a new algorithm for testing diagnosability of fuzzy discrete event systems failure diagnosis and detection of fuzzy discrete event systems play a significant role in the study of complex systems in this paper we investigate the diagnosability of fuzzy discrete event systems by proposing a new algorithm based on the concept of undistinguishable strings moreover a necessary and sufficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed with respect to the minimal observable event the computing process to check the diagnosability of fuzzy dess and some examples serving to illuminate the applications are developed and described

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

computation tree logic model checking based on possibility measures in order to deal with the systematic verification with uncertain information in possibility theory li and li 2013 introduced model checking of linear time properties in which the uncertainty is modeled by possibility measures xue lei and li 2011 defined computation tree logic ctl based on possibility measures which is called possibilistic ctl poctl this paper is a continuation of the above work first we study the expressiveness of poctl unlike probabilistic ctl it is shown that poctl in particular qualitative poctl is more powerful than ctl with respect to their expressiveness the equivalent expressions of basic ctl formulae using qualitative poctl formulae are presented in detail some poctl formulae that cannot be expressed by any ctl formulae are presented in particular some qualitative properties of repeated reachability and persistence are expressed using poctl formulae next adapting ctl model checking algorithm a method to solve the poctl model checking problem and its time complexity are discussed in detail finally an example is given to illustrate the poctl model checking method

diagnosability of fuzzy discrete event systems in this paper discrete event systems dess are reformulated as fuzzy discrete event systems fdess and fuzzy discrete event dynamical systems fdedss these frameworks include fuzzy states events and if then rules in these frameworks all events occur at the same time with different membership degrees fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems such as fault diagnosis applications to measure a diagnoser s fault discrimination ability a fuzzy diagnosability degree is proposed if the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system for any degree less than one researchers should not devote their time to distinguish all possible fault types correctly thus two different diagnosability definitions fdeds and fdes are introduced due to the specialized fuzzy rule base embedded in the fdeds it is capable of representing a class of non linear dynamic system computationally speaking the framework of diagnosability of the fdeds is structurally similar to the framework of diagnosability of a non linear system the crisp des diagnosability has been turned into the term fuzzy diagnosability for the fdes the newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non linear systems in addition a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development finally the potential applications of the proposed method are discussed

algebraic properties of l fuzzy finite automata fuzzy automata theory on lattice ordered monoids was introduced by li and pedrycz dropping the distributive laws fuzzy finite automata l ffas for short based on a more generalized structure l named a po monoid are presented and investigated from the view of algebra in this paper the notions of strong successor and source operators fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail using the weak primary submachines a unique decomposition theorem of a fuzzy finite automaton based on a lattice ordered monoid is obtained taking l as a quantale fuzzy subsystems are proved to be the same as fuzzy submachines of an l ffa in particular intrinsic connections between algebraic properties of l and properties of some operators of an l ffa are discovered it is shown that the join preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when l is a lattice ordered monoid

nonblocking check in fuzzy discrete event systems based on observation equivalence in this paper we deal with the synthesis about nonblocking check in fuzzy discrete event systems fdess by using abstraction and observation equivalence of fuzzy finite automaton ffa in fdess such a check imposes a great computational challenge because of the complexity incurred by the composition of plants and the supervisors with respect to ideas in modeling control system we present procedure based on ffa abstractions which removes internal transitions of irrelevant transitions allowing the nonblocking check to be performed on relatively small automata

diagnosability of fuzzy discrete event systems a fuzzy approach in order to more effectively cope with the real world problems of vagueness fuzzy discrete event systems fdess were proposed by lin and ying recently then we and cao and ying investigated the supervisory control of fdess independently in this paper we are concerned with another important issue of fdess the failure diagnosis more specifically 1 we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree which takes values in the interval 0 1 rather than 0 1 2 based on the observability of events we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis 3 a number of basic properties of the diagnosers are investigated in particular we present a necessary and sufficient condition for failure diagnosis of fdess our results generalize the important consequences of the diagnosability for crisp discrete event systems dess introduced by sampath et al the newly proposed approach allows us to deal with the problem of diagnosability for both crisp dess and fdess 4 in addition a method for checking the fuzzy diagnosability for fdess is proposed also some examples are provided to illustrate the application of the diagnosability of fdess

stationary lqg control of singular systems the stationary linear quadratic gaussian control problem is formulated and solved for single input single output singular systems the control system is required to be internally proper and stable in order to avoid both impulsive and unstable exponential behavior the set of all controllers resulting in such a control system is specified in parametric form all controllers that yield finite cost are identified once again in parametric form within this set necessary and sufficient conditions are then established for an optimal controller to exist all optimal controllers are shown to possess the same transfer function the problem is analyzed in the complex domain the transfer functions are expressed as quotients of proper strict hurwitz rational functions by means of this maneuver the powerful tools of algebra are made available the synthesis of the optimal controller is reduced to the solution of two linear diophantine equations whose coefficients are obtained by spectral factorization

