diagnosability of discrete event systems subject to permanent sensor failures this paper considers a failure diagnosis problem for discrete event systems subject to permanent sensor failures a notion of diagnosability subject to permanent sensor failures is introduced with respect to a certain nondeterministic observation mask for its verification an aggregated mealy automaton with a deterministic and state dependent observation mask is defined it is shown that the diagnosability of the aggregated mealy automaton is equivalent to the diagnosability of the original system subject to permanent sensor failures then a method for verifying the diagnosability of the aggregated mealy automaton is presented moreover the delay bound within which the occurrence of any failure string can be detected subject to permanent sensor failures is computed

on a weaker notion of controllability of a language k with respect to a language l a necessary and sufficient condition for a prefix closed language k contained in sigma to be controllable with respect to another prefix closed language l contained in sigma is that k contained in l a weaker notion of controllability where it is not required that k contained in l is considered here if l is the prefix closed language generated by a plant automaton g then essentially there exists a supervisor theta that is complete with respect to g such that l theta mod g k intersection l if and only if k is weakly controllable with respect to l for an arbitrary modeling formalism it is shown that the inclusion problem is reducible to the problem of deciding the weaker notion of controllability therefore removing the requirement that k contained in l from the original definition of controllability does not help the situation from a decidability viewpoint this observation is then used to identify modeling formalisms that are not viable for supervisory control of the untimed behaviors of discrete event dynamic systems

integral representations for elliptic functions we derive new integral representations for constituents of the classical theory of elliptic functions the eisenstein series and weierstrass and functions the derivations proceed from the laplace mellin representation of multipoles and an elementary lemma on the summation of 2d geometric series in addition we present results concerning the analytic continuation of the eisenstein series to an entire function in the complex plane and the value of the conditionally convergent series denoted by e 2 below as a function of summation over increasingly large rectangles with arbitrary fixed aspect ratio 1

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

robust and nonblocking supervisor for discrete event systems with model uncertainty under partial observation addresses a robust and nonblocking supervisory control problem based on a framework of discrete event systems with model uncertainty under partial observation the uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems the paper presents a systematic method for modeling uncertainty described as a spl delta transition representing the internal and unobservable events in particular at a state with the assigned positive integer value p a system is assumed to experience at most a p step state transition by the internal and unobservable event under the framework for model uncertainty the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property

coulomb interactions on planar structures inverting the square root of the laplacian we present an adaptive fast multipole method for inverting the square root of the laplacian in two dimensions solving this problem is the dominant computational cost in many applications arising in electrical engineering geophysical fluid dynamics and the study of thin films it corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity our algorithm is direct and assumes only that the source distribution is discretized using an adaptive quad tree the amount of work grows linearly with the number of mesh points

an input output construction of finite state rho mu approximations for control design we consider discrete time plants that interact with their controllers via fixed discrete alphabets for this class of systems and in the absence of exogenous inputs we propose a general methodical approach for constructing a sequence of finite state approximate models starting from finite length sequences of input and output signal pairs we explicitly derive conditions under which the proposed construct used in conjunction with a particular generalized structure satisfies desirable properties of approximations thereby leading to nominal deterministic finite state machine models that can be used in certified by design controller synthesis we also show that the cardinality of the min imal disturbance alphabet that can be used in this setting equals that of the sensor output alphabet finally we show that the pro posed construct satisfies a relevant semi completeness property

supervisory control of hybrid systems within a behavioural framework abstract this contribution addresses the synthesis of supervisory control for hybrid systems with discrete external signals such systems are in general neither l complete nor can they be represented by finite state machines we find an l complete approximation abstraction l for represent it by a finite state machine and investigate the control problem for the approximation if a solution exists we synthesize the maximally permissive supervisor for l we show that it also solves the control problem for the hybrid system if no solution exists approximation accuracy can be increased by computing a k complete abstraction k k l this paper is entirely set within the framework on willems behavioural systems theory

optimal nonblocking directed control of discrete event systems for the control of discrete event systems the notion of directed control refines that of supervisory control a directed controller is one that selects at most one controllable event to be enabled at any state without disabling any uncontrollable event which is in fact how a discrete event control is implemented in contrast a supervisory controller computes a maximal allowable set of controllable events at each state leaving undecided exactly which controllable event should be enabled in previous works we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants in this paper we present a novel synthesis approach for general plants i e plants with or without cycles thus providing a complete solution to the optimal directed control problem the complexity of the approach remains polynomial in the size of plant

theory of extended fuzzy discrete event systems for handling ranges of knowledge uncertainties and subjectivity in 2001 we originated a theory of fuzzy discrete event systems fdess that generalized the conventional crisp discrete event systems dess vagueness and imprecision concerning states and event transitions of dess were represented by membership grades and computed via fuzzy logic our application of the fdes theory to computerized human immunodeficiency virus acquired immune deficiency syndrome treatment regimen selection although preliminarily successful suggests that a more comprehensive fdes theory is needed to address two general issues critically important not only to biomedical applications but also to real world problems in other industries first domain experts should have means other than point estimates and type 1 fuzzy sets mandated in the current framework to describe uncertainties subjectivity and imprecision in their complex knowledge and experience second when a group of experts with distinct opinions is involved they should not be forced to reach consensus for the sake of system development this is because collective consensus may not be achievable which is often the case in medicine where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time the theory of extended fdes presented in this paper addresses both the problems and contains the fdes theory as a special case experts are now allowed to use interval numbers and type 1 and type 2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices accordingly we have established mathematical operations that cover the computations of fuzzy states fuzzy event transitions and parallel composition numerical examples are provided

