adaptive ode solvers in extended kalman filtering algorithms this paper studies numerical methods that are used to treat ordinary differential equations arising in extended kalman filtering algorithms such problems are called the moment equations and constitute an important subclass of differential equations they all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area for instance we show that built in matlab ode solvers are not able to cope with a number of tests considered here in contrast the hybrid method developed by mazzoni 2007 exhibits much better performance on the same examples the latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations

modelling merging and fragmentation in multiphase flows with surfer we introduce a new numerical method called surfer for the simulation of two and three dimensional flows with several fluid phases and free interfaces between them we consider incompressible fluids obeying the navier stokes equation with newtonian viscosity in the bulk of each phase capillary forces are taken into account even when interfaces merge or break up fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm thus allowing for full symmetry between fluid phases the navier stokes equation is solved using staggered finite differences on a mac grid and a split explicit time differencing scheme while incompressibility is enforced using an iterative multigrid poisson solver capillary effects are represented as a stress tensor computed from gradients of the volume fraction function this formulation is completely independent of the topology of interfaces and relatively easy to implement in 3d it also allows exact momentum conservation in the discretized algorithm numerical spurious effects or parasite currents are noticed and compared to similar effects in boltzmann lattice gas methods for immiscible fluids simulations of droplets pairs colliding in 2d and in 3d are shown interface reconnection is performed easily despite the large value of capillary forces during reconnection

interface reconstruction with least squares fit and split advection in three dimensional cartesian geometry in this paper we present and analyze different volume of fluid vof reconstruction and advection algorithms that approximate the interface separating two immiscible fluids in the three dimensional space the paper describes the improvement of the reconstruction when a least square fit algorithm which minimizes a distance functional is applied its performance is tested for several smooth surfaces against other simple reconstruction methods then eulerian lagrangian and mixed split advection schemes are presented and analyzed in particular one advection method is discussed that conserves mass exactly for a divergence free velocity field thus allowing computations to machine precision

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

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

nonlinear estimation by lmmse based estimation with optimized uncorrelated augmentation for nonlinear estimation the linear minimum mean square error lmmse estimator using the measurement augmented by its nonlinear conversion can achieve better performance than using the original measurement the main reason is that the original measurement cannot be fully utilized by the lmmse estimator in a linear way to effectively extract additional measurement information which can be further utilized by a linear estimator a nonlinear approach named uncorrelated conversion uc is proposed the uncorrelated conversions of the measurement are uncorrelated with the measurement itself two specific approaches to generating ucs are proposed based on a gaussian assumption and a reference distribution respectively then a uc based filter ucf is proposed based on lmmse estimation using the measurement augmented by its uncorrelated conversions to minimize the mean square error of the overall estimate an optimized ucf oucf with an analytical form is proposed by optimizing the reference distribution based ucs in the ucf measurement augmentation can be continued using the proposed nonlinear uc approach and all augmenting terms are uncorrelated under certain conditions thus the performance of the ucf and the oucf may be continually improved simulation results demonstrate the effectiveness of the proposed estimator compared with some popular nonlinear estimators

toward efficient and accurate interface capturing on arbitrary hybrid unstructured grids the thinc method with quadratic surface representation and gaussian quadrature abstract a novel interface capturing scheme is proposed to compute moving interface on arbitrary hybrid unstructured grids different from conventional volume of fluid vof schemes that require complicated geometric manipulations for interface reconstructions the present method can be viewed as a hybrid geometric algebraic type vof approach i e the interface is implictly retrieved from an algebraic function that effectively makes use of the geometrical information such as normal direction and curvature of the interface unlike previous versions of the thinc tangent of hyperbola interface capturing method the interface is represented by a quadratic surface for grid cells of arbitrary shapes in this scheme the gaussian quadrature is used to estimate the integration of the cell wise multi dimensional hyperbolic tangent reconstruction function which is then used to retrieve the interface from the volume fraction value of the target cell the gaussian quadrature is also used to compute the numerical fluxes from the reconstruction function numerical accuracy for reconstruction and flux computation can be effectively improved by increasing quadrature points the whole solution procedure follows the finite volume method for advection transport and is thus simple and easy to use for cells of arbitrary shapes as verified in the benchmark tests in this paper the presented scheme so called thinc qq thinc method with quadratic surface representation and gaussian quadrature scheme shows significantly improved geometrical fidelity of interface representation particularly for curved surface despite algorithmic simplicity the solution quality of thinc qq is comparable to other existing vof methods with plic geometrical interface reconstructions and thus an accurate and efficient vof scheme of great practical significance for unstructured grids

