144 research outputs found
Supervisory Control of Fuzzy Discrete Event Systems
In order to cope with situations in which a plant's dynamics are not
precisely known, we consider the problem of supervisory control for a class of
discrete event systems modelled by fuzzy automata. The behavior of such
discrete event systems is described by fuzzy languages; the supervisors are
event feedback and can disable only controllable events with any degree. The
concept of discrete event system controllability is thus extended by
incorporating fuzziness. In this new sense, we present a necessary and
sufficient condition for a fuzzy language to be controllable. We also study the
supremal controllable fuzzy sublanguage and the infimal controllable fuzzy
superlanguage when a given pre-specified desired fuzzy language is
uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to
Ramadge-Wonham framework when membership grades in all fuzzy languages must be
either 0 or 1. The theoretical development is accompanied by illustrative
numerical examples.Comment: 12 pages, 2 figure
Observability and Decentralized Control of Fuzzy Discrete Event Systems
Fuzzy discrete event systems as a generalization of (crisp) discrete event
systems have been introduced in order that it is possible to effectively
represent uncertainty, imprecision, and vagueness arising from the dynamic of
systems. A fuzzy discrete event system has been modelled by a fuzzy automaton;
its behavior is described in terms of the fuzzy language generated by the
automaton. In this paper, we are concerned with the supervisory control problem
for fuzzy discrete event systems with partial observation. Observability,
normality, and co-observability of crisp languages are extended to fuzzy
languages. It is shown that the observability, together with controllability,
of the desired fuzzy language is a necessary and sufficient condition for the
existence of a partially observable fuzzy supervisor. When a decentralized
solution is desired, it is proved that there exist local fuzzy supervisors if
and only if the fuzzy language to be synthesized is controllable and
co-observable. Moreover, the infimal controllable and observable fuzzy
superlanguage, and the supremal controllable and normal fuzzy sublanguage are
also discussed. Simple examples are provided to illustrate the theoretical
development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy
System
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
Similarity-Based Supervisory Control of Discrete Event Systems
Due to the appearance of uncontrollable events in discrete event systems, one
may wish to replace the behavior leading to the uncontrollability of
pre-specified language by some quite similar one. To capture this similarity,
we introduce metric to traditional supervisory control theory and generalize
the concept of original controllability to \ld-controllability, where \ld
indicates the similarity degree of two languages. A necessary and sufficient
condition for a language to be \ld-controllable is provided. We then examine
some properties of \ld-controllable languages and present an approach to
optimizing a realization.Comment: 22 pages, 5 figure
On the quasi-heredity and the semi-simplicity of cellular algebras
AbstractSome simpler homological characterizations of quasi-hereditary algebras inside the class of cellular algebras are presented in terms of cell modules. Moreover, some new criteria for the semi-simplicity of cellular algebras are given by using the cohomology groups of cell modules and simple modules
State-Based Control of Fuzzy Discrete Event Systems
To effectively represent possibility arising from states and dynamics of a
system, fuzzy discrete event systems as a generalization of conventional
discrete event systems have been introduced recently. Supervisory control
theory based on event feedback has been well established for such systems.
Noting that the system state description, from the viewpoint of specification,
seems more convenient, we investigate the state-based control of fuzzy discrete
event systems in this paper. We first present an approach to finding all fuzzy
states that are reachable by controlling the system. After introducing the
notion of controllability for fuzzy states, we then provide a necessary and
sufficient condition for a set of fuzzy states to be controllable. We also find
that event-based control and state-based control are not equivalent and further
discuss the relationship between them. Finally, we examine the possibility of
driving a fuzzy discrete event system under control from a given initial state
to a prescribed set of fuzzy states and then keeping it there indefinitely.Comment: 14 double column pages; 4 figures; to be published in the IEEE
Transactions on Systems, Man, and Cybernetics--Part B: Cybernetic
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