on a misconception involving point collocation and the rayleigh hypothesis it is shown that the rayleigh hypothesis does not govern convergence of the simple point collocation approach to the numerical solution of scattering by a sinusoidal grating a previously developed numerical technique interval arithmetic is employed to perform some decisive numerical experiments which not only support but guarantee the validity of this conclusion

random rotations of the wiener path let w h be an abstract wiener space and letr w be a strongly measurable random variable with values in the set of isometries onh suppose that rh is smooth in the sobolev sense and that it is a quasi nilpotent operator onh for everyh h it is shown that r w h is again a gaussian 0 h 2 random variable consequently if e i i w is a complete orthonormal basis ofh then tilde w sum nolimits i delta r w e i e i defines a measure preserving transformation a rotation onw it is also shown that if for some strongly measurable operator valued onh random variabler r w k h is 0 h 2 gaussian for allk h h thenr is an isometry and rh is quasi nilpotent for allh h the relation between the stochastic calculi for these wiener pathsw and tilde w as well as the conditions of the inverbibility of the map w to tilde w are discussed and the problem of the absolute continuity of the image of the wiener measure under euclidean motion on the wiener space i e w to tilde w composed with a shift is studied

design of decentralized critical observers for networks of finite state machines a formal method approach abstract motivated by safety critical applications in cyber physical systems in this paper we study the notion of critical observability and design of observers for networks of finite state machines fsms critical observability corresponds to the possibility of detecting if the current state of an fsm is in a given region of interest called set of critical states a critical observer detects on line the occurrence of critical states when a large scale network of fsms is considered the construction of such an observer is prohibitive because of the large computational effort needed we propose a decentralized architecture for critical observers of networks of fsms where on line detection of critical states is performed by local critical observers each associated with an fsm of the network which do not need to interact for the efficient design of decentralized critical observers we first extend on the fly algorithms traditionally used in the community of formal methods for the verification and control design of fsms we then extend to networks of fsms bisimulation theory traditionally given in the community of formal methods for single fsms the proposed techniques provide a remarkable computational complexity reduction as discussed throughout the paper and also demonstrated by means of illustrative examples

regularity of invariant measures on finite and infinite dimensional spaces and applications abstract in this paper we prove new results on the regularity i e smoothness of measures solving the equation l 0 for operators of type l b on finite and infinite dimensional state spaces e in particular we settle a conjecture of i shigekawa in the situation where h is the gross laplacian e h is an abstract wiener space and b id e v where v takes values in the cameron martin space h using gross logarithmic sobolev inequality in an essential way we show that is always absolutely continuous w r t the gaussian measure and that the square root of the density is in the malliavin test function space of order 1 in l 2 furthermore we discuss applications to infinite dimensional stochastic differential equations and prove some new existence results for l 0 these include results on the inverse problem i e we give conditions ensuring that b is the vector logarithmic derivative of a measure we also prove necessary and sufficient conditions for to be symmetrizing i e l is symmetric on l 2 finally a substantial part of this work is devoted to the uniqueness of symmetrizing measures for l we characterize the cases where we have uniqueness by the irreducibility of the associated classical dirichlet forms

equations differentielles sur l espace de wiener et formules de cameron martin non lineaires proprietes algebriques des approximations sur r n une formule de perturbation des flots et convergence des approximations formule de changement de variable sur x et equation differentielle

distributed trace estimation under timing mismatch and channel distortion in conservative or complete trace based distributed fault diagnosis it is common to compute for each component a preliminary local estimate consisting of all possible traces that can generate the same local symptom i e a collection of sequences of observable events as the one being received from that component up to a specific time instant then communication among local trace estimators can be used to refine those preliminary local estimates an approach has been proposed by su and wonham to perform such refinement in terms of achieving global or local consistency among local estimates but that approach does not consider timing mismatch and channel distortion in the process of collecting local symptoms which may result in incorrect estimates in practical applications in this paper we will provide a new approach to handle trace estimation under timing mismatch and channel distortion

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

mechanics of granular materials the discrete and the continuum descriptions juxtaposed abstract in recent years a discussion could be followed where the pros and cons of the applicability of the cosserat continuum model to granular materials were debated bardet j p vardoulakis i 2001 the asymmetry of stress in granular media int j solids struct 38 353 367 kruyt n p 2003 static and kinematics of discrete cosserat type granular materials int j solids struct 40 511 534 bagi k 2003 discussion on the asymmetry of stress in granular media int j solids struct 40 1329 1331 bardet j p vardoulakis i 2003a reply to discussion by dr katalin bagi int j solids struct 40 1035 kuhn m 2003 discussion on the asymmetry of stress in granular media int j solids struct 40 1805 1807 bardet j p vardoulakis i 2003b reply to dr kuhn s discussion int j solids struct 40 1809 ehlers w ramm e diebels s d addetta g a 2003 from particle ensembles to cosserat continua homogenization of contact forces towards stresses and couple stresses int j solids struct 40 6681 6702 chang c s kuhn m r 2005 on virtual work and stress in granular media int j solids struct 42 3773 3793 the authors follow closely this debate and try with this paper to provide a platform where the various viewpoints could find their position we consider an ensemble of rigid arbitrarily shaped grains as a set with structure we establish a basic mathematical framework which allows to express the balance laws and the action reaction laws for the discrete system in a global form through the concepts of part granular surface separately additive function and flux the independent variable in the balance laws is then the arbitrary part of the assembly rather than the single grain a parallel framework is constructed for cosserat continua by applying the axiomatics established by noll w 1959 the foundation of classical mechanics in the light of recent advances in continuum mechanics in the axiomatic method with special reference to geometry and physics north holland publishing co amsterdam pp 266 281 gurtin m e williams w o 1967 an axiomatic foundation of continuum thermodynamics arch rat mech anal 26 83 117 gurtin m e martins l c 1976 cauchy s theorem in classical physics arch rat mech anal 60 305 324 the comparison between the two realisations suggests the microscopic interpretation for some features of cosserat mechanics among which the asymmetry of the cauchy stress tensor and the couple stress

polynomial time verification of diagnosability of partially observed discrete event systems the problem of verifying the properties of diagnosability and i diagnosability is considered we present new polynomial time algorithms for deciding diagnosability and i diagnosability these algorithms are based on the construction of a nondeterministic automaton called a verifier

on the decidability and complexity of diagnosability for labeled petri nets in this paper we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled petri nets first we show that checking diagnosability for unbounded petri nets is decidable we present a new necessary and sufficient condition for diagnosability which can be reduced to a model checking problem for unbounded petri nets then we show that checking diagnosability for unbounded petri nets is expspace complete this complexity result is further extended to various subclasses of petri nets to the best of our knowledge this is the first paper that establishes decidability and complexity results for diagnosability of unbounded petri nets

a polynomial algorithm for testing diagnosability of discrete event systems failure diagnosis in large and complex systems is a critical task in the realm of discrete event systems sampath et al 1995 proposed a language based failure diagnosis approach they introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system the complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types we give an algorithm for testing diagnosability that does not construct a diagnoser for the system and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types

numerical algorithm based on the mode matching method with a singular smoothing procedure for analyzing edge type scattering problems an effective numerical method for analyzing edge type scattering problems is presented with its analytical foundations the general theory is applied to an arbitrarily shaped two dimensional scatterer with an edge point convergence of the approximate solutions is proven and an algorithm for numerical computation is derived the algorithm is employed for the resolution of the problem of a rectangular cylinder numerical data on the speed of the convergence show the validity and the efficiency of this method some examples for far field patterns and back scattering cross sections as functions of the wavenumber are given

brief paper on line fault detection in discrete event systems by petri nets and integer linear programming the paper addresses the fault detection problem for discrete event systems in a petri net pn framework assuming that the structure of the pn model and the initial marking are known faults are modelled by unobservable transitions moreover we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown the proposed diagnoser works on line it waits for the firing of an observable transition and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults the results characterize the properties that the pn modelling the system fault behaviour has to fulfill in order to reduce the on line computational effort

optimal sensor selection for ensuring diagnosability in labeled petri nets this paper studies the problem of optimal static sensor selection for ensuring diagnosability in labeled bounded and unbounded petri nets starting from a non diagnosable labeled petri net system we present a systematic procedure to design a new labeling function that makes the system diagnosable and optimizes a given objective function this procedure employs a particular net called verifier net that is built from the original petri net and provides necessary and sufficient conditions for diagnosability we exploit the system structure captured in the verifier net to guide the search for the desired new labeling function the search is performed over an unfolding of the reachability coverability tree of the verifier net and follows a set of rules that capture the relabeling strategy we allow for unobservable transitions that cannot be labeled as well as for multiple fault classes we formulate an integer linear programming problem that finds an optimal labeling function when numerical costs are associated with transition relabeling

more on solving systems of power equations it is known that a system of power equations can be reduced to a single variable polynomial equation by exploiting the so called newton s identities in this work we investigate four new types of power equation systems in the first two types we allow the powers to be a mix of positive and negative terms whereas in the literature the system of power equations involves only positive powers the first type involves only positive signs of powers whereas the second type expands to involve both positive and negative signs we present algebraic methods to solve the system and furthermore fully characterize the number of nontrivial solutions the other two types are defined over finite fields and otherwise are the same as the conventional system of power equations the methodology for solving the third type can be viewed as a generalization of the berlekamp algorithm the solution space of the last system is fully characterized despite the fact that the number of equations is two less than the number of unknowns

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

numerical method for calculating surface current density on a two dimensional scatterer with smooth contour a numerical method is presented for finding the surface current density on a two dimensional smooth scatterer this method is an improved version of a method which one of the authors presented as an adjoint method to the conventional mode matching method mmm for finding the scattered field after formulating the problem we interpret the method being adjoint to the conventional mode matching method and show that the method yields a sequence of approximate current densities converging to the true density in the mean squares sense next we propose the improved method and prove the fact that this method yields a sequence of approximate solutions which converges to the true density uniformly on the contour of the scatterer we then state that the method is an adjoint one to the mode matching method with a smoothing procedure sp which we proposed as a powerful numerical method for the scattered field numerical results of some sample calculation are attached to show the effectiveness of the new method

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

generalized detectability for discrete event systems in our previous work we investigated detectability of discrete event systems which is defined as the ability to determine the current and subsequent states of a system based on observation for different applications we defined four types of detectabilities weak detectability strong detectability weak periodic detectability and strong periodic detectability in this paper we extend our results in three aspects 1 we extend detectability from deterministic systems to nondeterministic systems such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems 2 we develop polynomial algorithms to check strong detectability the previous algorithms are based on observer whose construction is of exponential complexity while the new algorithms are based on a new automaton called detector 3 we extend detectability to d detectability while detectability requires determining the exact state of a system d detectability relaxes this requirement by asking only to distinguish certain pairs of states with these extensions the theory on detectability of discrete event systems becomes more applicable in solving many practical problems

unicite de solutions d equations differentielles sur l espace de wiener soit x l espace de wiener et a un champ de vecteurs sur x on definit la notion de solution de l equation differentielle du dt 1 u t u 0 x on demontre un theoreme d unicite

absolutely continuous flows generated by sobolev class vector fields in finite and infinite dimensions abstract we prove the existence of the global flow ut generated by a vector field a from a sobolev class w1 1 on a finite or infinite dimensional space x with a measure provided is sufficiently smooth and that a a and a where a is the divergence with respect to are exponentially integrable in addition the measure is shown to be quasi invariant under ut in the case x r n and p dx where p w1 1loc r n is a locally uniformly positive probability density a sufficient condition is exp c a exp c a p p l1 for all c in the infinite dimensional case we get analogous results for measures differentiable along sufficiently many directions examples of measures which fit our framework important for applications are symmetric invariant measures of infinite dimensional diffusions and gibbs measures typically in both cases such measures are essentially non gaussian our result in infinite dimensions significantly extends previously studied cases where was a gaussian measure finally we study flows generated by vector fields whose values are not necessarily in the cameron martin space

anticipating flows on the wiener space generated by vector fields of low regularity abstract sobolev spaces for banach space valued wiener functionals are constructed using the operator norm for the h derivatives the corresponding sobolev norms are shown to be strictly weaker than the usual malliavin sobolev norms existing results on flows on an abstract wiener space generated by a vector field are generalized to the case where the vector field is a sum of a not necessarily bounded skew adjoint operator and a non linear part whose regularity is measured by the new sobolev norms this is equivalent to a non linear perturbation of a semi group of rotations

abstraction based failure diagnosis for discrete event systems in this paper we introduce the idea of abstraction based diagnosability for large scale composed discrete event systems that consist of multiple subsystems to this end we determine sufficient conditions such that diagnosability of the original system follows from diagnosability of an abstracted system model on a smaller state space in addition we prove that also the reverse implication is true if an additional requirement for the abstraction is fulfilled then we show how our method can be applied to compute abstracted models for the diagnosability verification of composed systems without enumerating the whole system state space in this way considerable computational savings can be achieved as illustrated by a small manufacturing system example

differentiable families of measures abstract the paper studies differential and related properties of functions of a real variable with values in the space of signed measures in particular the connections between different definitions of differentiability are described corresponding to different topologies on the measures some conditions are given for the equivalence of the measures in the range of such a function these conditions are in terms of so called logarithmic derivatives and yield a generalization of the cameron martin maruyama girsanov formula questions of this kind appear both in the theory of differentiable mesures on infinite dimensional spaces and in the theory of statistical experiments

opacity of discrete event systems and its applications in this paper we investigate opacity of discrete event systems we define two types of opacities strong opacity and weak opacity given a general observation mapping a language is strongly opaque if all strings in the language are confused with some strings in another language and it is weakly opaque if some strings in the language are confused with some strings in another language we show that security and privacy of computer systems and communication protocols can be investigated in terms of opacity in particular two important properties in security and privacy namely anonymity and secrecy can be studied as special cases of opacity we also show that by properly specifying the languages and the observation mapping three important properties of discrete event systems namely observability diagnosability and detectability can all be reformulated as opacity thus opacity has a wide range of applications also in this paper we provide algorithms for checking strong opacity and weak opacity for systems described by regular languages and having a generalized projection as the observation mapping

transformation of wiener measure under anticipative flows lett f be a transformation from the wiener space to itself with the range off assumed to be in the cameron martin space the absolute continuity and the density function associated witht is considered t is assumed to be embedded in or defined through a parameterizationt t f t andf t is assumed to be differentiable int the paper deals first with the case where the range of thet derivative off t is also in the cameron martin space and new representations for the radon nikodym derivative and the carleman fredholm determinant are derived the case where thet derivative off t is not in the cameron martin space is considered next and results on the absolute continuity and the density function under conditions which are considerably weaker than previously known conditions are presented

algebraic approaches for fault identification in discrete event systems in this note we develop algebraic approaches for fault identification in discrete event systems that are described by petri nets we consider faults in both petri net transitions and places and assume that system events are not directly observable but that the system state is periodically observable the particular methodology we explore incorporates redundancy into a given petri net in a way that enables fault detection and identification to be performed efficiently using algebraic decoding techniques the guiding principle in adding redundancy is to keep the number of additional petri net places small while retaining enough information to be able to systematically detect and identify faults when the system state becomes available the end result is a redundant petri net embedding that uses 2k additional places and enables the simultaneous identification of 2k 1 transition faults and k place faults that may occur at various instants during the operation of the petri net the proposed identification scheme has worst case complexity of o k m n operations where m and n are respectively the number of transitions and places in the given petri net

on the equivalence of observation structures for petri net generators observation structures considered for petri net generators usually assume that the firing of transitions may be observed through a static mask and that the marking of some places may be measurable these observation structures however are rather limited namely they do not cover all cases of practical interest where complex observations are possible we consider in this paper more general ones by correspondingly defining two new classes of petri net generators labeled petri nets with outputs lpnos and adaptive labeled petri nets alpns to compare the modeling power of different petri net generators the notion of observation equivalence is proposed alpns are shown to be the class of bounded generators possessing the highest modeling power looking for bridges between the different formalisms we first present a general procedure to convert a bounded lpno into an equivalent alpn or even into an equivalent labeled petri net if any exists finally we discuss the possibility of converting an unbounded lpno into an equivalent alpn

brief paper abstraction based verification of codiagnosability for discrete event systems in this paper we investigate the verification of codiagnosability for discrete event systems des that is it is desired to ascertain if the occurrence of system faults can be detected based on the information of multiple local sites that partially observe the overall des as an improvement of existing codiagnosability tests that resort to the original des with a potentially computationally infeasible state space we propose a method that employs an abstracted system model on a smaller state space for the codiagnosability verification furthermore we show that this abstraction can be computed without explicitly evaluating the state space of the original model in the practical case where the des is composed of multiple subsystems

observability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds observations are assumed to be a subset of the event alphabet observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions a polynomial test for observability is given it is shown that an observer may be constructed and implemented in polynomial time and space a bound on the cardinality of the observer state space is also presented a notion of resiliency is defined for observers and a test for resilient observability and a procedure for the construction of a resilient observer are presented

on line fault diagnosis with partially observed petri nets this technical note concerns fault detection and diagnosis for discrete event systems modeled with partially observed petri nets the proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system to this end the observation sequences are decomposed into elementary observation sequences linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence and an algorithm of linear complexity with respect to the length of the observation sequences is proposed to provide on line diagnosis decisions

complexity results for 1 safe nets we study the complexity of several standard problems for 1 safe petri nets and some of its subclasses we prove that reachability liveness and deadlock are all pspace complete for 1 safe nets we also prove that deadlock is np complete for free choice nets and for 1 safe free choice nets finally we prove that for arbitrary petri nets deadlock is equivalent to reachability and liveness

on k diagnosability of petri nets via integer linear programming this paper deals with the problem of diagnosability of a fault after the firing of a finite number events i e k diagnosability this problem corresponds to diagnosability of a fault within a finite delay in the context of discrete event systems the main contribution of this paper is a necessary and sufficient condition for k diagnosability of bounded nets the proposed approach exploits the mathematical representation of petri nets and the integer linear programming optimization tool in particular no specific assumptions are made on the structure of the net induced by the unobservable transitions since the proposed approach permits to detect also the undiagnosability due to the presence of unobservable cycles

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

failure diagnosis of discrete event systems with linear time temporal logic specifications the paper studies failure diagnosis of discrete event systems dess with linear time temporal logic ltl specifications the ltl formulas are used for specifying failures in the system the ltl based specifications make the specification specifying process easier and more user friendly than the formal language automata based specifications and they can capture the failures representing the violation of both liveness and safety properties whereas the prior formal language automaton based specifications can capture the failures representing the violation of only the safety properties such as the occurrence of a faulty event or the arrival at a failed state prediagnosability and diagnosability of dess in the temporal logic setting are defined the problem of testing prediagnosability and diagnosability is reduced to the problem of model checking an algorithm for the test of prediagnosability and diagnosability and the synthesis of a diagnoser is obtained the complexity of the algorithm is exponential in the length of each specification ltl formula and polynomial in the number of system states and the number of specifications the requirement of nonexistence of unobservable cycles in the system which is needed for the diagnosis algorithms in prior methods to work is relaxed finally a simple example is given for illustration

polynomial time verification of decentralized diagnosability of discrete event systems the first step in the diagnosis of failure occurrences in discrete event systems is the verification of the system diagnosability several works have addressed this problem using either diagnosers or verifiers for both centralized and decentralized architectures in this technical note we propose a new algorithm to verify decentralized diagnosability of discrete event systems the proposed algorithm requires polynomial time in the number of states and events of the system and has lower computational complexity than all other methods found in the literature in addition it can also be applied to the centralized case

computation of diagnosable fault occurrence indices for systems with repeatable faults certain faults such as intermittent or non persistent faults may occur repeatedly for discrete event systems prone to repeated faults jiang kumar and garcia in 2003 introduced the notion of l diagnosability requiring the diagnosis of the l th occurrence of a fault within a bounded delay the present paper studies the identification of the set of all indices l for which the system is not l diagnosable these are precisely the occurrence indices for which a repeatable fault cannot be diagnosed we present an algorithm of cubic complexity to determine whether a system is diagnosable for every fault occurrence index for those systems for which the answer is negative we show that the set of indices for which the system is non diagnosable possesses the property that it is either finite or consists of a finite number of eventually periodic sets

integration on loop groups i quasi invariant measures on a riemannian manifold m the brownian motion defines a wiener measure on the loops over m in the case of r quasi invariance means the cameron martin theorem s which fully describes the quasi invariance by translation of the wiener measure in order to state a generalization of this theorem we suppose that m is an homogeneous space under the action of a compact lie group the noncommutativity of this situation introduces a completely new phenomenon the hypoellipticity associated to the lie bracket of the basic vector fields curiously enough hypoellipticity which helps to get regularity in finite dimensions works against quasi invariance in infinite dimensions 18 we denote by g a compact connected lie group by h a connected subgroup of g and by m the homogeneous space g h we denote by y and 2 the corresponding lie algebras we choose a euclidean metric on 9 which is ad g invariant this metric induces a riemannian metric on g and on m we denote p g the paths space on g that is the space of continuous maps y from 0 l into g such that y o e we denote by l g the space of loops on g that is

smoothing properties of semigroups for dirichlet operators of gibbs measures abstract in this paper is investigated the special class of elliptic differential second order operators with an infinite number of variables with the property of a finite radius of dependence for variables this class is formed by the dirichlet operators associated with energy forms of gibbs measures on compact riemannian manifolds with a finite radius of interaction using this property we represent the dirichlet operator as a finite sum of self adjoint operators with independent variables and prove that the dirichlet operator semigroups preserve the specially constructed scales of continuously differentiable functions we also obtain that these semigroups raise the smoothness of initial functions

a cameron martin type quasi invariance theorem for brownian motion on a compact riemannian manifold abstract let m be a compact manifold without boundary o be a fixed base point in m g be a riemannian metric on m and be a g compatible covariant derivative on tm the tangent space to m assume the torsion t of satisfies the skew symmetry condition g t x y y 0 for all vector fields x and y on m for example take to be the levi civita covariant derivative on m g also let denote the wiener measure on w0 m c 0 1 m 0 o and let h s denote stochastic parallel translation relative to along the path w0 m up to time s 0 1 given a c1 function h 0 1 t0m it is shown that the differential equation t h t h with initial condition 0 id w m w m has a solution r maps w m w m the measurable maps from w m to w m this function is a flow on w m i e for all t r t t furthermore t has the quasi invariance property the law t of t with respect to the wiener measure is equivalent to for all t r this result is used to prove an integration by parts formula for the h derivative hf defined by h f d dt 0 f t where f is a c2 cylinder function on w m

on the structure of independence on wiener space motives par des resultats de travaux anterieurs sur la caracterisation de l independance de variables aleatoires dans l espace de wiener les auteurs etudient ici la relation entre l independance de certaines classes de sous algebres et l orthogonalite des h derivees faibles des variables aleatoires qui engendrent ces sous algebres ou c h est l espace de wiener classique

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

flows associated to adapted vector fields on the wiener space the existence and uniqueness of a flow associated to an adapted vector field on the wiener space with d a d b d are proved by a modified picard s iteration method mainly under the conditions of exponential integrability concerning b as well as the first order malliavin gradients of a and b a newton leibnitz type inequality for a kind of malliavin differentiable functionals is also proved which is the key point to prove the above result and has an independent interest

on solving composite power polynomial equations it is well known that a system of power polynomial equations can be reduced to a single variable polynomial equation by exploiting the so called newton s identities in this work by further exploring newton s identities we discover a binomial decomposition rule for composite elementary symmetric polynomials utilizing this decomposition rule we solve three types of systems of composite power polynomial equations by converting each type to single variable polynomial equations that can be solved easily for each type of system we discuss potential applications and characterize the number of nontrivial solutions up to permutations and the complexity of our proposed algorithmic solution

generalized mehler semigroups and applications we construct and study generalized mehler semigroups p t t 0 and their associated markov processesm the construction methods for p t t 0 are based on some new purely functional analytic results implying in particular that any strongly continuous semigroup on a hilbert spaceh can be extended to some larger hilbert spacee with the embeddingh e being hilbert schmidt the same analytic extension results are applied to construct strong solutions to stochastic differential equations of typedx t c dw t ax t dt with possibly unbounded linear operatorsa andc onh on a suitably chosen larger spacee for gaussian generalized mehler semigroups p t t 0 with corresponding markov processm the associated non symmetric dirichlet forms ed e are explicitly calculated and a necessary and sufficient condition for path regularity ofm in terms of e d e is proved then using dirichlet form methods it is shown thatm weakly solves the above stochastic differential equation if the state spacee is chosen appropriately finally we discuss the differences between these two methods yielding strong resp weak solutions

anticipative girsanov transformations the transformations of measures induced by left w int limits 0 bullet k s ds right with ks possibly anticipating the wiener process ws is discussed and a girsanovtype theorem under rather weak assumptions on ks is derived

dynamic observers as asymptotic limits of recursive filters special cases a method for constructing observers for dynamical systems as asymptotic limits of filters is described the program is carried out in detail for linear systems and in addition an observer is obtai

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

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

maximum likelihood failure diagnosis in finite state machines under unreliable observations in this paper we develop a probabilistic methodology for failure diagnosis in finite state machines based on a sequence of unreliable observations given prior knowledge of the input probability distribution but without actual knowledge of the applied input sequence the core problem we consider is to choose from a pool of known deterministic finite state machines fsms the one that most likely matches the given sequence of observations the problem becomes challenging because of sensor failures which may corrupt the observed sequence by inserting deleting and transposing symbols with certain probabilities that are assumed known we propose an efficient recursive algorithm for obtaining the most likely underlying fsm given the possibly erroneous observed sequence the proposed algorithm essentially allows us to perform online maximum likelihood failure diagnosis and is applicable to more general settings where one is required to choose the most likely underlying hidden markov model hmm based on a sequence of observations that may get corrupted with known probabilities the algorithm generalizes existing recursive algorithms for likelihood calculation in hmms by allowing loops in the associated trellis diagram we illustrate the proposed methodology using an example of diagnosis in the context of communication protocols

the diagnosability of petri net models using minimal explanations for a bounded petri net model the diagnosability property is usually checked via its regular language represented by the reachability graph rg however this is problematic because the computational complexity of the diagnosability test is polynomial in the cardinality of the state space of the model which is typically very large this limitation can be overcome by using for the diagnosability test an rof automaton with a state space significantly smaller than rg that generates the same language as rg after projecting out all non faulty unobservable transitions rof is efficiently constructed based on the calculation of the minimal explanations of the fault and of the observable transitions

reduction of constraints for controller synthesis based on safe petri nets in this paper we present an efficient method based on safe petri nets to construct a controller a set of linear constraints allows forbidding the reachability of specific states the number of these so called forbidden states and consequently the number of constraints are large and lead to a large number of control places a systematic method to reduce the size and the number of constraints for safe petri nets is offered by using a method based on petri net invariants maximal permissive controllers are determined

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

renormalized differential geometry on path space structural equation curvature abstract the theory of integration in infinite dimensions is in some sense the backbone of probability theory on this backbone the stochastic calculus of variations has given rise to the flesh of differential calculus its first step is the construction at each point of the probability space of a cameron martin like tangent space in which the desired differential calculus can be developed this construction proceeds along the lines of first order differential geometry in this paper we address the following questions what could be the meaning of curvature of the probability space how and why how can curvatures be defined and computed why could a second order differential geometry be relevant to stochastic analysis we try to answer these questions for the probability space associated to the brownian motion of a compact riemannian manifold why a basicenergy identity for anticipative stochastic integralswill be obtained as a byproduct of our computation of curvature how there are essentially four bottlenecks in the development of differential geometry on wiener riemann manifolds i the difficulty of finding an atlas of local charts such that the changes of charts preserve the class of the wiener like measures together with their associated cameron martin like tangent spaces ii the difficulty of finding cylindrical approximations preserving the natural geometrical objects iii the difficulty of renormalizing the divergent series to which the summation operations of finite dimensional differential geometry give rise in the non intrinsic context of local charts iv the nonavailability of the computational procedures analogous to the local coordinates systems of the classical differential geometry in the context of path space the ito filtration provides a much richer structure than that available in the framework of an abstract wiener riemann manifold our work is a systematic attempt to replace the machinery of local charts with amethodology of moving frames in our context stochastic parallel transport provides a canonical moving frame on the path space the concept of a cylindrical approximation has to be reshaped in our new situation into some geometric limit theorems establishing that the riemannian geometric objects of the cylindrical approximations induce by a limiting procedure geometric objects on the path space those limit theorems are reminiscent of the classical theorems which say that a stratonovich sde is the limit of an appropriate sequence of ode the canonical coordinate system provided by the moving frame will make it possible to proceed to the needed renormalizations byintrinsicstochastic integrals in this context the anticipative stochastic integral theory of nualart and pardoux will play a decisive role finally the moving frame will provide aneffective algorithm of computation for this differential geometry in infinite dimensions in our study we encounter a new type of renormalization thehypoelliptic renormalization which corresponds to the fact that the bracket of smooth vector fields taking their values in the cameron martin space can get out of this cameron martin space this hypoelliptic problem induces the nonrenormalizability of some geometrical objects it leads also to a concept oftangent processesto probability spaces extending that based on the cameron martin theorem for tangent processes a formula of integration by parts still holds furthermore the tangent processes form a lie algebra under the bracket on the other hand tangent processes cannot be stochastically integrated this operation is well defined only for cameron martin type vector fields

a petri net diagnoser for discrete event systems modeled by finite state automata we propose in this paper a petri net approach to online diagnosis of discrete event systems dess modeled by finite state automata the diagnosis method is based on the construction of a petri net diagnoser pnd which is constructed in polynomial time and requires less memory than other methods proposed in the literature we also present methods for the conversion of the pnd to both sequential function chart and ladder diagram for implementation on a programmable logic controller plc implementation issues are also addressed in the paper

brief paper suboptimal supervisory control of petri nets in presence of uncontrollable transitions via monitor places this paper deals with the problem of enforcing generalized mutual exclusion constraints gmec on place transition nets with uncontrollable transitions an efficient control synthesis technique which has been proposed in the literature enforces gmec constraints by introducing monitor places to create suitable place invariants the method has been shown to be maximally permissive and to give a unique control structure in the case that the set of legal markings is controllable this paper investigates on and formally shows that the class of controllers obtained by this technique may not have a supremal element for uncontrollable specifications moreover it is shown that the family of monitor places enforcing an uncontrollable specification can be parameterized with respect to the solution of a linear system of equation an algorithm to obtain such parameterization is presented here

petr nets algebras morphisms and compositionality abstract it is shown how a category of petri nets can be viewed as a subcategory of two sorted algebras over multisets this casts petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition the morphisms here respect the behaviour of nets the categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components for example various forms of parallel composition of petri nets arise naturally from the product in the category this abstract setting makes plain a useful functor from the category of petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of petri nets for instance the coloured and higher level nets of kurt jensen arise through a simple modification of the sorts of the algebras underlying nets further it provides a smooth formal relation with other models of concurrency such as milner s calculus of communicating systems ccs and hoare s communicating sequential processes csp though this is only indicated in this paper

computation of minimal diagnosis bases of discrete event systems using verifiers abstract in order to diagnose the occurrence of a fault event in a discrete event system des it is first necessary to verify if the language of the system is diagnosable with respect to an observable event set and a fault event set in some cases the language of the system is also diagnosable even when a subset of the set of observable events under consideration is used as the actual observable event set among the benefits that such a reduction may bring we list the reduction in the number of sensors used in the diagnosis therefore reducing the cost of the system and the possibility to deploy the sensor redundancy to obtain a more reliable diagnosis decision in this work we propose two algorithms to find in a systematic way all minimal subsets of the observable event set that ensure the diagnosability of the des minimal diagnosis bases the methods are based on the construction of verifiers and have lower computational complexity than another method recently proposed in the literature