a volume of fluid method based on multidimensional advection and spline interface reconstruction a new volume of fluid method for tracking two dimensional interfaces is presented the method involves a multidimensional advection algorithm based on the use of edge matched flux polygons to integrate the volume fraction evolution equation and a spline based reconstruction algorithm the accuracy and efficiency of the proposed method are analyzed using different tests and the results are compared with those obtained recently by other authors despite its simplicity the proposed method represents a significant improvement and compares favorably with other volume of fluid methods as regards the accuracy and efficiency of both the advection and reconstruction steps

short note revisit to the thinc scheme a simple algebraic vof algorithm this short note presents an improved multi dimensional algebraic vof method to capture moving interfaces the interface jump in the thinc tangent of hyperbola for interface capturing scheme is adaptively scaled to a proper thickness according to the interface orientation the numerical accuracy in computing multi dimensional moving interfaces is significantly improved without any geometrical reconstruction the proposed method is extremely simple and easy to use and its numerical accuracy is superior to other existing methods of its kind and comparable to the conventional plic piecewise linear interface calculation type vof schemes

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

a surface marker algorithm coupled to an area preserving marker redistribution method for three dimensional interface tracking in this work we present a new interface tracking algorithm based on surface markers to reconstruct and advect interfaces in three dimensional space the algorithm is coupled to a marker redistribution method which is area preserving along the interface the interface is described by a set of closed lines which define a coarse lagrangian quadrangular mesh in the fixed computational grid fixed markers are located where the lines cross and are maintained during the whole simulation at each time step the interface is first reconstructed and then all markers are advected by following streamlines in the reconstruction step new markers are determined by computing the intersections of the interface lines with the grid cell faces and by adding area conservation markers between fixed and grid intersection markers intersection and conservation markers defined at the previous time step are discarded the method maintains a smooth geometrical description of the interface for both two dimensional and three dimensional tests with accurate volume conservation even in very challenging situations where the fluid bodies progressively deform and stretch developing localized regions with very high curvature and thin fluid filaments the method compares favorably with front capturing methods such as volume of fluid and level set and other hybrid techniques such as the particle level set method

a sharp interface method for incompressible two phase flows we present a sharp interface method for computing incompressible immiscible two phase flows it couples the level set and volume of fluid techniques and retains their advantages while overcoming their weaknesses it is stable and robust even for large density and viscosity ratios on the order of 1000 to 1 the numerical method is an extension of the second order method presented by sussman m sussman a second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles journal of computational physics 187 2003 110 136 in which the previous method treated the gas pressure as spatially constant and the present method treats the gas as a second incompressible fluid the new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant this improvement in accuracy allows one to compute accurate solutions on relatively coarse grids thereby providing a speed up over continuum or ghost fluid methods

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

stability analysis for stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotic stability analysis problem is considered for a class of stochastic cohen grossberg neural networks with mixed time delays which consist of both the discrete and distributed time delays based on an lyapunov krasovskii functional and the stochastic stability analysis theory a linear matrix inequality lmi approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square it is shown that the addressed stochastic cohen grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two lmis are feasible where the feasibility of lmis can be readily checked by the matlab lmi toolbox it is also pointed out that the main results comprise some existing results as special cases a numerical example is given to demonstrate the usefulness of the proposed global stability criteria

unified formulation for compressible and incompressible flows by using multi integrated moments ii multi dimensional version for compressible and incompressible flows following our previous paper on a novel finite volume formulation for computing flows of any mach number we present the multi dimensional extension of the method in this paper treating two kinds of averages which are generically called moments and defined as the volume integrated average via and the surface integrated average sia in this paper as the prognostic variables makes the present method different from the conventional finite volume method where only via is the basic variable the resulting discretization approach which is a type of the cip multi moment finite volume method and called vsiam3 volume surface integrated average based multi moment method is combined with a pressure based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows the numerical algorithm for multi dimensions will be reported in this paper numerical experiments with flows of a wide range mach numbers will be also presented

a new volume of fluid advection algorithm a new vof advection algorithm is presented termed the stream scheme the algorithm uses a linear piecewise method for free surface reconstruction coupled to a unique fully multidimensional method of cell boundary flux integration the performance of the new algorithm is compared against other vof advection algorithms using a variety of standard advection tests in general the performance of the stream scheme appears superior to existing multidimensional and dimensionally split advection algorithms

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

an arbitrary lagrangian eulerian method for three phase flows with triple junction points we present a moving mesh method suitable for solving two dimensional and axisymmetric three liquid flows with triple junction points this method employs a body fitted unstructured mesh where the interfaces between liquids are lines of the mesh system and the triple junction points if exist are mesh nodes to enhance the accuracy and the efficiency of the method the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally dynamic boundary conditions on interfaces in particular the triple points are therefore incorporated naturally and accurately in a finite element formulation in order to allow pressure discontinuity across interfaces double values of pressure are necessary for interface nodes and triple values of pressure on triple junction points the resulting non linear system of mass and momentum conservation is then solved by an uzawa method with the zero resultant condition on triple points reinforced at each time step the method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid

sharp interface cartesian grid method i an easily implemented technique for 3d moving boundary computations a cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three dimensional immersed boundaries the embedded boundaries are represented using level sets and treated in a sharp manner without the use of source terms to represent boundary effects the narrow band distance function field in the level set boundary representation facilitates implementation of the finite difference flow solver the resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second order accuracy the accuracy of the finite difference scheme is established and shown to be comparable to finite volume schemes that are considerably more difficult to implement moving boundaries are handled naturally the pressure solver is accelerated using an algebraic multigrid technique adapted to be effective in the presence of moving embedded boundaries benchmarking of the method is performed against available numerical as well as experimental results

a filtered cumulant lattice boltzmann method for violent two phase flows abstract the lattice boltzmann method lbm has been successfully applied to simulate various two phase flow problems such as rayleigh taylor instability rising bubble and droplet dynamics however the method known as two phase lbm faces difficulty in simulating violent two phase flow problems such as dam breaking and liquid jet breakup where the density ratio and reynolds number are high and there are rapid and complex topological changes in this paper we address the problem by using a filtered cumulant lbm the incompressible two phase flow equations are solved by using a velocity based formulation of two phase lbm with a cumulant collision model to stably simulate problems with high density ratio and reynolds number there is no pressure iteration in this formulation and we can keep the simplicity of the cumulant model to further enhance the stability in violent flows a second order filter is applied on the velocity field which can be turned off for non violent flows for interface capturing a conservative phase field lbm which guarantees the mass conservation is employed the proposed method is first validated using five non violent flow problems and the results are in good agreements with experimental and computational references the proposed method is then employed to solve three violent flow problems and the results are in qualitatively good agreements with experimental and computational references the proposed method is more diffusive than the unfiltered model but is stable for all problems simulated in this paper these results can be used as a preliminary study on violent two phase flow simulation using two phase lbm

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

lmi based stability criteria for neural networks with multiple time varying delays abstract in this paper the stability of neural networks with multiple time varying delays is studied a new class of lyapunov krasovskii functionals is constructed and the s procedure and free weighting matrix method are employed to derive a delay dependent stability criterion from which a delay independent criterion is obtained as a special case moreover the result is also extended to delay dependent and rate independent stability criteria for multiple unknown time varying delays finally numerical examples are given to illustrate the effectiveness of our methods and improvement over the existing ones

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

numerical method for a moving solid object in flows we propose a numerical method for dealing with a moving solid body that interacts with a complex liquid surface the method is based on the level set method the cip method and the ghost fluid method the validity of the method was shown by applying it to poiseuille and couette flow problems the method can precisely capture the boundary layer as well as a moving solid object

an improved plic vof method for tracking thin fluid structures in incompressible two phase flows a drawback common to plic schemes is the difficulty of reconstructing the interface when filaments of a thickness smaller than the cell size are present in this work we present an improvement of the reconstruction method proposed by lopez et al a volume of fluid method based on multidimensional advection and spline interface reconstruction j comput phys 195 2004 718 for two dimensional flows which allows tracking fluid structures thinner than the cell size by allowing the interface to be represented in each cell by two non contiguous linear segments the method is based on using markers that are placed every time step at the mid points of the reconstructed cell interface segments the markers are used to improve the orientation and location of the interface segments although the method essentially remains of a vof type numerical tests show that a substantial improvement in accuracy is achieved over previous volume of fluid methods and that the proposed method compares well even with a recent hybrid markers and volume of fluid method

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions

nonlinear estimation based on conversion sample optimization abstract for nonlinear estimation the linear minimum mean square error lmmse estimator using the original measurement is the best of all estimators linear in the measurement recently it has been proven that an lmmse estimator using a stacked measurement vector composed of the original measurement and its nonlinear conversion transformation or function outperforms the original lmmse estimator however to find an optimal conversion for various nonlinear problems is very difficult because it involves functional optimization recognizing that the conversion affects estimation performance only through conversion dependent quantities needed by the augmented lmmse based estimator this paper proposes an optimized conversion sample filter ocf which optimizes all these quantities to optimize estimation performance these quantities are much easier to obtain than the optimal conversion itself using deterministic sampling obtaining these quantities amounts to determining the converted values at both the deterministic sample points and the measurement value in the ocf these values are obtained optimally and analytically by solving a constrained rayleigh quotient problem the proposed ocf has a simple and analytical form and can be generally applied to nonlinear estimation simulation results demonstrate the effectiveness of the proposed ocf compared with some popular nonlinear estimators including several lmmse based filters a recently proposed uncorrelated conversion based filter and a particle filter

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

conditional gauss hermite filtering with application to volatility estimation the conditional gauss hermite filter cghf utilizes a decomposition of the filter density by conditioning on an appropriate part of the state vector in contrast to the usual gauss hermite filter ghf it is only assumed that the terms in the decomposition can be approximated by gaussians due to the nonlinear dependence on the condition quite complicated densities can be modeled but the advantages of the normal distribution are preserved for example in models with multiplicative noise occuring in bayesian estimation the joint density of state and variance parameter strongly deviates from a bivariate gaussian whereas the conditional density can be well approximated by a normal distribution as in the ghf integrals in the time and measurement updates are computed by gauss hermite quadrature alternatively the unscented transform can be used leading to a conditional unscented kalman filter cukf

second order accurate volume of fluid algorithms for tracking material interfaces we introduce two new volume of fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume of fluid interface reconstruction algorithms we find that when the interface is smooth e g continuous with two continuous derivatives the new methods are second order accurate and the other algorithms are first order accurate we propose a design criteria for a volume of fluid interface reconstruction algorithm to be second order accurate namely that it reproduce lines in two space dimensions or planes in three space dimensions exactly we also introduce a second order unsplit volume of fluid advection algorithm that is based on a second order finite difference method for scalar conservation laws due to bell dawson and shubin we test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second order operator split advection algorithm although both methods are second order accurate when the interface is smooth we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives such as at corners

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

square root quadrature kalman filtering the quadrature kalman filter qkf is a recursive nonlinear filtering algorithm developed in the kalman filtering framework it computes the mean and covariance of all conditional densities using the gauss hermite quadrature rule in this correspondence we develop a square root extension of the quadrature kalman filter using matrix triangularizations the square root quadrature kalman filter sqkf propagates the mean and the square root of the covariance although equivalent to the qkf algebraically the sqkf exhibits excellent numerical characteristics but at the expense of increased computational complexity we also present possible refinements of the generic sqkf

an investigation of interface sharpening schemes for multi phase mixture flows this work evaluates several approaches for sharp phase interface capturing in computations of multi phase mixture flows attention is focused on algebraic interface capturing strategies that fit directly within a finite volume muscl type framework in which dimension by dimension reconstruction of interface states based on extrapolated fluid properties is the norm in this scope linear sine wave and tangent hyperbola volume fraction reconstructions are examined for a range of problems including advection of a volume fraction discontinuity the rayleigh taylor instability a dam break problem an axisymmetric jet instability the rayleigh instability and flow within an aerated liquid injector an implicit dual time stepping approach applied directly to a preconditioned form of the governing equations is used for time advancement the results show that the sharpening strategies are successful in providing two to three cell capturing of volume fraction discontinuities

stability analysis based on partition trajectory approach for switched neural networks with fractional brown noise disturbance abstractin this brief the stability problem based on feedback control for two types of stochastic neural networks driven by fractional brown noise is considered one class is the switched neural networks without time delays and the other one is with time delays a novel analysis method very different to the usual approach based on the ito formula and infinitesimal operator is proposed in this paper by the idea of splitting time of trajectory and associating with holder inequality some criteria are obtained to guarantee the switched neural networks with two types to be stable in the end two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results

multiple quadrature kalman filtering bayesian filtering is a statistical approach that naturally appears in many signal processing problems ranging from kalman filter to particle filters there is a plethora of alternatives depending on model assumptions with the exception of very few tractable cases one has to resort to suboptimal methods due to the inability to analytically compute the bayesian recursion in general dynamical systems this is why it has attracted the attention of many researchers in order to develop efficient algorithms to implement it we focus our interest into a recently developed algorithm known as the quadrature kalman filter qkf under the gaussian assumption the qkf can tackle arbitrary nonlinearities by resorting to the gauss hermite quadrature rules however its complexity increases exponentially with the state space dimension in this paper we study a complexity reduction technique for the qkf based on the partitioning of the state space referred to as the multiple qkf we prove that partitioning schemes can effectively be used to reduce the curse of dimensionality in the qkf simulation results are also provided to show that a nearly optimal performance can be attained while drastically reducing the computational complexity with respect to state of the art algorithms that are able to deal with such nonlinear filtering problems

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

numerical method for complex moving boundary problems in a cartesian fixed grid we propose a numerical method to capture and track complex moving boundaries advected in flows our method is based on the level set method but it overcomes the problem of accumulation of reinitialization error in the level set method

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature

multiple conversions of measurements for nonlinear estimation a multiple conversion approach mca to nonlinear estimation is proposed in this paper it jointly considers multiple hypotheses on the joint distribution of the quantity to be estimated and its measurement the overall mca estimate is a probabilistically weighted sum of the hypothesis conditional estimates to describe the hypothesized joint distributions used to match the truth a general distribution form characterized by a linear or nonlinear measurement conversion is found this form is more general than gaussian and includes gaussian as a special case moreover the minimum mean square error mmse optimal estimate given a hypothesized distribution in this form is simply the linear mmse lmmse estimate using the converted measurement lmmse based estimators including the original lmmse estimator and its generalization the recently proposed uncorrelated conversion based filter can all be incorporated into the mca framework given a nonlinear problem a specific form of the hypothesized distribution can be optimally obtained by quadratic programming using the information in the nonlinear measurement function and the measurement conversion then the mca estimate can be obtained easily for dynamic problems an interacting multiple conversion algorithm is proposed for recursive estimation the mca approach has a simple and flexible structure and takes advantage of multiple lmmse based nonlinear estimators the overall estimates are obtained adaptively depending on the performance of the candidate estimators simulation results demonstrate the effectiveness of the proposed approach compared with other nonlinear filters

an interface capturing method with a continuous function the thinc method with multi dimensional reconstruction an interface capturing method with a continuous function is proposed within the framework of the volume of fluid vof method being different from the traditional vof methods that require a geometrical reconstruction and identify the interface by a discontinuous heaviside function the present method makes use of the hyperbolic tangent function known as one of the sigmoid type functions in the tangent of hyperbola interface capturing thinc method f xiao y honma k kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer methods fluids 48 2005 1023 1040 to retrieve the interface in an algebraic way from the volume fraction data of multi component materials instead of the 1d reconstruction in the original thinc method a multi dimensional hyperbolic tangent function is employed in the present new approach the present scheme resolves moving interface with geometric faithfulness and compact thickness and has at least the following advantages 1 the geometric reconstruction is not required in constructing piecewise approximate functions 2 besides a piecewise linear interface curved quadratic surface can be easily constructed as well and 3 the continuous multi dimensional hyperbolic tangent function allows the direct calculations of derivatives and normal vectors numerical benchmark tests including transport of moving interface and incompressible interfacial flows are presented to validate the numerical accuracy for interface capturing and to show the capability for practical problems such as a stationary circular droplet a drop oscillation a shear induced drop deformation and a rising bubble

an eulerian interface sharpening algorithm for compressible two phase flow the algebraic thinc approach article history we describe a novel interface sharpening approach for efficient numerical resolution of a compressible homogeneous two phase flow governed by a quasi conservative five equation model of allaire et al 2001 1 the algorithm uses a semi discrete wave propagation method to find approximate solution of this model numerically in the algorithm in regions near the interfaces where two different fluid components are present within a cell the thinc tangent of hyperbola for interface capturing scheme is used as a basis for the reconstruction of a sub grid discontinuity of volume fractions at each cell edge and it is complemented by a homogeneous equilibrium consistent technique that is derived to ensure a consistent modeling of the other interpolated physical variables in the model in regions away from the interfaces where the flow is single phase standard reconstruction scheme such as muscl or weno can be used for obtaining high order interpolated states these reconstructions are then used as the initial data for riemann problems and the resulting fluctuations form the basis for the spatial discretization time integration of the algorithm is done by employing a strong stability preserving runge kutta method numerical results are shown for sample problems with the mie gruneisen equation of state for characterizing the materials of interests in both one and two space dimensions that demonstrate the feasibility of the proposed method for interface sharpening of compressible two phase flow to demonstrate the competitiveness of our approach we have also included results obtained using the anti diffusion interface sharpening method

robust stability analysis for interval cohen grossberg neural networks with unknown time varying delays in this paper robust stability problems for interval cohen grossberg neural networks with unknown time varying delays are investigated using linear matrix inequality m matrix theory and halanay inequality techniques new sufficient conditions independent of time varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval cohen grossberg neural networks with time varying delays all these results have no restriction on the rate of change of the time varying delays compared to some existing results these new criteria are less conservative and are more convenient to check two numerical examples are used to show the effectiveness of the present results

simplified exponential stability analysis for recurrent neural networks with discrete and distributed time varying delays this paper provides simplified exponential stability criteria for a class of recurrent neural networks rnns with discrete and distributed time varying delays the activation functions of the rnns are assumed to be more general and the proposed criteria are obtained by only using a integral inequality and are not involved any free weighting matrices this feature makes the computational burden largely reduced numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

dynamic system methods for solving mixed linear matrix inequalities and linear vector inequalities and equalities a novel idea is proposed for solving a system of mixed linear matrix inequalities and linear vector inequalities and equalities first the problem is converted into an unconstrained minimization problem with a continuously differentiable convex objective function then a continuous time dynamic system and a discrete time dynamic system are proposed for solving it under some mild conditions the proposed dynamic systems are shown to be globally convergent to a solution of the problem the merits of the methods refer to their simple numerical implementations and capability for handling nonstrict lmis easily in addition the methods are promising in neural circuits realization and therefore have potential applications in many online control problems several numerical examples are presented to illustrate the performance of the methods and substantiate the theoretical results

an adaptive coupled level set volume of fluid interface capturing method for unstructured triangular grids we present an adaptive coupled level set volume of fluid aclsvof method for interfacial flow simulations on unstructured triangular grids at each time step we evolve both the level set function and the volume fraction the level set function is evolved by solving the level set advection equation using a discontinuous galerkin finite element method the volume fraction advection is performed using a lagrangian eulerian method the interface is reconstructed based on both the level set and the volume fraction information in particular the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction different from previous works we have developed an analytic method for finding the line constant on triangular grids which makes interface reconstruction efficient and conserves volume of fluid exactly the level set function is finally reinitialized to the signed distance to the reconstructed interface since the level set function is continuous the normal vector calculation is easy and accurate compared to a classic volume of fluid method while tracking the volume fraction is essential for enforcing mass conservation the method is also coupled to a finite element based stokes flow solver the code validation shows that our method is second order and mass is conserved very accurately in addition owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately

new delay dependent stability criteria for neural networks with two additive time varying delay components this brief is concerned with delay dependent stability for neural networks with two additive time varying delay components by constructing a new lyapunov functional and using a convex polyhedron method to estimate the derivative of the lyapunov functional some new delay dependent stability criteria are derived these stability criteria are less conservative than some existing ones an example is given to demonstrate the less conservatism of the stability results

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

novel stability analysis for recurrent neural networks with multiple delays via line integral type l k functional this paper studies the stability problem of a class of recurrent neural networks rnns with multiple delays by using an augmented matrix vector transformation for delays and a novel line integral type lyapunov krasovskii functional a less conservative delay dependent global asymptotical stability criterion is first proposed for rnns with multiple delays the obtained stability result is easy to check and improve upon the existing ones then two numerical examples are given to verify the effectiveness of the proposed criterion

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

a weakly compressible scheme with a diffuse interface method for low mach number two phase flows abstract a weakly compressible scheme for gas liquid two phase flows with low mach number is proposed for a fully explicit time integration the scheme is based on the fractional step method with the euler equation solver and time integration for viscous surface tension and gravity terms for the efficient solution of the euler equation we introduce the directional splitting method and the method of characteristics which is applicable to semi lagrangian methods a reduction of the speed of sound is also taken into consideration to enlarge the time step intervals the primitive flow variables are time integrated on the node center configuration to capture the gas liquid interface the conservative phase field equation is solved by using the multi moment method it is computed as a conservative form for the volume averaged value defined at the cell center in which the flow velocities are given on the node we discard the exact momentum conservation however the total mass of gas and liquid is conserved by introducing a phase field variable several benchmark problems are examined and the results of the explicit scheme are in good agreement with the experimental and computational references

global asymptotic stability of delayed cellular neural networks a new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented the obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior point algorithm a numerical example is used to show the effectiveness of the obtained result

short note an interface capturing method with a continuous function the thinc method on unstructured triangular and tetrahedral meshes a novel interface capturing method is proposed to compute moving interfaces on unstructured grids with triangular 2d and tetrahedral 3d elements different from the conventional vof volume of fluid method which involves geometric reconstructions of the interface the present method is based on the algebraic reconstruction approach originally developed in the thinc tangent of hyperbola interface capturing scheme by xiao et al 2005 17 a continuous multidimensional hyperbolic tangent function is employed for retrieving the jump like distribution of the indicator function which avoids the explicit geometric representation of the interface and thus substantially reduces the algorithmic complexity in unstructured grids numerical diffusion and smearing are effectively eliminated and the compact thickness of the jump transition layer in the volume fraction is retained throughout the computation even for largely deformed interface the solution quality of the present scheme is comparable to the vof method with plic piecewise linear interface calculation algorithm

new delay dependent robust stability criterion for uncertain neural networks with time varying delays in this paper the problem of delay dependent stability of uncertain neural networks with time varying delays is considered the parameter uncertainties are time varying and assumed to be bounded in magnitude by constructing a new augmented lyapunov functional a delay dependent stability criterion for the network is derived in terms of lmi linear matrix inequality which can be easily solved by various convex optimization algorithms three numerical examples are included to show the effectiveness of proposed criterion

improved delay dependent stability results of recurrent neural networks abstract by using the fact that the activation functions are sector bounded and a tighter inequality this paper presents a new method to the stability analysis of a class of recurrent neural networks rnns with time varying delays this method includes more the slope of activation functions and less variables matrices in constructed lyapunov krasovskii functional with the present stability conditions the computational burden and conservatism are largely reduced both theoretical analysis and numerical example are given to illustrate the effectiveness and the benefits of the proposed method

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

a generalized lmi based approach to the global asymptotic stability of delayed cellular neural networks a novel linear matrix inequality lmi based criterion for the global asymptotic stability and uniqueness of the equilibrium point of a class of delayed cellular neural networks cnns is presented the criterion turns out to be a generalization and improvement over some previous criteria

a new augmented lyapunov krasovskii functional approach to exponential passivity for neural networks with time varying delays abstract in this paper the problem of exponential passivity analysis for uncertain neural networks with time varying delays is considered by constructing new augmented lyapunov krasovskii s functionals and some novel analysis techniques improved delay dependent criteria for checking the exponential passivity of the neural networks are established the proposed criteria are represented in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is included to show the superiority of our results

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

a direct time integral thinc scheme for sharp interfaces abstract this paper describes an improved multi dimensional tangent of hyperbola interface capturing thinc scheme that uses a direct time integration of the hyperbolic tangent function the new time integral thinc scheme is based on the assumption that the interface remains unchanged and moves with the velocity of the cell center during a computational time step a time varying hyperbolic tangent function representing the two phase distribution is then constructed and directly integrated in time compared with existing thinc methods that generally use third order total variation diminishing runge kutta rk3 schemes to update the volume fraction the proposed method requires only one reconstruction step thus reducing the computational cost several classical advection tests have been implemented and the results indicate that the proposed direct time integral thinc method 1 achieves computational errors close to those of the rk3 scheme at a computational cost that is close to that of the first order explicit scheme and 2 preserves better boundedness of the volume fractions than the original rk3 based thinc methods when using a larger steepness parameter and higher courant numbers the proposed approach is employed with the incompressible navier stokes equations to solve a 2d dambreak problem and the numerical results agree well with the corresponding experimental data demonstrating the applicability of the direct time integral thinc method

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

stability criteria for recurrent neural networks with time varying delay based on secondary delay partitioning method a secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks rnns with time varying delay the total interval of the time varying delay is first divided into two parts and then each part is further divided into several subintervals to deal with the state variables associated with these subintervals an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a lyapunov functional are proposed which help to obtain the stability criterion the main feature of the proposed result is more effective for the rnns with fast time varying delay a numerical example is used to show the effectiveness of the proposed stability result

adaptive sparse grid gauss hermite filter abstract in this paper a new nonlinear filter based on sparse grid quadrature method has been proposed the proposed filter is named as adaptive sparse grid gauss hermite filter asghf ordinary sparse grid technique treats all the dimensions equally whereas the asghf assigns a fewer number of points along the dimensions with lower nonlinearity it uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached the performance of the proposed filter is illustrated with two nonlinear filtering problems simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse grid gauss hermite filter sghf and gauss hermite filter ghf with a considerable reduction in computational load further in the conventional ghf and sghf any increase in the accuracy level may result in an unacceptably high increase in the computational burden however in asghf a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter this enables the online estimator to operate near full efficiency with a predefined computational budget

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

a mixed markers and volume of fluid method for the reconstruction and advection of interfaces in two phase and free boundary flows in this work we present a new mixed markers and volume of fluid vof algorithm for the reconstruction and advection of interfaces in the two dimensional space the interface is described by using both the volume fraction function c as in vof methods and surface markers which locate the interface within the computational cells the c field and the markers are advected by following the streamlines new markers are determined by computing the intersections of the advected interface with the grid lines then other markers are added inside each cut cell to conserve the volume fraction c a smooth motion of the interface is obtained typical of the marker approach with a good volume conservation as in standard vof methods in this article we consider a few typical two dimensional tests and compare the results of the mixed algorithm with those obtained with vof methods translations rotations and vortex tests are performed showing that many problems of the vof technique can be solved and a good accuracy in the geometrical motion and mass conservation can be achieved

nonlinear filtering methods for harmonic retrieval and model order selection in gaussian and non gaussian noise this paper addresses the problem of high resolution parameter estimation harmonic retrieval and model order selection for superimposed sinusoids the harmonic retrieval problem is analyzed using a nonlinear parameter estimation approach estimation is performed using several nonlinear estimators with signals embedded in white and colored gaussian noise simulation results demonstrate that the nonlinear filters perform close to the cramer rao bound model order selection is performed in gaussian and non gaussian noise the problem is formulated using a multiple hypothesis testing approach with assumed known a priori probabilities for each hypothesis parameter estimation is performed using the extended kalman filter when the noise is gaussian the extended high order filter ehof is implemented in non gaussian noise simulation results demonstrate excellent performance in selecting the correct model order and estimating the signal parameters

a geometrical area preserving volume of fluid advection method a new class of algorithms that preserve mass exactly for incompressible flows on a cartesian mesh are presented they amount to piecewise linear area preserving mappings of tessellations of the plane they are equivalent to volume of fluid vof advection methods which are decomposed into an eulerian implicit scheme in one direction followed by a lagrangian explicit step in the other one it is demonstrated that mass conservation is exact for incompressible flows and that there are no undershoots or overshoots of the volume fraction which thus always remains constrained between 0 and 1

a class of stable square root nonlinear information filters information filters can process nonlinear systems with uncertain prior knowledge and the particular square root form of adaptive filters can improve numerical stability based on a square root decomposition of information matrix and an extra positive definite matrix the unscented transform and the cubature rule are applied to the information filtering architecture for nonlinear estimation a class of stable square root nonlinear information filters is then proposed in this technical note in addition the boundedness of their estimation errors is also proven results from simulations of filtering a chaotic map demonstrate that the proposed square root nonlinear filters can improve numerical stability and has better filtering performance than other information filters

numerical aspects of different kalman filter implementations a theoretical analysis is made of the error propagation due to numerical roundoff for four different kalman filter implementations the conventional kalman filter the square root covariance filter the square root information filter and the chandrasekhar square root filter an experimental analysis is performed to validate the new insights gained by the theoretical analysis

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

delay dependent state feedback stabilization for a networked control model with two additive input delays this paper is centered on delay dependent state feedback stabilization for a networked control model with two additive input delays firstly delay dependent stability is investigated by splitting the whole delay interval into subintervals according to the delays a lyapunov functional is constructed to reduce conservatism we handle the lyapunov functional in two ways more specifically we take the lyapunov functional as a whole to examine its positive definite rather than restrict each term of it to positive definite as usual in addition when estimating the derivative of the lyapunov functional we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals the resulting stability results turn out dependent on the two delays separately and less conservative than some existing ones then based on the stability results state feedback stabilization is studied delay dependent conditions are formulated for the controller such that the closed loop system is asymptotically stable finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method

improved delay dependent stability criteria for generalized neural networks with time varying delays abstract this paper is concerned with the problem of stability analysis for generalized neural networks with time varying delays a novel integral inequality which includes several existing inequalities as special cases is presented by employing a suitable lyapunov krasovskii functional lkf and using the proposed integral inequality to estimate the derivative of the lkf improved delay dependent stability criteria expressed in terms of linear matrix inequalities are derived finally four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method

observer based optimal fault detection and diagnosis using conditional probability distributions a new optimal fault detection and diagnosis fdd scheme is studied in this paper for the continuous time stochastic dynamic systems with time delays where the available information for the fdd is the input and the measured output probability density functions pdf s of the system the square root b spline functional approximation technique is used to formulate the output pdf s with the dynamic weightings as a result the concerned fdd problem can be transformed into a robust fdd problem subjected to a continuous time uncertain nonlinear system with time delays feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality lmi techniques in order to improve fdd performances two optimization measures namely guaranteed cost performance and hinfin performance are applied to optimize the observer design simulations are given to demonstrate the efficiency of the proposed approach