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

theory of generalized fuzzy discrete event systems there exist a large number of systems whose state variables are continuous signals and transit based on event driven mechanisms to model the transitions of these state variables the theory of extended fuzzy discrete event systems efdess was developed by extending the fuzzy discrete event system fdes theory however the efdes theory remains limited in modeling these event driven systems a primary reason for this is that the efdes theory allows every event to be characterized by one variable only and thus every event can be modeled by a fuzzy set fs only although the efdes theory provides the steps for computing the next states of the state variables how to compute their next states remains unknown when any event is modeled by multiple fss to overcome this limitation this paper will present the theory of generalized fuzzy discrete event systems gfdess by generalizing the efdes theory in the proposed gfdes theory events are characterized by their multiple attributes which may determine the transitions of the state variables and are modeled by representing each of their attributes using one fs to establish the gfdes theory models for gfdess will be presented by extending the concepts of efdess to make this theory complete the procedures for computing the next states of the state variables will also be provided in addition numerical examples will be presented to further illustrate the proposed gfdes theory

a belief evolution based approach for online control of fuzzy discrete event systems under partial observation in this paper we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete event systems dess the goal is to synthesize a fuzzy supervisor such that the behavior of the closed loop system is within a given fuzzy language a new approach for solving this problem is proposed based on the idea of belief evolution specifically we propose an algorithm that can be implemented in an online manner we show that the proposed algorithm is both sound and complete i e it effectively solves the supervisor synthesis problem to the best of our knowledge this is the first algorithm with such a property for fuzzy dess as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem

feedback capacity of the gaussian interference channel to within 2 bits we characterize the capacity region to within 2 bits s hz and the symmetric capacity to within 1 bit s hz for the two user gaussian interference channel ic with feedback we develop achievable schemes and derive a new outer bound to arrive at this conclusion one consequence of the result is that feedback provides multiplicative gain at high signal to noise ratio the gain becomes arbitrarily large for certain channel parameters this finding is in contrast to point to point and multiple access channels where feedback provides no gain and only bounded additive gain respectively the result makes use of a linear deterministic model to provide insights into the gaussian channel this deterministic model is a special case of the el gamal costa deterministic model and as a side generalization we establish the exact feedback capacity region of this general class of deterministic ics

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

outer bounds on the capacity of gaussian interference channels two outer bounds on the capacity region of the two user gaussian interference channel ifc are derived the idea of the first bound is to let a genie give each receiver just enough information to decode both messages this bound unifies and improves the best known outer bounds of sato and carleial furthermore the bound extends to discrete memoryless ifcs and is shown to be equivalent to another bound of carleial the second bound follows directly from existing results of costa and sato and possesses certain optimality properties for weak interference

decentralized diagnosis of stochastic discrete event systems we investigate the decentralized diagnosis of stochastic discrete event systems sdess by using multiple local stochastic diagnosers each possessing its own sensors to deal with different information we formalize the notions of decentralized diagnosis for sdess by defining the concept of codiagnosability for stochastic automata in which any communication among the local stochastic diagnosers or to any coordinators is not involved these notions are weaker than the corresponding notions of decentralized diagnosis of classical dess a stochastic system being codiagnosable means that a fault can be detected by at least one local stochastic diagnoser within a finite delay we construct a codiagnoser from a given stochastic system with a finite number of projections whose each diagnosis component uses the complete model of the system we also deal with a number of basic properties of the codiagnoser in particular a necessary and sufficient condition of the codiagnosability for sdess is presented which generalizes the corresponding results of centralized diagnosis for sdess also we give a computing method in detail to check the codiagnosability of sdess as an application of our results some examples are described

state based decentralized diagnosis of bi fuzzy discrete event systems recently we have introduced bi fuzzy discrete event systems bfdess and established their supervisory control theory under full observations and partial observations respectively compared with the models of discrete event systems and fuzzy discrete event systems bfdess are more satisfactory models to characterize some high uncertainty systems in this paper we study the fault diagnosis problems of bfdess first the framework of state based decentralized diagnosis is introduced then the notion of state based codiagnosability is defined and a necessary and sufficient condition for state based codiagnosability is provided in particular a polynomial time algorithm for state based codiagnosability verification and an online decentralized diagnosis method are presented in addition a compact state based decentralized diagnosis framework is introduced and the notion of state based jointly diagnosability and its verification algorithm are proposed finally the implication relationships between the two diagnosabilities are investigated

