Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1

Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

Flexible Nets: a modeling formalism for dynamic systems with uncertain parameters

Funder: FP7 People: Marie-Curie Actions; doi: https://doi.org/10.13039/100011264; Grant(s): 623995Abstract: The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner

Structural Sequence Detectability in Free Choice Interpreted Petri Nets

This paper is concerned with the structural sequence detectability problem in Free Choice Interpreted Petri nets, i.e. with the possibility of recovering the firing transition sequence in Free Choice Interpreted Petri nets using the output information when the initial marking is unknown. Based on the Free Choice Interpreted Petri net structure, three relationships are proposed which are devoted to capture the confusion over the transitions. These relationships depend on interpreted Petri nets structures such as T-invariants, P-Invariants, attribution and distribution places. Thus, the approach herein presented exploits the interpreted Petri nets structural information in order to determine the structural sequence detectability of an interpreted Petri net.Consejo Nacional de Ciencia y Tecnologí

On the decidability of problems in liveness of controlled Discrete Event Systems modeled by Petri Nets

A Discrete Event System (DES) is a discrete-state system, where the state changes at discrete-time instants due to the occurrence of events. Informally, a liveness property stipulates that a 'good thing' happens during the evolution of a system. Some examples of liveness properties include starvation freedom -- where the 'good thing' is the process making progress; termination -- in which the good thing is for an evolution to not run forever; and guaranteed service -- such as in resource allocation systems, when every request for resource is satisfied eventually. In this thesis, we consider supervisory policies for DESs that, when they exist, enforce a liveness property by appropriately disabling a subset of preventable events at certain states in the evolution of DES. One of the main contributions of this thesis is the development of a system-theoretic framework for the analysis of Liveness Enforcing Supervisory Policies (LESPs) for DESs. We model uncertainties in the forward- and feedback-path, and present necessary and sufficient conditions for the existence of Liveness Enforcing Supervisory Policies (LESPs) for a general model of DESs in this framework. The existence of an LESP reduces to the membership of the initial state to an appropriately defined set. The membership problem is undecidable. For characterizing decidable instances of this membership problem, we consider a modeling paradigm of DESs known as Petri Nets, which have applications in modeling concurrent systems, software design, manufacturing systems, etc. Petri Net (PN) models are inherently monotonic in the sense that if a transition (which loosely represents an event of the DES) can fire from a marking (a non-negative integer-valued vector that represents the state of the DES being modeled), then it can also fire from any larger marking. The monotonicity creates a possibility of representing an infinite-state system using what can be called a "finite basis" that can lead to decidability. However, we prove that several problems of our interest are still undecidable for arbitrary PN models. That is, informally, a general PN model is still too powerful for the analysis that we are interested in. Much of the thesis is devoted to the characterization of decidable instances of the existence of LESPs for arbitrary PN models within the system-theoretic framework introduced in the thesis. The philosophical implication of the results in this thesis is the existence of what can be called a "finite basis" of an infinite state system under supervision, on which the membership tests can be performed in finite time; hence resulting in the decidability of problems and finite-time termination of algorithms. The thesis discusses various scenarios where such a finite basis exists and how to find them

A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words--fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure