Modeling, monitoring and optimization of discrete event systems using Petri nets

Abstract

Yan, Jiaxiang. M.S.E.C.E., Purdue University, May 2013. Modeling, Monitoring and Optimization of Discrete Event Systems Using Petri Nets. Major Professor: Lingxi Li. In last decades, the research of discrete event systems (DESs) has attracts more and more attention because of the fast development of intelligent control strategies. Such control measures combine the conventional control strategies with discrete decision-making processes which simulate human decision-making processes. Due to the scale and complexity of common DESs, the dedicated models, monitoring methods and optimal control strategies for them are necessary. Among various DES models, Petri nets are famous for the advantage in dealing with asynchronous processes. They have been widely applied in intelligent transportation systems (ITS) and communication technology in recent years. With encoding of the Petri net state, we can also enable fault detection and identification capability in DESs and mitigate potential human errors. This thesis studies various problems in the context of DESs that can be modeled by Petri nets. In particular, we focus on systematic modeling, asynchronous monitoring and optimal control strategies design of Petri nets. This thesis starts by looking at the systematic modeling of ITS. A microscopic model of signalized intersection and its two-layer timed Petri net representation is proposed in this thesis, where the first layer is the representation of the intersection and the second layer is the representation of the traffic light system. Deterministic and stochastic transitions are both involved in such Petri net representation. The detailed operation process of such Petri net representation is stated. The improvement of such Petri net representation is also provided with comparison to previous models. Then we study the asynchronous monitoring of sensor networks. An event sequence reconstruction algorithm for a given sensor network based on asynchronous observations of its state changes is proposed in this thesis. We assume that the sensor network is modeled as a Petri net and the asynchronous observations are in the form of state (token) changes at different places in the Petri net. More specifically, the observed sequences of state changes are provided by local sensors and are asynchronous, i.e., they only contain partial information about the ordering of the state changes that occur. We propose an approach that is able to partition the given net into several subnets and reconstruct the event sequence for each subnet. Then we develop an algorithm that is able to reconstruct the event sequences for the entire net that are consistent with: 1) the asynchronous observations of state changes; 2) the event sequences of each subnet; and 3) the structure of the given Petri net. We discuss the algorithmic complexity. The final problem studied in this thesis is the optimal design method of Petri net controllers with fault-tolerant ability. In particular, we consider multiple faults detection and identification in Petri nets that have state machine structures (i.e., every transition in the net has only one input place and one output place). We develop the approximation algorithms to design the fault-tolerant Petri net controller which achieves the minimal number of connections with the original controller. A design example for an automated guided vehicle (AGV) system is also provided to illustrate our approaches.