learning regular sets from queries and counterexamples the problem of identifying an unknown regular set from examples of its members and nonmembers is addressed it is assumed that the regular set is presented by a minimamy adequate teacher which can answer membership queries about the set and can also test a conjecture and indicate whether it is equal to the unknown set and provide a counterexample if not a counterexample is a string in the symmetric difference of the correct set and the conjectured set a learning algorithm l is described that correctly learns any regular set from any minimally adequate teacher in time polynomial in the number of states of the minimum dfa for the set and the maximum length of any counterexample provided by the teacher it is shown that in a stochastic setting the ability of the teacher to test conjectures may be replaced by a random sampling oracle ex a polynomial time learning algorithm is shown for a particular problem of context free language identification

codiagnosability of discrete event systems revisited a new necessary and sufficient condition and its applications abstract it has been argued for some time now based on classroom textbook and practical examples that the size of verifiers and diagnosers is comparable this belief has been corroborated by a recent paper where it is conjectured based on a rigorous statistical analysis that the size of the states of diagnosers is n 0 77 log k 0 63 on the average where k resp n is the number of events resp states of the plant automaton however there is another difficulty that hampers the use of diagnosers in diagnosability verification the search for cycle which has been proved to be factorial we present in this paper a necessary and sufficient condition for a language codiagnosability of des and based on this condition we propose a new test for its verification that is based on a diagnoser like automaton that has following advantages i the diagnosability verification test is based on the search for strongly connected components which is linear in the state size ii it has both observable and unobservable events of the plant in its event set and so the usual assumptions on language liveness and nonexistence of unobservable cycles of states connected with unobservable events only are no longer required and iii t codiagnosability can be computed by adding weights associated with transitions of the plant automaton and as a consequence k codiagnosability since it is a particular case of t codiagnosability when all weights are set equal to 1

some relations among classes of σ fields on wiener space in this work we study sigma fields and their tangent spaces on the wiener space which are invariant in some sense with respect to the basic operators of the malliavin calculus

detectability of discrete event systems in this note we investigate the detectability problem in discrete event systems we assume that we do not know initially which state the system is in the problem is to determine the current and subsequent states of the system based on a sequence of observations the observation includes partial event observation and or partial state observation which leads to four possible cases we further define four types of detectabilities strong detectability weak detectability strong periodic detectability and weak periodic detectability we derive necessary and sufficient conditions for these detectabilities these conditions can be checked by constructing an observer which models the estimation of states under different observations the theory developed in this note can be used in feedback control and diagnosis if the system is detectable then the observer can be used as a diagnoser to diagnose the failure states of the system

delayed detectability of discrete event systems in this paper we extend detectability to delayed detectability in order to answer the following question after observing k1 k2 observable events can we determine the state of a system at the time when the k1th event was observed if the answer is yes we say that the system is delayed detectable it involves two delays the prior delay k1 before the estimation is attempted and the post delay k2 after which the estimation is completed we investigate various properties of delayed detectability we also provide polynomial algorithms to check delayed detectability the usefulness of delayed detectability is not only evident by the state estimation problems it solves which include current state estimation problem and initial state estimation problem but also evident by the fact that two important properties in discrete event systems namely observability and diagnosability can both be shown to be special cases of delayed detectability

real time identification of discrete event systems using petri nets the paper defines the identification problem for discrete event systems des as the problem of inferring a petri net pn model using the observation of the events and the available output vectors that correspond to the markings of the measurable places two cases are studied considering different levels of the system knowledge in the first case the place and transition sets are assumed known hence an integer linear programming problem is defined in order to determine a pn modelling the des in the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given hence the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors the integer linear programming problem is defined at each observation so that the pn can be recursively identified some results and examples characterize the identified pn systems and show the flexibility and simplicity of the proposed technique moreover an application to the synthesis of supervisory control of pn systems via monitor places is proposed

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

robust diagnosis of discrete event systems against intermittent loss of observations in the usual approaches to fault diagnosis of discrete event systems it is assumed that not only all sensors work properly but also all information reported by sensors always reaches the diagnoser any bad sensor operation or communication failure between sensors and the diagnoser can be regarded as loss of observations of events initially assumed as observable in such situations it may be possible that either the diagnoser stands still or report some wrong information regarding the fault occurrence in this paper we assume that intermittent loss of observations may occur and we propose an automaton model based on a new language operation language dilation that takes it into account we refer to this problem as robust diagnosability against intermittent loss of observations or simply robust diagnosability where the context allows we present a necessary and sufficient condition for robust diagnosability in terms of the language generated by the original automaton and propose two tests for robust language diagnosability one that deploys diagnosers and another one that uses verifiers we also extend the results to robust codiagnosability against intermittent loss of observations

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

a quasi invariance theorem for measures on banach spaces we show that for a measure on a banach space directional differentiability implies quasi translation invariance this result is shown to imply the cameron martin theorem a second application is given in which ty is the image of a gaussian measure under a suitably regular map

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems