Automation Automata under Nominal and Faulty Conditions

Investigated the environmental assessment from the point of system simulation, the environment assessment system belongs to the discrete event dynamic system. According to the comparison between the environment assessment system and the military command automation system, there are many common grounds in essence. Therefore, in order to solve the problems exist in environmental assessment field nowadays, the relative theories of the military command automation system (C4ISR) were transplanted to environmental assessment field. Finally, based on the information technology and the simulation technology one solution was constructed named Environmental Assessment Automation System-C4ISRE (Command, Control, Communications, Computer, Intelligence, Surveillance, Reconnaissance, Environmental Assessment). The relative theories of C4ISRE including Discrete Event Dynamic Systems (DEDS), the technology of using Petri Net (PN) to analyze and model the DEDS, Distributed Virtual Reality (DVR), Computer Generated Forces (CGF), Synthetic Natural Environment (SNE), Dynamic Environment Simulation (DSE), Environmental Assessment(EA). The integration of upper contents constructs the theory frame of Informatization Environmental Assessment (IEA?and also makes a stable theoretical base for IEA’s further research.

The Supervisory Control Problem Solved VIA Petri Nets

Discrete event dynamical systems are used to model a number of engineering applications ranging from communication networks, distributed computing systems to manufacturing systems. A new analytical model is proposed for the analysis of asynchronous, optimistic distributed simulation of discrete event dynamical systems. The performance of traditional timewarp algorithms and that of a new rollback algorithm, Wolf, are examined in this framework and a comparison is attempted. A few preliminary implementations of Wolf on a distributed computing system confirm analytical results predicting a considerable reduction in error propagation, a decrease in the number of cancellations and an enhancement in the forward computation.

A new Petri net modeling technique for the performance analysis of discrete event dynamic systems

The objective of this paper is to show a numbering system directed to event graphs. To do so, we show two applications of this numbering system, the first one in arithmetic, to clarify the numbering system, and the other one in discrete event dynamic systems. This numbering system takes expressions from an alphabet. These expressions, also known as strings, are associated with integers. For each given alphabet, each expression can be put in unique correspondence with a positive integer. To illustrate this numbering system, the first application is in arithmetic. We show an arithmetic without the traditional zero symbols and compare it with the decimal numbering system used in elementary school. A different symbol is introduced, the square zero. One of the consequences of this system is that leading square zeros change the number being represented. The second application – the main objective in this paper – consists in using this numbering system to represent discrete event dynamic systems modeled by event graphs. As a consequence of this we hope that the properties of event graphs can be analyzed through the number theory since each expression, which determines a particular event graph, is associated to a single integer.

Recent research has demonstrated that ordinal comparison, i.e., comparing relative orders of performance measures of different designs, is efficient in the comparison and selection of designs for discrete event dynamic systems. This paper is concerned with comparison and selection in concurrent simulation where a large number of sample paths under different designs are generated efficiently. Particularly, effect of correlation among simulation processes on the convergence of ordinal comparison is investigated. By using a concept of indicator process, bounds on the rate of convergence of ordinal comparison are obtained. Such bounds imply that perturbation analysis, a powerful technique for performance analysis of discrete event dynamic systems, can be advantageous for ordinal comparison. Simulation examples show that appropriate correlation can significantly increase the convergence of ordinal comparison. Furthermore, it is shown that positive quadrant dependence provides guaranteed acceleration of the convergence of ordinal comparison compared with independent simulations.

Impetuous multiplication of mobility and road traffic proliferation lead to concerns for increasing the attractiveness of urban public transport. Compared to private car use, urban public transport attractiveness is conditioned, in particular, by travel times and certainty of respecting the transport schedules, meaning planned traffic stability. Traffic schedules are considered to be more stable as the primary delays from the announced schedule have low probabilities and values and their propagation as repeated delays is least noticed in time and space. Solutions for assuring traffic stability must take into consideration contradictory aspects, because introducing time reserves in the schedules means time travel extensions. In order to assure the stability of planned traffic, present paper develops studies of various models and methods that aim to reduce inherent primary delays. Thereby, for studying repeated delays on a complex network, a mathematical model adequate to a Discrete Event Dynamic System (DEDS), that in MAX-PLUS algebra becomes a linear system, was used. The paper concludes with a case study on an integrated network resulted from the superposition of Bucharest’s existing suburban rail network with the underground network designed for 2030, being identified measures for improving the stability indicators. Traffic stability is assessed on the basis of two indicators: instability coefficient and delay elimination rate. Main measure for improving stability indicators is the growth of time reserves taking into consideration the quality requirements resulting from the condition of maintaining a reduced planned travel time.