robust and nonblocking supervisory control of nondeterministic discrete event systems using trajectory models this note considers the robust supervisory control problems of uncertain nondeterministic discrete event systems dess the uncertain des to be controlled is assumed to be modeled as a set of some possible nondeterministic automata then the control objective is to achieve a given language specification and guarantee the nonblockingness of any nondeterministic automata of the set which are controlled by a robust nonblocking supervisor based on trajectory models this note presents the necessary and sufficient conditions for the existence of a robust nonblocking supervisor for a given uncertain nondeterministic des

doomsday equilibria for omega regular games abstract two player games on graphs provide the theoretical framework for many important problems such as reactive synthesis while the traditional study of two player zero sum games has been extended to multi player games with several notions of equilibria they are decidable only for perfect information games whereas several applications require imperfect information in this paper we propose a new notion of equilibria called doomsday equilibria which is a strategy profile where all players satisfy their own objective and if any coalition of players deviates and violates even one of the players objective then the objective of every player is violated we present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of regular objectives both for imperfect information games and for perfect information games we provide optimal complexity bounds for imperfect information games and in most cases for perfect information games

similarity based supervisory control of discrete event systems due to the appearance of uncontrollable events in discrete event systems one may wish to replace the behavior leading to the uncontrollability of pre specified language by some quite similar one to capture this similarity we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to spl lambda controllability where spl lambda indicates the similarity degree of two languages a necessary and sufficient condition for a language to be spl lambda controllable is provided we then examine some properties of spl lambda controllable languages and present an approach to optimizing a realization

on petri net models of infinite state supervisors a class of supervisory control problems that require infinite state supervisors is considered and petri nets with inhibitor arcs pns are introduced to model the supervisors this pn based approach to supervisory control is compared to automata based approaches the primary advantage of a pn based supervisory controller is that it provides a finite representation of an infinite state supervisor for verification implementation and testing reasons a finite pn based representation of an infinite state supervisor is preferred over an automata based supervisor it is shown that this modeling advantage is accompanied by a decision disadvantage in that in general the controllability of a language that can be generated by the closed loop system is undecidable

supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models the supervisory control of nondeterministic discrete event dynamical systems dedss with driven events in the setting of prioritized synchronization and trajectory models introduced by heymann are studied prioritized synchronization captures the notions of controllable uncontrollable and driven events in a natural way and the authors use it for constructing supervisory controllers the trajectory model is used for characterizing the behavior of nondeterministic dedss since it is a sufficiently detailed model in contrast to the less detailed language or failures models and serves as a language congruence with respect to the operation of prioritized synchronization results concerning controllability and observability in this general setting are obtained

robust supervisory control of a class of timed discrete event systems under partial observation this paper studies robust supervisory control of timed discrete event systems proposed by brandin and wonham given a set of possible models which includes the exact model of the plant the objective is to synthesize a robust supervisor such that it achieves legal behavior for all possible models we show that controllability for each possible model and observability for a suitably defined aggregate model are necessary and sufficient conditions for the existence of a solution to the robust supervisory control problem moreover when there does not exist a solution a maximally permissive robust supervisor is synthesized under the assumption that all controllable events are observable

faster fast evaluation of thin plate splines in two dimensions a new method for fast evaluation of thin plate splines in two dimensions is presented the paper first develops exponential approximations to thin plate splines these are the analytical basis for an improved fast multipole evaluator analytic error bounds are supplemented by offline parallel numerical computation of the underlying error constants these error constants enable adaptive selection of series lengths as a function of the weights associated with a source panel and the desired accuracy numerical comparisons with a competing algorithm show that the new method is significantly faster when moderate to high precision is required

verification of initial state opacity in security applications of discrete event systems in this paper we formulate and analyze methodologies for verifying the notion of initial state opacity in discrete event systems that are modeled as non deterministic finite automata with partial observation on their transitions a system is initial state opaque if the membership of its true initial state to a set of secret states remains opaque i e uncertain to an intruder who observes system activity through some projection map initial state opacity can be used to characterize security requirements in a variety of applications including tracking problems in sensor networks in order to model and analyze the intruder capabilities regarding initial state opacity we first address the initial state estimation problem in a non deterministic finite automaton via the construction of an initial state estimator we analyze the properties and complexity of the initial state estimator and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant we also establish that the verification of initial state opacity is a pspace complete problem

control of discrete event systems modeled as hierarchical state machines discrete event systems dess are systems in which state changes take place in response to events that occur discretely asynchronously and often nondeterministically a class of dess modeled as hierarchical state machines hsms a special case of the statecharts formalism introduced recently is considered an efficient algorithm is provided for solving reachability problems in the hsm framework it utilizes the hierarchical structure of hsms this efficient solution is used extensively in control applications where controllers achieving a desired behavior are synthesized online

the computational complexity of decentralized discrete event control problems computational complexity results are obtained for decentralized discrete event control problems these results generalize the earlier work of tsitsiklis 1989 who showed that for a special class of centralized supervisory control problems under partial observation there is an algorithm for determining in polynomial time whether or not a solution exists the negative complexity results associated with tsitsiklis work also carry over to the decentralized case so that solution existence for the more general class is not decidable in polynomial time nor does there exist a polynomial time algorithm for producing supervisor solutions when such solutions exist

robust and nonblocking supervisory control of nondeterministic discrete event systems with communication delay and partial observation for an uncertain nondeterministic discrete event system des modelled as a set of possible nondeterministic finite state automata uncontrollable events may subsequently occur before a control action issued by a robust supervisor is applied to the system due to delays in sensing communicating and actuating for an uncertain nondeterministic des under such communication delays and partial observation this article presents necessary and sufficient conditions for the existence of a robust and nonblocking supervisor to achieve a given language specification for any nondeterministic model in the set moreover this article addresses a synthesis problem of a robust and nonblocking supervisor

a generalized one dimensional fast multipole method with application to filtering of spherical harmonics the need to filter functions defined on the sphere arises in a number of applications such as climate modeling electromagnetic and acoustic scattering and several other areas recently it has been observed that the problem of uniform resolution filtering on the sphere can be performed efficiently via the fast multipole method fmm in one dimension in this paper we introduce a generalization of the fmm that leads to an accelerated version of the filtering process instead of multipole expansions the scheme uses special purpose bases constructed via the singular value decomposition of appropriately chosen submatrices of the filtering matrix the algorithm is applicable to a fairly wide class of projection operators its performance is illustrated with several numerical examples

on the computation of ground state and dynamics of schrodinger poisson slater system in this paper we deal with the computation of ground state and dynamics of the schrodinger poisson slater sps system to this end backward euler and time splitting pseudospectral methods are proposed for the nonlinear schrodinger equation with the nonlocal hartree potential approximated by solving a poisson equation the approximation approaches for the hartree potential include fast convolution algorithms which are accelerated by using fft in 1d and fast multipole method fmm in 2d and 3d and sine fourier pseudospectral methods the inconsistency in 0 mode in fourier pseudospectral approach is pointed out which results in a significant loss of high order of accuracy as expected for spectral methods numerical comparisons show that in 1d the fast convolution and sine pseudospectral approaches are compatible while in 3d the fast convolution approach based on fmm is second order accurate and the fourier pseudospectral approach is better than it from both efficiency and accuracy point of view among all these approaches the sine pseudospectral one is the best candidate in the numerics of the sps system finally we apply the backward euler and time splitting sine pseudospectral methods to study the ground state and dynamics of 3d sps system in different setups

robust optimal control of regular languages this paper presents an algorithm for robust optimal control of regular languages under specified uncertainty bounds on the event cost parameters of the language measure that has been recently reported in literature the performance index for the proposed robust optimal policy is obtained by combining the measure of the supervised plant language with uncertainty the performance of a controller is represented by the language measure of the supervised plant and is minimized over the given range of event cost uncertainties synthesis of the robust optimal supervisory control policy requires at most n iterations where n is the number of states of the deterministic finite state automaton dfsa model generated from the regular language of the unsupervised plant behavior the computational complexity of the control synthesis method is polynomial in n

an improved fast multipole algorithm for potential fields on the line a new version of the fast multipole method fmm for the evaluation of potential fields on the line is introduced it uses a new representation of potential fields based on generalized gaussian quadratures j ma v rokhlin and s wandzura siam j numer anal 33 1996 pp 971 996 n yarvin and v rokhlin siam j sci comput 20 1999 pp 699 718 in this representation most translation operators are diagonal to efficiently incorporate this representation into the fmm an apparatus is introduced for transforming between different types of expansions this apparatus is highly general and is based on formulae for the least squares approximation of linear operators the performance of the method is illustrated with several numerical examples it is roughly twice as fast as previously published algorithms

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

limited lookahead policies in supervisory control of discrete event systems a supervisory control scheme which is based on limited lookahead control policies is proposed using an online scheme where after the occurrence of an event the next control action is determined on the basis of an n step ahead projection of the behavior of the process represented as an n level tree this procedure then repeats after the execution of the next event different attitudes can be adopted to calculate a control action for the given n level tree in order to resolve uncertainties about the process behavior beyond n steps two such attitudes termed conservative and optimistic are studied results are presented pertaining to monotonicity and convergence properties of the optimistic and conservative n step policies in terms of n and comparison of these policies with the optimal offline solution closed form expression for the language generated by the n step conservative policy for prefix closed legal languages and lower bounds for n that guarantee that the online scheme performs as well as an offline scheme with complete information

a parallel fast multipole accelerated integral equation scheme for 3d stokes equations in this paper we discuss a numerical scheme for the stokes equations in three dimensions it uses an integral equation formulation and is accelerated by the new version of fast multipole method first introduced by greengard and rokhlin in 1997 acta numerica 1997 6 229 269 the code is parallelized to solve problems of extremely large size the resulting numerical solver can be applied to stokes flows in complex geometry and also serves as a building block for solving the navier stokes equations of low to moderate reynold s numbers copyright 2006 john wiley sons ltd

communications overlapping in fast multipole particle dynamics methods in molecular dynamics the fast multipole method fmm is an attractive alternative to ewald summation for calculating electrostatic interactions due to the operation counts however when applied to small particle systems and taken to many processors it has a high demand for interprocessor communication in a distributed memory environment this demand severely limits applicability of the fmm to systems with o 10 k atoms we present an algorithm that allows for fine grained overlap of communication and computation while not sacrificing synchronization and determinism in the equations of motion the method avoids contention in the communication subsystem making it feasible to use the fmm for smaller systems on larger numbers of processors our algorithm also facilitates application of multiple time stepping techniques within the fmm we present scaling at a reasonably high level of accuracy compared with optimized ewald methods

output stabilizability of discrete event dynamic systems the authors investigate the problem of designing stabilizing feedback compensators for discrete event dynamic systems deds modeled as finite state automata in which some transition events are controllable and some events are observed the problem of output stabilization is defined as the construction of a compensator such that all state trajectories in the closed loop system go through a given set e infinitely often the authors also define a stronger notion of output stabilizability which requires that the state not only pass through e infinitely often but that the set of instants when the state is in e and one knows it is in e is also infinite necessary and sufficient conditions are presented for both notions the authors also introduce and characterize a notion of resiliency that corresponds to the system being able to recover from observation errors in addition they provide some general bounds for the algorithms considered and discuss several conditions under which far smaller bounds can be achieved

a note on the properties of the supremal controllable sublanguage in pushdown systems consider an event alphabet sigma the supervisory control theory of ramadge and wonham asks the question given a plant model g with language lm g sube sigma and another language k sube lm g is there a supervisor phi such that lm phi g k ramadge and wonham showed that a necessary condition for this to be true is the so called controllability of k with respect to lm g they showed that when g is a finite state automaton and k is a regular language also generated by a finite state automaton then there is a regular supremal controllable sublanguage supc k sube k that is effectively constructable from generators of k and g in this paper we show 1 there is an algorithm to compute the supremal controllable sublanguage of a prefix closed k accepted by a deterministic pushdown automaton dpda when the plant language is also prefix closed and accepted by a finite state automaton and 2 in this case we show that this supremal controllable sublanguage is also accepted by a dpda

control of networked discrete event systems dealing with communication delays and losses in this paper we investigate supervisory control of networked discrete event systems such systems are now widely used in practice the key feature of a networked discrete event system is communication delays and losses in observation and control without addressing communication delays and losses in networked systems no control will be effective we propose to use some special observation mappings to deal with observation delays and losses based on these mappings we define network observability we also consider control delays and losses in networked discrete event systems and define network controllability we show that these definitions capture precisely the requirements on effective supervisory control in networked discrete event systems in the sense that a networked supervisor exists if and only if both network controllability and network observability are satisfied

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

algorithms for numerical analysis in high dimensions nearly every numerical analysis algorithm has computational complexity that scales exponentially in the underlying physical dimension the separated representation introduced previously allows many operations to be performed with scaling that is formally linear in the dimension in this paper we further develop this representation by i discussing the variety of mechanisms that allow it to be surprisingly efficient ii addressing the issue of conditioning iii presenting algorithms for solving linear systems within this framework and iv demonstrating methods for dealing with antisymmetric functions as arise in the multiparticle schrodinger equation in quantum mechanics numerical examples are given

synthesis of maximally permissive and robust supervisors for prefix closed language specifications j e r cury and b h krogh 1999 have formulated a robust supervisory control problem to synthesize a supervisor for the nominal plant which maximizes robustness they have solved the problem by unnecessarily restricting the upper bound of the legal behavior we show that the problem can be solved without restricting the upper bound of the legal behavior when the specification is described by prefix closed languages we synthesize a maximally permissive supervisor for the nominal plant which maximizes not only robustness but also permissiveness for the maximal set of admissible plant variations

on supervisory control of sequential behaviors the authors address the supervisory synthesis problem of controlling the sequential behaviors of discrete event dynamical systems dedss under complete and partial information through the use of synchronous composition of the plants and the supervisors the authors present the notion of complete languages discuss some of its algebraic properties and show its close relation to omega languages the authors prove that the supremal closed complete and controllable sublanguage of a given language exists and present an algorithm to compute it they present a closed form expression for the supremal omega controllable sublanguage of a given omega language in terms of the supremal closed complete and controllable sublanguage this closed form expression suggests that certain operations on a given omega language can alternatively be achieved by performing certain other similar operations on its prefix which is a finite language and then taking the limit to obtain the desired omega language a necessary and sufficient condition for the existence of a supervisor in case of partial observation is presented in terms of omega observability notion of omega normality is also introduced and a closed form expression for the supremal omega normal sublanguage in terms of the supremal closed complete and normal sublanguage is presented

a language measure for partially observed discrete event systems recent literature has introduced and validated a signed real measure of regular languages for quantitative analysis and synthesis of discrete event supervisory des control systems where all events are assumed to be observable this paper presents a modification of the language measure for supervisory control under partial observation and shows how to generalize the analysis when some of the events may not be observable at the supervisory level in the context of des control synthesis the language measure of partially observable discrete event processes is expressed in a closed form which is structurally similar to that of completely observable discrete event processes examples are provided to elucidate the concept of des control under partial observation

a new fast multipole accelerated poisson solver in two dimensions we present an adaptive fast multipole method for solving the poisson equation in two dimensions the algorithm is direct assumes that the source distribution is discretized using an adaptive quad tree and allows for dirichlet neumann periodic and free space conditions to be imposed on the boundary of a square the amount of work per grid point is comparable to that of classical fast solvers even for highly nonuniform grids

functions of matrices abstract we use the cayley hamilton theorem and the sequence of horner polynomials associated with a polynomial w z to obtain explicit formulas for functions of the form f ta where f is defined by a convergent power series and a is a square matrix we use a well known explicit formula for the resolvent of a and show that f ta is the hadamard product of f t and the function i ta 1 which is easily obtained from the resolvent

controlled markov chains with safety upper bound in this note we introduce and study the notion of safety control of stochastic discrete event systems dess modeled as controlled markov chains for nonstochastic dess modeled by state machines or automata safety is specified as a set of forbidden states or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited we generalize this notion of safety to the setting of stochastic dess by specifying it as an unit interval valued vector that imposes an upper bound on the state probability distribution vector under the assumption of complete state observation we identify 1 the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution and 2 the set of all safe initial state probability distributions for a given state feedback controller

on controllability and normality of discrete event dynamical systems abstract this paper studies the supervisor synthesis problem of discrete event dynamical systems deds s through the use of synchronous composition of the plant and the supervisor and discusses some of the simplifications achieved by using the synchronous composition to model supervisory control an alternate definition of controllability is presented this definition of controllability is then used to derive an algorithm that is computationally more efficient than previously existing ones for the construction of the supremal controllable sublanguage the algorithm is also shown to be optimal the observability and normality issues arising due to the partial observation of the system dynamics under an arbitrary mask are then investigated closed form representations of the supremal normal and supremal closd and normal sublanguages are derived in the more general setting of arbitrary mask and nonclosed languages thus extending earlier results of the authors and others

a framework for state attraction of discrete event systems under partial observation state attraction for discrete event systems des addresses the problem of reaching a desired subset of the plant state space after a bounded number of event occurrences the problem of state attraction arises for example in fault tolerant supervisory control or in the control of reconfigurable manufacturing systems and is also applicable to systems biological problems such as the control of gene regulatory networks state attraction is investigated with the assumption of full event observation in the existing literature this paper extends the concept of state attraction to the case of partial observation the notion of weak attraction under partial observation wapo is introduced and necessary and sufficient conditions for the existence of a supervisor under partial observation that achieves wapo are derived furthermore a solution algorithm is proposed that finds such supervisor whenever it exists it is shown that such supervisor can always be realized as a subautomaton of the observer automaton of the des plant an application example from systems biology illustrates the obtained results

an improved fast multipole algorithm for potential fields a new version of the fast multipole method fmm for potential fields is presented we introduce a new representation of potentials in which most translation operators are diagonal as a result for double precision calculations in two dimensions we obtain an improvement of a factor of two to four in speed compared to previously published algorithms the improvement is expected to be much greater in three dimensions the performance of the method is illustrated with several numerical examples

approximately bisimilar symbolic models for nonlinear control systems control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs although these models are very powerful when dealing with physical phenomena they are less suited to describe software and hardware interfacing with the physical world for this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics where each symbol corresponds to an aggregate of states in the continuous model since these symbolic models are of the same nature of the models used in computer science to describe software and hardware they provide a unified language to study problems of control in which software and hardware interact with the physical world furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes in this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent bisimilar to a symbolic model the approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired furthermore if the state space of the control system is bounded the obtained symbolic model is finite for digital control systems and under the stronger assumption of incremental input to state stability symbolic models can be constructed through a suitable quantization of the inputs

preconditioned adaptive multipole accelerated iterative methods for three dimensional first kind integral equations of potential theory this paper presents a preconditioned krylov subspace iterative algorithm where a modified multipole algorithm with a novel adaptation scheme is used to compute the iterates for solving dense matrix problems generated by galerkin or collocation schemes applied to three dimensional first kind integral equations that arise in potential theory a proof is given that this adaptive algorithm reduces both matrix vector product computation time and storage to order n and experimental evidence is given to demonstrate that the combined preconditioned adaptive multipole accelerated pama method is nearly order n in practice examples from engineering applications are given to demonstrate that the accelerated method is substantially faster than standard algorithms on practical problems

accurate computation of the zeros of the generalized bessel polynomials a general method for approximating polynomial solutions of second order linear homogeneous differential equations with polynomial coefficients is applied to the case of the families of differential equations defining the generalized bessel polynomials and an algorithm is derived for simultaneously finding their zeros then a comparison with several alternative algorithms is carried out it shows that the computational problem of approximating the zeros of the generalized bessel polynomials is not an easy matter at all and that the only algorithm able to give an accurate solution seems to be the one presented in this paper

stirling matrix via pascal matrix abstract the pascal type matrices obtained from the stirling numbers of the first kind s n k and of the second kind s n k are studied respectively it is shown that these matrices can be factorized by the pascal matrices also the ldu factorization of a vandermonde matrix of the form v n x x 1 x n 1 for any real number x is obtained furthermore some well known combinatorial identities are obtained from the matrix representation of the stirling numbers and these matrices are generalized in one or two variables

matrix characterizations of riordan arrays abstract here we discuss two matrix characterizations of riordan arrays p matrix characterization and a matrix characterization p matrix is an extension of the stieltjes matrix defined in 28 and the production matrix defined in 8 by modifying the marked succession rule introduced in 21 a combinatorial interpretation of the p matrix is given the p matrix characterizations of some subgroups of riordan group are presented which are used to find some algebraic structures of the subgroups we also give the p matrix characterizations of the inverse of a riordan array and the product of two riordan arrays a matrix characterization is defined in 20 and it is proved to be a useful tool for a riordan array while on the other side the a sequence characterization is very complex sometimes by using the fundamental theorem of riordan arrays a method of construction of a matrix characterizations from riordan arrays is given the converse process is also discussed several examples and applications of two matrix characterizations are presented

a constructive method for plane wave representations of special functions abstract a general constructive scheme for the derivation of plane wave representations of special functions is proposed illustrative examples of the construction are given as one case study new integral representations of the elliptic weierstrass function are derived these complement and generalize similar new plane wave integral representations of the same function recently found by dienstfrey and huang 2006 8 using other techniques our approach is inspired by recent developments in the so called fokas transform for the solution of boundary value problems for partial differential equations

polynomial synthesis of supervisor for partially observed discrete event systems by allowing nondeterminism in control we study the supervisory control of discrete event systems dess under partial observation using nondeterministic supervisors we formally define a nondeterministic control policy and also a control observation compatible nondeterministic state machine and prove their equivalence the control action of a nondeterministic supervisor is chosen online nondeterministically from among a set of choices determined offline also the control action can be changed online nondeterministically prior to any new observation in accordance with choices determined offline the online choices once made can be used to affect the set of control action choices in future we show that when control is exercised using a nondeterministic supervisor the specification language is required to satisfy a weaker notion of observability which we define in terms of recognizability and achievability achievability serves as necessary and sufficient condition for the existence of a nondeterministic supervisor and it is weaker than controllability and observability combined when all events are controllable achievability reduces to recognizability we show that both existence and synthesis of nondeterministic supervisors can be determined polynomially for deterministic supervisors only existence can be determined polynomially both achievability and recognizability are preserved under union and also under intersection when restricted over prefix closed languages using the intersection closure property we derive a necessary and sufficient condition for the range control problem for the prefix closed case unlike the deterministic supervisory setting where the complexity of existence is exponential our existence condition is polynomially verifiable and also a supervisor can be polynomially synthesized

a fast quasi multiple medium method for 3 d bem calculation of parasitic capacitance abstract a quasi multiple medium qmm method is proposed to accelerate the boundary element method bem for the 3 d parasitic capacitance calculation in the qmm method a homogeneous dielectric is decomposed into a number of fictitious medium blocks each with the same permittivity of original medium by the localization character of bem the qmm method makes great sparsity to the coefficient matrix of the overall discretized bem equations then using storing technique of sparse matrix and iterative equation solvers the sparsity is explored to greatly reduce cpu time and memory usage of bem computation the computational complexity of the qmm accelerated bem for a single medium model problem is analyzed and it is concluded as o n if the number of iterations is bounded numerical results verify the theoretical analysis and show the accelerating efficiency of the qmm method for calculation of 3 d parasitic capacitance

functions and jordan canonical forms of riordan matrices abstract this paper collects results about riordan arrays in the framework of matrix functions actually the following methodology applies to any square matrix m m with exactly one eigenvalue of algebraic multiplicity m n generalized lagrange bases are used to construct hermite polynomials that interpolate a family of functions moreover we show a parallel application of such functions via jordan canonical forms and case studies are given

on deadlock free modular supervisory control of discrete event systems in this paper the problem of synthesizing deadlock free modular supervisors for discrete event systems is discussed by introducing the d invariant relation between a pair of supervisors it is shown that when the control objective is described in terms of intersection of two languages a necessary and sufficient condition for the modular supervisor to be deadlock free is that this pair of subsupervisors satisfies a d invariant relation a procedure for synthesizing the deadlock free modular supervisor is presented some issues concerning deadlock free modular supervisory control are also discussed

optimal supervisory control of discrete event systems cyclicity and interleaving of tasks a substantial number of tasks in production systems are executed in a repetitive cyclic fashion specifically production systems run different production cycles of different products as well as different instances of the same production cycle in this paper we consider the optimal control and interleaving of such production cycles in a supervisory control framework for discrete event systems dess that is different from other approaches our work is based on a behavioral specification of each production cycle first we adapt an optimal control approach for dess in order to optimize the operation of individual production cycles second we employ the interleaving composition to design a supervisor that enables the simultaneous execution of different production cycles combining both results we can further determine the maximum number of production cycles that can be executed simultaneously on a given production system

robust nonblocking supervisory control of discrete event systems under partial observation in this paper we extend previous results on robust nonblocking supervisory control of discrete event systems with full observation to the case of control under partial observation where only a subset of events are observable and can be monitored the exact model of the plant is not known but is assumed to be among a finite set of possible models for each plant model a legal marked behavior is assumed given we manage to characterize the entire set of solutions of the robust control problem and obtain a set of necessary and sufficient conditions for the existence of a solution for the robust control problem

robust prognosability for a set of partially observed discrete event systems abstract in this paper we consider a robust failure prognosis problem for partially observed discrete event systems given a set of possible models each of which has its own nonfailure specification we consider a single prognoser such that for all possible models it predicts any failure prior to its occurrence we call such a prognoser a robust prognoser we introduce a notion of robust prognosability and show that it serves as a necessary and sufficient condition for the existence of a robust prognoser we then present a method for verifying the robust prognosability condition moreover we discuss online synthesis of a robust prognoser

verification of robust diagnosability for partially observed discrete event systems in this paper we study robust failure diagnosis of discrete event systems given a set of possible models each of which has its own nonfailure specification we consider the existence of a single diagnoser such that for all possible models it detects any occurrence of a failure within a uniformly bounded number of steps we call such a diagnoser a robust diagnoser we introduce a notion of robust diagnosability and prove that it serves as a necessary and sufficient condition for the existence of a robust diagnoser we then present an algorithm for verifying the robust diagnosability condition

modular implementation of robust supervisory controllers for discrete event systems in this paper the problem of designing robust supervisory controllers for uncertain discrete event systems is studied it is assumed that both the plant behavior and the design specifications can be represented by regular languages it is also assumed that the unknown model of the uncertain plant belongs to a finite set of possibilities to solve the problem a modular approach based on a general recursive robust control scheme is developed the contribution of the present paper consists in deriving a maximally permissive modular robust supervisory controller for the case of prefix closed languages having the advantage of linear complexity in the number of models as opposed to the exponential complexity of the worst case scenario in the direct implementation of standard supervisors for augmented 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

on the complexity of synthesizing a minimum weighted supervisor under partial observation abstract with full observation the problem of synthesizing a minimum weighted supervisor has been shown polynomial time solvable with partial observation the problem becomes np hard in this paper we will show that the decision version of the problem becomes np complete when the natural projection is a natural observer this np completeness result is unexpected considering that the logic supervisor synthesis problem under the same assumption becomes polynomial time solvable

supervisory control of partially observable marked graphs this note presents a control synthesis approach for discrete event systems modeled by marked graphs with unobservable transitions it solves forbidden state problems characterized by a set of general mutual exclusion constraints we prove that for any sequence of observable transitions there exist a unique marking from which all other possible current markings can be reached unobservably this salient feature allows us to design efficient control policies based on proper separation of observation and control

practical computation of matrix functions abstract several new representations for an analytic function f a of a complex matrix a and in particular for e at and a t are derived which also are numerically useful in that they avoid the computation of eigenvalues of a

a tutorial on the extended perturbation analysis abstract in this paper we explain the simple idea of infinitesimal and extended perturbation analysis the motivation of the new technique the difficulties as well as the advantages and contributions

feedback stabilization of some event graph models the authors introduce several notions of stability for event graph models timed or not the stability is similar to the boundedness notion for petri nets the event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions the controller itself is composed of an event graph in this framework the authors solve the corresponding stabilization problems i e they wonder if such a controller may prevent the explosion of the number of tokens

application of fast multipole galerkin boundary integral equation method to elastostatic crack problems in 3d fast multipole method fmm has been developed as a technique to reduce the computational cost and memory requirements in solving large scale problems this paper discusses an application of fmm to three dimensional boundary integral equation method for elastostatic crack problems the boundary integral equation for many crack problems is discretized with fmm and galerkin s method the resulting algebraic equation is solved with generalized minimum residual method gmres the numerical results show that fmm is more efficient than conventional methods when the number of unknowns is more than about 1200 and therefore can be useful in large scale analyses of fracture mechanics copyright 2001 john wiley sons ltd

an adaptive fast multipole accelerated poisson solver for complex geometries abstract we present a fast direct and adaptive poisson solver for complex two dimensional geometries based on potential theory and fast multipole acceleration more precisely the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition the volume integral is computed by applying the fmm on a square box that encloses the domain of interest for the sake of efficiency and convergence acceleration we first extend the source distribution the right hand side in the poisson equation to the enclosing box as a c 0 function using a fast boundary integral based method we demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and as a result to an extremely efficient black box fast solver

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

some inverse limit approaches to the riordan group abstract using the inverse limit tool we obtain the riordan group in its infinite and bi infinite representations from groups of finite riordan matrices we define two different reflections for bi infinite riordan matrices employing these definitions we give answers to the problems d d and d d in the riordan group so we describe the self complementary and self dual riordan matrices

exploiting symmetry in the synthesis of supervisors for discrete event systems we investigate a method to exploit the symmetry inherent to many discrete event systems in order to reduce the computational complexity of the supervisory control problem scp we characterize symmetry using notions of group theory and derive conditions under which there exists a quotient reduced automaton representation for a language with in general a much smaller state space than the original minimal in number of states automaton representation for the language we then propose an algorithm to synthesize a solution to the scp which is similar to the classical one but performed on reduced automata special attention is given to the particular case of systems whose models contain similar components the approach is illustrated by an example of control of a small production line

maximally permissive feedback and modular control synthesis in petri nets with external input places a necessary and sufficient condition is presented for the unique existence of a maximally permissive feedback mpf in a concurrent discrete event system modeled by a petri net the concept of the weak interaction of a predicate is introduced in addition to reviewing fundamental definitions and notations the author defines the control invariance of a predicate and an mpf a modular synthesis problem of mpf is discussed

nonlinear optimization quadrature and interpolation we present a nonlinear optimization procedure for the design of generalized gaussian quadratures for a fairly broad class of functions while some of the components of the algorithm have been published previously we introduce an improved procedure for the determination of an acceptable initial point for the continuation scheme that stabilizes the newton type process used to find the quadratures the resulting procedure never failed when applied to chebyshev systems for which the existence and uniqueness of generalized gaussian quadratures are well known it also worked for many non chebyshev systems for which the generalized gaussian quadratures are not guaranteed to exist the performance of the algorithm is illustrated with several numerical examples some of the presented quadratures integrate efficiently large classes of singular functions

decentralized control of discrete event systems using prioritized composition with exclusion a necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion pcx is provided pcx was extended from prioritized synchronous composition psc in order to model various boolean modes of decision fusion by allowing the exclusivity of participation in system interactions a notion of pcx coobservability is introduced that captures the nature of pcx based decision fusion and a testing algorithm with polynomial complexity in the states of plant and specification is presented the result is extended for multiple supervisors with multiple exclusivity sets based on an extended pcx definition

on optimal attraction in discrete event processes abstract the concept of attraction has been shown to play a basic role in the synthesis of supervisors for stabilizing discrete event processes in this paper we define and investigate optimal attraction in the sense that the cost or distance of the convergent path is minimized with respect to some distance measure we find conditions for the existence of supervisors achieving optimal attraction and provide efficient algorithms for their synthesis

robustness of supervisors for discrete event systems supervisory control in the context of spl omega languages is considered the nominal supervisor design problem is to find a non blocking supervisor for a nominal plant such that the closed loop infinite behavior equals a specified closed loop behavior the robustness of solutions to the nominal problem is defined with respect to variations in the plant it is shown there exists a supervisor solving the nominal problem which maximizes the set of plants for which the closed loop languages for all other plants in the set satisfy lower and upper bounds in the sense of language containment computational issues are discussed and the theoretical results are illustrated with an example

integral representations of harmonic lattice sums we present new integral formulas for coulombic lattice sums that arise in solid state physics material science and complex analysis unlike ewald summation which can yield approximate integral representations the formulas described here are exact simple quadrature rules with modest numbers of nodes yield highly accurate results

an adaptive fast solver for the modified helmholtz equation in two dimensions in this paper we present a fast multipole accelerated integral equation method for solving the modified helmholtz equation du x b 2u x f x in two dimensions the method is direct and unlike classical fft based fast solvers it allows for adaptive mesh refinement but with comparable amount of work per grid point when the computational domain is rectangular dirichlet neumann periodic and free space boundary conditions can be imposed analytically without the need to solve a system of linear equations several important features of the algorithm are discussed including the use of precomputed tables diagonal translation operators and lattice sums to impose periodic boundary conditions numerical experiments show that for a wide range of the parameter b the algorithm is stable and high order accurate

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

minimizing the cardinality of an events set for supervisors of discrete event dynamical systems in this paper we study sufficient observation and work spaces for supervisors of a class of discrete event dynamical systems deds we use finite state automata to model a deds the finite automata generates a formal language defined over the set of events in the deds a supervisor is a feedback system that observes a generated trace of events and dynamically disables or enables a subset of controllable events such that the closed loop system behaves as desired we model the desired behavior of the deds by a sublanguage defined over the set of events a sufficient observation space is a collection of events whose observation by a supervisor is enough to realize a given desired behavior a sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space we construct algorithms to evaluate a sufficient work or observation space the reduction of work or observation spaces results in reducing the number of event detectors communication and command channels between the supervisor and the plant

on the existence of finite state supervisors for arbitrary supervisory control problems given two prefix closed languages k l spl sube spl sigma where k spl sube l represents the desired closed loop behavior and l is the open loop behavior there exists a finite state supervisor that enforces k in the closed loop if and only if there is a regular prefix closed language m spl sube spl sigma such that 1 m spl sigma sub u spl cup l spl sube m and 2 m spl cup l k in this paper we show that this is equivalent to 1 the controllability of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub with respect to spl sigma and 2 the regularity of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub where l spl macr spl sigma spl minus l and pr spl middot is the set of prefixes of strings in the language argument we use this property to investigate the issue of deciding the existence of a finite state supervisor for different representations we also present some properties of the language sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub along with implications to the synthesis of solutions to the supervisory control problem with the fewest states

formulas for calculating supremal controllable and normal sublanguages abstract supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis in this paper we discuss the computation of supremal controllable and normal sublanguages we derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed as a result those languages can be computed without applying recursive algorithms we also discuss those aspects of these formulas