effective computation of an lm g closed controllable and observable sublanguage arising in supervisory control abstract in this paper we study nonblocking supervisory control of discrete event systems under partial observation a nonblocking supervisor can be synthesized for the supremal l m g closed controllable and normal sublanguage of a given nonclosed marked language however such a supervisor may be too restrictive as a solution to the supervisory control problem we identify a subclass of observable sublanguages of a given language which has the supremal element larger than the supremal normal sublanguage by using the supremal element we present an iterative algorithm for computing an l m g closed controllable and observable sublanguage of a given marked language which is larger than the supremal l m g closed controllable and normal sublanguage

the transfer function analysis of various schemes for the two dimensional shallow water equations in this paper various finite difference and finite element approximations to the linearized two dimensional shallow water equations are analyzed this analysis complements previous results for the one dimensional case

dispersion and group velocity in numerical schemes for three dimensional hydrodynamic equations we investigate dispersion and group velocity relations of numerical schemes for the three dimensional hydrodynamic equations by using the transform function method the numerical methods are developed for two of arakawa s spatial grid types namely b grid and c grid using a spectral method in the vertical direction one of our results is that if the horizontal scale length is greater than the rossby radius of deformation then the b grid is more appropriate than the commonly used c grid

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

analysis of mixed finite elements methods for the stokes problem a unified approach we develop a method for the analysis of mixed finite element methods for the stokes problem in the velocity pressure formulation a technical macroelement condition which is sufficient for the classical babuska brezzi inequality to be valid is introduced using this condition we are able to verify the stability and optimal order of convergence of several known mixed finite element methods

hybrid eulerian lagrangian semi implicit time integrators hybrid eulerian lagrangian semi implicit time integrators helsi are presented which use the standard semi implicit formulation as their starting point the advantage of such an approach is that existing models which employ eulerian semi implicit time integrators can easily be augmented to use the helsi approach that is provided that either a series of advection problems can be solved efficiently as in the operator integration factor splitting oifs method or that the grid and underlying numerics allow the construction of efficient search and interpolation stencils typically required of semi lagrangian methods once the advection problem is solved the approach then follows the standard semi implicit approach an important caveat of this approach is that the semi implicit time integrator must be constructed around the implicit backward difference formulas

analysis of the turkel zwas scheme for the two dimensional shallow water equations in spherical coordinates a linear analysis of the shallow water equations in spherical coordinates for the turkel zwas t z explicit large time step scheme is presented this paper complements the results of schoenstadt neta and navon and others in 1 d and of neta and devito in 2 d but applied to the spherical coordinate case of the t z scheme this coordinate system is more realistic in meteorology and more complicated to analyze since the coefficients are no longer constant the analysis suggests that the t z scheme must be staggered in a certain way in order to get eigenvalues and eigenfunctions approaching those of the continuous case the importance of such an analysis is the fact that it is also valid for nonconstant coefficients and thereby applicable to any numerical scheme numerical experiments comparing the original unstaggered and staggered versions of the t z scheme are presented these experiments corroborate the analysis by showing the improvements in accuracy gained by staggering the turkel zwas scheme

a mixed finite element method for approximating incompressible materials a mixed finite element method is proposed for approximating the deformation u of a plane incompressible material satisfying the condition det nabla u 1 for piecewise linear shape functions it is proved that the discrete solutions exist and converge with nearly quasi optimal rates in l infty the corresponding nonlinear system is iteratively solved by a multigrid method

a spectral element semi lagrangian sesl method for the spherical shallow water equations a spectral element semi lagrangian sesl method for the shallow water equations on the sphere is presented the sphere is discretized using a hexahedral grid although any grid imaginable can be used as long as it is comprised of quadrilaterals the equations are written in cartesian coordinates to eliminate the pole singularity which plagues the equations in spherical coordinates in a previous paper int j numer methods fluids 35 2001 869 we showed how to construct an explicit eulerian spectral element se model on the sphere we now extend this work to a semi lagrangian formulation the novelty of the lagrangian formulation presented is that the high order se basis functions are used as the interpolation functions for evaluating the values at the lagrangian departure points this makes the method not only high order accurate but quite general and thus applicable to unstructured grids and portable to distributed memory computers the equations are discretized fully implicitly in time in order to avoid having to interpolate derivatives at departure points by incorporating the coriolis terms into the lagrangian derivative the block lu decomposition of the equations results in a symmetric positive definite pseudo helmholtz operator which we solve using the generalized minimum residual method gmres with a fast projection method comput methods appl mech eng 163 1998 193 results for eight test cases are presented to confirm the accuracy and stability of the method these results show that sesl yields the same accuracy as an eulerian spectral element semi implicit sesi while allowing for time steps 10 times as large and being up to 70 more efficient

brief paper formulae relating controllability observability and co observability we present formulae relating controllability observability and co observability arising in the context of supervisory control of discrete event systems given a discrete event plant g with event set e uncontrollable event set e u i and observation mask m i of the ith supervisor we first show that the infimal prefix closed l g i e u i controllable and l g e u i m i co observable superlanguage equals the intersection taken over all i s of the infimal prefix closed l g e u i controllable and l g m i observable superlanguage next we show that the infimal prefix closed and e m observable superlanguage computation preserves e e u controllability these results can be used to compute individual supervisors in the decentralized control setting

analysis of the turkel zwas scheme for the shallow water equations abstract a transfer function analysis is used to analyze the turkel zwas explicit large time step scheme applied to the shallow water equations the transfer function concept leads to insight into the behavior of this discretization scheme in terms of comparison between continuous and discrete amplitude phase and group velocity coefficients the dependence of the distortion increases with the increase in the time step size taken for the turkel zwas scheme which depends on the ratio between a coarse and a fine mesh a comparison with earlier results of schoenstadt naval post graduate school report nps 53 79 001 1978 unpublished shows the turkel zwas scheme to give reasonable results up to time steps three times larger than the cfl limit

relative observability of discrete event systems and its supremal sublanguages we identify a new observability concept called relative observability in supervisory control of discrete event systems under partial observation a fixed ambient language is given relative to which observability is tested relative observability is stronger than observability but enjoys the important property that it is preserved under set union hence there exists the supremal relatively observable sublanguage of a given language relative observability is weaker than normality and thus yields when combined with controllability a generally larger controlled behavior in particular no constraint is imposed that only observable controllable events may be disabled we design new algorithms which compute the supremal relatively observable and controllable sublanguage of a given language which is generally larger than the normal counterpart we demonstrate the new observability concept and algorithms with a guideway and an agv example

finite element schemes for extended integrations of atmospheric models abstract the effect of conservation of integral invariants by finite element discretization schemes of the shallow water equations as a model for long term integrations of atmospheric models is investigated two finite element models are used the first uses rectangular elements and conserves total energy using an intrinsic method the second model uses triangular elements and a high accuracy two stage numerov galerkin method it well conserves total energy and potential enstrophy by applying a periodical shuman filter every 48 or 96 time steps different conserving and non conserving versions of these finite element schemes are compared in terms of their conservation of the integral invariants of the shallow water equations for long term integrations 20 100 model days critical times for numerical non linear instability are investigated along with the determination of the critical amount of dissipation required to achieve stable long term integrations comparisons of the two finite element schemes namely the rectangular and the triangular in terms of their relative computational efficiency and accuracy are also provided similarities and differences in the behavior of finite element schemes and finite difference schemes for long term stable integrations of the shallow water equations are finally discussed

lagrange galerkin methods on spherical geodesic grids the weak lagrange galerkin finite element method for the 2d shallow water equations on the sphere is presented this method offers stable and accurate solutions because the equations are integrated along the characteristics the equations are written in 3d cartesian conservation form and the domains are discretized using linear triangular elements the use of linear triangular elements permits the construction of accurate by virtue of the second order spatial and temporal accuracies of the scheme and efficient by virtue of the less stringent cfl condition of lagrangian methods schemes on unstructured domains using linear triangles in 3d cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals the triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers an efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations in addition a high order scheme for computing the characteristic curves in 3d cartesian space is presented a general family of runge kutta schemes results for six test cases are reported in order to confirm the accuracy of the scheme

on the convergence of the bilinear velocity constant pressure finite element method in viscous flow abstract in this paper we show that the standard isoparametric q 1 q 0 velocity pressure finite element method for solving viscous flow problems leads to a fully and optimally convergent sequence of approximations if an appropriate quadrangulation of the domain is used

compatibility condition and existence results in discrete finite incompressible elasticity abstract a theory on the existence of solutions of the discretized equilibrium equations in incompressible finite elasticity is given a compatibility condition between the space of displacements and the space of pressures is introduced and is studied in a particular case of finite element spaces using q 1 and q 0 isoparametric elements an original assembling of these elements is presented which leads to discrete spaces satisfying the compatibility condition

numerical solution of problems in incompressible finite elasticity by augmented lagrangian methods ii three dimensional problems in a first paper siam j appl math 42 1982 pp 400 429 we introduced an augmented lagrangian methodology for solving equilibrium problems in incompressible finite elasticity and then applied it to the solution of several two dimensional and axisymmetric test problems in this second paper we extend our methods to the solution of genuine three dimensional problems actually using these augmented lagrangian techniques we can reduce the solution of these complicated nonlinear nonconvex problems to the solution of a sequence of linear problems and also to the solution of a sequence of minimization problems for convex functionals on convex sets the capabilities of our methods are illustrated by the results of numerical experiments

lagrange galerkin methods on spherical geodesic grids the shallow water equations abstract the weak lagrange galerkin finite element method for the 2d shallow water equations on the sphere is presented this method offers stable and accurate solutions because the equations are integrated along the characteristics the equations are written in 3d cartesian conservation form and the domains are discretized using linear triangular elements the use of linear triangular elements permits the construction of accurate by virtue of the second order spatial and temporal accuracies of the scheme and efficient by virtue of the less stringent cfl condition of lagrangian methods schemes on unstructured domains using linear triangles in 3d cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals the triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers an efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations in addition a high order scheme for computing the characteristic curves in 3d cartesian space is presented a general family of runge kutta schemes results for six test cases are reported in order to confirm the accuracy of the scheme

existence and approximation results for nonlinear mixed problems application to incompressible finite elasticity this paper considers the problems of minimizing gateaux differentiable functionals over subsets of real banach spaces defined by a non linear equality constraint the existence of a lagrange multiplier is proved together with approximation results on the constrained subset provided a nonlinear compatibility condition generalizing the classical inf sup condition is satisfied these ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems

diamond elements a finite element discrete mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity we present a finite element discretization scheme for the compressible and incompressible elasticity problems that possess the following properties i the discretization scheme is defined on a triangulation of the domain ii the discretization scheme is defined and is identical in all spatial dimensions iii the displacement field converges optimally with mesh refinement and iv the inf sup condition is automatically satisfied the discretization scheme is motivated both by considerations of topology and analysis and it consists of the combination of a certain mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures rigorous proofs of the satisfaction of the inf sup condition are presented for the problem of linearized incompressible elasticity we additionally show that the discretization schemes can be given a compelling interpretation in terms of discrete differential operators in particular we develop a discrete analogue of the classical tensor differential complex in terms of which the discrete and continuous boundary value problems are formally identical we also present numerical tests that demonstrate the dimension independent scope of the scheme and its good performance in problems of finite elasticity

a galerkin finite element spectral weather forecast model in hybrid coordinates abstract an atmospheric model is presented using the spectral method for horizontal discretization and a finite element method for the vetrical the vertical coordinate is discretized in a hybrid system being a p system at the top of the atmosphere and a system near the surface for intermediate levels there is a smooth transition between the two systems an energy conserving scheme is obtained by using a petrov galerkin method with density as a weight an efficient method of computing the galerkin integrals is achieved by introducing a collocation grid the horizontal discretization uses the spectral method with spherical harmonic basis functions and triangular truncation with meridional wavenumber up to 106 a set of test forecasts was done using 19 vertical levels the forecasts were compared to those of a model using a finite difference technique for the vertical the finite element model showed an advantage with respect to an averaged correlation measure

synthesis of maximally permissive supervisors for the range control problem we investigate the supervisor synthesis problem for centralized partially observed discrete event systems subject to safety specifications it is well known that this problem does not have a unique supremal solution in general instead there may be several incomparable locally maximal solutions one then needs a mechanism to select one locally maximal solution our approach in this paper is to consider a lower bound specification on the controlled behavior in addition to the upper bound for the safety specification this leads to a generalized supervisory control problem called the range control problem while the upper bound captures the prefix closed legal behavior the lower bound captures the prefix closed minimum required behavior we provide a synthesis algorithm that solves this problem by effectively constructing a maximally permissive safe supervisor that contains the required lower bound behavior this is the first algorithm with such properties as previous works solve either the maximally permissive safety problem with no lower bound or the lower bound containment problem without maximal permissiveness

effective control synthesis for partially observed discrete event systems control under partial observations is studied within the infinite string supervisory control framework it is shown that provided that there are no pure liveness assumptions embodied in the plant model technically the omega language generated by the plant is the limit of the finite string language generated the problem of synthesizing a centralized supervisor reduces to the case of complete observations the result involves constructions similar to those used to determinize nondeterministic automata on infinite strings

numerical models of steady rolling for non linear viscoelastic structures in finite deformations a lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented these laws are expressed by a non linear differential equation governing the evolution of an internal variable then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics a finite element approximation and a solution technique of the algebraic system is proposed the eiimination of the internal variable allows one to keep an elastic like algorithm with an independent solution of the viscoelastic equation numerical tests show the feasibility and the efficiency of the proposed methods in large three dimensional situations

a numerov galerkin technique applied to a finite element shallow water equations model with enforced conservation of integral invariants and selective lumping abstract a new two stage numerov galerkin method is presented and applied following a suggestion by cullen and morton 1 to achieve higher accuracy by combining the galerkin product with a high order compact numerov difference approximation to derivatives in the nonlinear advection operator of the shallow water equations the practical applicability of the new method is supported by computational examples involving medium 10 days and longterm 20 days integrations of the nonlinear shallow water equations small scale noise was eliminated by periodical application of a shuman filter to only one component of the velocity conservation of integral invariants is ensured by using a new augmented lagrangian multiplier penalty method in the numerov galerkin method experiments were performed using the new method with differently weighted selective lumping schemes for the mass matrix the new method exhibits a consistently higher accuracy than the single stage galerkin method and requires much less computational effort a hypothesis is offered to explain the increased accuracy obtained by selective lumping schemes in the long term numerical integrations 10 20 days as compared to the consistent mass approach in numerov galerkin schemes

the infimal prefix closed and observable superlanguage of given language abstract the supervisory control of discrete event systems under partial observation is examined in particular the condition of observability needed to solve the two main existing problems is investigated a fixed point characterization of observability is given and is shown to yield an effective test for observability where the system under consideration is specified by regular languages a formula for the infimal prefix closed observable superlanguage of a given language is presented where the system is specified by regular languages the formula for the infimal observable language is effectively computable

automatically inf sup compliant diamond mixed finite elements for kirchhoff plates we develop a mixed finite element approximation scheme for kirchhoff plate theory based on the reformulation of kirchhoff plate theory of ortiz and morris 1 in this reformulation the moment equilibrium problem for the rotations is in direct analogy to the problem of incompressible two dimensional elasticity this analogy in turn opens the way for the application of diamond approximation schemes hauret et al 2 to kirchhoff plate theory we show that a special class of meshes derived from an arbitrary triangulation of the domain the diamond meshes results in the automatic satisfaction of the corresponding inf sup condition for kirchhoff plate theory the attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests we also provide a reinterpretation of the diamond approximation scheme for kirchhoff plate theory within the framework of discrete mechanics in this interpretation the discrete moment equilibrium problem is formally identical to the classical continuous problem and the two differ only in the choice of differential structures it also follows that the satisfaction of the inf sup condition is a property of the cohomology of a certain discrete transverse differential complex this close connection between the classical inf sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems

synthesis of maximally permissive supervisors for partially observed discrete event systems we present new results on the synthesis of safe non blocking and maximally permissive supervisors for partially observed discrete event systems we consider the case where the legal language is a non prefix closed sublanguage of the system language i e non blockingness must be ensured in addition to safety to solve this problem we define a new bipartite transition system called the non blocking all inclusive controller nb aic that embeds all safe and non blocking supervisors we present an algorithm for the construction of the nb aic and discuss its properties we obtain the necessary and sufficient conditions for the solvability of the maximally permissive control problem we then provide a synthesis algorithm based on the nb aic that constructs a supervisor that is safe non blocking and maximally permissive if one exists this is the first algorithm with such properties

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