Alessandro Giua

A Survey of Petri Net Methods for Controlled Discrete EventSystems

This paper surveys recent research on the application of Petri net models to the analysis and synthesis of controllers for discrete event systems. Petri nets have been used extensively in applications such as automated manufacturing, and there exists a large body of tools for qualitative and quantitative analysis of Petri nets. The goal of Petri net research in discrete event systems is to exploit the structural properties of Petri net models in computationally efficient algorithms for computing controls. We present an overview of the various models and problems formulated in the literature focusing on two particular models, the controlled Petri nets and the labeled nets. We describe two basic approaches for controller synthesis, based on state feedback and event feedback. We also discuss two efficient techniques for the on-line computation of the control law, namely the linear integer programming approach which takes advantage of the linear structure of the Petri net state transition equation, and path-based algorithms which take advantage of the graphical structure of Petri net models. Extensions to timed models are briefly described. The paper concludes with a discussion of directions for future research.

Generalized mutual exclusion contraints on nets with uncontrollable transitions

The authors study a class of specifications, called generalized mutual exclusion constraints, for discrete event systems modeled using place/transition nets. These specifications may be easily enforced by a set of places called monitors on a net system where all transitions are controllable. However, when some of the transitions of the net are uncontrollable, this technique is not always applicable. For some classes of nets, the authors prove that generalized mutual exclusion constraints may always be enforced by monitors, even in the presence of uncontrollable transitions.<<ETX>>

First-order hybrid Petri nets: a model for optimization and control

We consider in this paper first-order hybrid Petri nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the first-order continuous behavior of this model and show how its control can be framed as a conflict resolution policy that aims at optimizing a given objective function. The use of linear algebra leads to sensitivity analysis that allows one to study of how changes in the structure of the model influence the optimal behavior. As an example of application, we show how the proposed formalism can be applied to flexible manufacturing systems with arbitrary layout and different classes of products.

An implicit gain-scheduling controller for cranes

To improve the efficiency of cargo handling with cranes it is necessary to control the crane trolley position so that the swing of the hanging load is minimized. In this paper we consider a linear parameter-varying model of the crane, where the time-varying parameter is the length of the suspending rope. We consider the set of models given by frozen values of the rope length and show how all these models can be reduced to a single time-invariant model using a suitable time scaling. The time scaling relation can be used to derive a control law for the time-varying system that implements an implicit gain scheduling. Using a Lyapunov-like theorem, it is also possible to find relative upper bounds for the rate of change of the varying parameter that ensure the stability of the time-varying system.

Observability of place/transition nets

We discuss the problem of estimating the marking of a place/transition (P/T) net based on event observation. We assume that the net structure is known while the initial marking is totally or partially unknown. We give algorithms to compute a marking estimate that is a lower bound of the actual marking. The special structure of Petri nets allows us to use a simple linear algebraic formalism for estimate and error computation. The error between actual marking and estimate is a monotonically nonincreasing function of the observed word length, and words that lead to null error are said to be complete. We define several observability properties related to the existence of complete words, and show how they can be proved. To prove some of them, we also introduce a useful tool, the observer coverability graph, i.e., the usual coverability graph of a P/T net augmented with a vector that keeps track of the estimation error on each place of the net. Finally, we show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications.

Brief paper: Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present an efficient approach for the fault detection of discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. We prove that the set of all possible firing sequences corresponding to a given observation can be described as follows. First a set of basis markings corresponding to the observation are computed together with the minimal set of transitions firings that justify them. Any other marking consistent with the observation must be reachable from a basis marking by firing only unobservable transitions. For the computation of the set of basis markings we propose a simple tabular algorithm and use it to determine a basis reachability tree that can be used as a diagnoser.

Optimal control of continuous-time switched affine systems

This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.

Optimal control of switched autonomous linear systems

The paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is that of minimizing a quadratic performance index over an infinite time horizon. We assume that the switching sequence and the corresponding jump matrix sequence is known, while the unknown switching times are the optimization parameters. The optimal control for this class of systems, assuming a switching sequence of finite length, takes the form of a homogeneous state feedback, i.e., it is possible to identify a homogeneous region of the state space such that an optimal switch should occur if and only if the present state belongs to this region. We show how such a region can be computed with a numerical procedure. As the number of allowed switches goes to infinity, we study the stability of the system and discuss some preliminary results related to the convergence of the state feedback law.

Modeling and Supervisory Control of Railway Networks Using Petri Nets

In this paper, we deal with the problem of modeling railway networks with Petri nets so as to apply the theory of supervisory control for discrete event systems to automatically design the system controller. We provide a modular representation of railway networks in terms of stations and tracks including sensors and semaphores. We first ensure safeness and local liveness imposing both generalized mutual exclusion constraints and constraints also involving the firing vector. The detailed model used in this first step can be abstracted, considering a higher level description of a railway network that belongs to the class of ES PR (extended simple sequential process with resources) nets and show that global liveness may be enforced by adding appropriate monitor places designed using siphon analysis. In our approach, this can be done without an exhaustive computation of all siphons and we can characterize the cases in which the procedure can be recursively applied, giving a simple test for closed-loop net to remain an ES PR net.

Marking estimation of Petri nets with silent transitions

In this paper we deal with the problem of estimating the marking of a labeled Petri net system based on the observation of transitions labels. In particular, we assume that a certain number of transitions are labeled with the empty string /spl epsi/, while a different label taken from a given alphabet is assigned to all the other transitions. Transitions labeled with the empty string are called silent because their firing cannot be observed. Under some technical assumptions on the structure of the T/sub /spl epsiv// -induced subnet, where T/sub /spl epsiv// denotes the set of silent transitions, we formally prove that the set of markings consistent with the observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.