Carla Seatzu

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.

Brief Observer-controller design for cranes via Lyapunov equivalence

We consider a linearized parameter-varying model of a planar crane and show how a controller can be designed, following the state-feedback stabilization technique for time-varying systems proposed by Wolovich. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. We also show that an observer can be designed applying Wolovich procedure to the dual system of the plant. The proposed procedure leads to the computation of the desired time-varying gains for controller and observer in a parameterized form. The results of several simulations with data taken from a real container crane, are also shown.

A New Approach for Diagnosability Analysis of Petri Nets Using Verifier Nets

In this paper, we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a fixed bound of K event occurrences after the fault. We give necessary and sufficient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verifier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented.

Modelling and simulation of manufacturing systems with first-order hybrid Petri nets

First-order hybrid Petri nets are models that consist of continuous places holding fluid, discrete places containing a non-negative integer number of tokens, and transitions, either discrete or continuous. In the first part of the paper, we provide a framework to describe the overall hybrid net behaviour that combines both time-driven and event-driven dynamics. The resulting model is a linear discrete-time, time-varying state variable model that can be directly used by an efficient simulation tool. In the second part of the paper, we focus on manufacturing systems. Manufacturing systems are discrete-event dynamic systems whose number of reachable states is typically very large, hence approximating fluid models have often been used in this context. We describe the net models of the elementary components of a flexible manufacturing system (machines and buffers) and we show in a final example how these modules can be put together in a bottom-up fashion.

Observer-based state-feedback control of timed Petri nets with deadlock recovery

This paper discusses the problem of controlling a timed Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all transitions are assumed to be controllable. We show that the use of marking estimates may significantly reduce the performance of the closed-loop system and in particular may lead to a deadlock. First, we present a linear algebraic characterization of deadlock markings based on siphon analysis. Second, we show how this characterization may be used to derive a procedure that may be invoked to recover from a controller induced deadlock. Finally, we assume that the timing delays associated to transitions are known and show how this knowledge can be used to improve the marking estimate and to recover the net from partial deadlocks. This procedure is similar to the one used for deadlock recovery and may be invoked whenever a transition has not fired for a time longer than its expected delay.