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

safe diagnosability of fuzzy discrete event systems and a polynomial time verification since fuzzy discrete event systems fdess were significantly brought forward the study of fdess has received increasing attention recently this paper addresses the safe diagnosability under the framework of fdess the contributions are threefold first the notion of safe diagnosability for fuzzy systems is formalized a safe diagnosable fdes means that not only each failure can be detected in terms of fuzziness as well as the detection must be completed before any unsafe operation is executed then a necessary and sufficient condition of safe diagnosability of fdess is proposed by constructing the safe diagnoser finally we present an algorithm for verifying the safe diagnosability of fdess based on a constructive nondeterministic automaton namely verifier it is worth noting that both constructing the verifier and verifying the safe diagnosability of fdess can be realized with a polynomial complexity

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

on factorized l fuzzy automaton and its l fuzzy topological characterization abstract this paper is towards the study of l fuzzy automata via theory of factorizations where l is a complete residuated lattice we study the concept of factorization of l fuzzy sets and factorization of collection of l fuzzy sets such factorizations are used i to study the concept of minimal l fuzzy automaton and ii to introduce l fuzzy topologies for the study of concepts associated with an l fuzzy automaton specifically we introduce the notion of factorized l fuzzy automaton corresponding to a given l fuzzy automaton and study the minimality of such automaton further we associate l fuzzy topologies for factorized l fuzzy automaton and use these to characterize some algebraic concepts

model checking of linear time properties based on possibility measure using possibility measure we study model checking of linear time properties in possibilistic kripke structures first the notion of possibilistic kripke structures and the related possibility measure are introduced and then model checking of reachability and repeated reachability linear time properties in finite possibilistic kripke structures are studied standard safety properties and regular properties in possibilistic kripke structures are introduced the verification of regular safety properties and regular properties using finite automata are thoroughly studied it has been shown that the verification of regular safety properties and regular properties in a finite possibilistic kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic kripke structure that is introduced in this paper several examples are given to illustrate the methods that are presented in this paper

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

safe diagnosability of stochastic discrete event systems recently safe diagnosability of discrete event systems dess was investigated by paoli and lafortune which was viewed as the first necessary step of fault tolerant supervision in this paper we consider the problem of safe diagnosability in the framework of stochastic discrete event systems sdess we define the notion of safe diagnosability for stochastic automata in which fault detection occurs before any given forbidden string in the failed mode of system is executed the relationship between diagnosability and safe diagnosability for sdess is analyzed in particular a necessary and sufficient condition for safe diagnosability of sdess is presented by constructing the recognizer of illegal language and the safe diagnoser some examples are described to illustrate the results

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

fuzzy discrete event systems for multiobjective control framework and application to mobile robot navigation fuzzy discrete event systems fdess have been introduced in recent years to model systems whose discrete states or discrete state transitions can be uncertain and are hence determined by a possibility degree this paper develops an fdes framework for the control of sampled data systems that have to fulfill multiple objectives the choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements the proposed framework consists of three basic steps that are performed at each sampling instant first the current fuzzy state of the system is determined by a sensor evaluation second the fuzzy state in the future sampling instant is predicted for all possible control actions of the system finally an original multiobjective weighting strategy is proposed to determine the control action to be applied in the current sampling instant the features of the proposed approach are demonstrated by a detailed mobile robot example which includes a simulation study

when does output feedback enlarge the capacity of the interference channel in this paper the benefits of channel output feedback in the gaussian interference channel g ic are studied under the effect of additive gaussian noise using a linear deterministic ld model the signal to noise ratios snrs in the feedback links beyond which feedback plays a significant role in terms of increasing the individual rates or the sum rate are approximated the relevance of this work lies in the fact that it identifies the feedback snrs for which in any g ic one of the following statements is true a feedback does not enlarge the capacity region b feedback enlarges the capacity region and the sum rate is greater than the largest sum rate without feedback and c feedback enlarges the capacity region but no significant improvement is observed in the sum rate

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

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 modeled 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

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

approximate capacity region for the symmetric gaussian interference channel with noisy feedback recent results have shown that feedback can significantly increase the capacity of interference networks this paper considers the impact of noise on such gains due to feedback in particular this paper considers the two user linear deterministic interference channel with noisy feedback as a stepping stone to characterize the approximate capacity region for the two user gaussian interference channel with noisy feedback first the capacity region for the symmetric linear deterministic interference channel with noisy feedback is obtained it is shown that noisy feedback enlarges the capacity region if and only if the number of feedback bits l is greater than a certain threshold l it is found that excluding the regime 1 2 leq alpha leq 2 where alpha is the normalized interference level in which even full feedback does not increase symmetric capacity this threshold l is equal to the per user symmetric capacity without feedback one of the key ideas is a novel converse outer bounding technique for the weighted sum rates 2r 1 r 2 and r 1 2r 2 these results and the techniques developed for the linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric gaussian interference channel with noisy feedback the outer bounds are shown to be at most 4 7 b s hz away from the achievable rate region as a corollary the generalized degrees of freedom region which approximates the capacity region of the symmetric gaussian interference channel at high snr is found