on the stability of receding horizon lq control with zero state terminal constraint receding horizon control with zero state terminal constraint for linear time varying discrete systems is considered it is shown that uniform controllability suffices to ensure closed loop exponential stability thus relaxing the reversibility and or detectability requirements made in the existing literature the result has interesting implications in the design of predictive controllers with guaranteed closed loop stability

a gaussian approximation recursive filter for nonlinear systems with correlated noises this paper proposes a gaussian approximation recursive filter gasf for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other through presenting the gaussian approximations about the two step state posterior predictive probability density function pdf and the one step measurement posterior predictive pdf a general gasf framework in the minimum mean square error mmse sense is derived based on the framework the gasf implementation is transformed into computing the multi dimensional integrals which is solved by developing a new divided difference filter ddf with correlated noises simulation results demonstrate the superior performance of the proposed ddf as compared to the standard ddf the existing ukf and ekf with correlated noises

stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic riccati equation this note addresses the jump linear quadratic problem of markov jump linear systems and the associated algebraic riccati equation necessary and sufficient conditions for stability of the optimal control and positiveness of riccati solutions are developed we show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory but also a necessary one this together with a characterization developed here for the kernel of the riccati solution allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable and that the riccati solution is positive definite if and only if the system is weakly observable the connection between the algebraic riccati equation and the control problem is made as far as the minimal positive semidefinite solution for the algebraic riccati equation is identified with the optimal solution of the linear quadratic problem illustrative numerical examples and comparisons are included

correspondence author s reply to comments on performance evaluation of ukf based nonlinear filtering it is stated in the above mentioned comment that the main result of the paper xiong zhang et al 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of filters such as the extended kalman filter ekf as we show here this belief can be justified in a rigorous way even for the nonlinear stochastic system with a nonlinear measurement equation

unsteady flow calculations with a parallel multiblock moving mesh algorithm a novel parallel dynamic moving mesh algorithm designed for multiblock parallel unsteady flow calculations using body fitted grids is presented the moving grid algorithm within each block uses a method of arc length based transfinite interpolation which is performed independently on local processors where the blocks reside a spring network approach is used to determine the motion of the corner points of the blocks which may be connected in an unstructured fashion in a general multiblock method a smoothing operator is applied to the points of the block face boundaries and edges to maintain grid smoothness and grid angles a multiblock parallel euler navier stokes solver using multigrid and dual time stepping is developed along with the moving mesh method computational results are presented for the unsteady flow calculations of airfoils and wings with deforming shapes as found in flutter simulations

unsteady flow calculations with a multigrid navier stokes method a multigrid navier stokes method with a two equation k u turbulence model is developed for calculating unsteady flows the method uses a staggered finite volume scheme to discretize the navier stokes and the turbulence model equations in space a fully implicit time accurate scheme is reformulated so that an efficient explicit multistage method with local time stepping residual smoothing and multigrid can be used to accelerate convergence within each unsteady time step the method combines the advantages of implicit and explicit schemes for unsteady flow calculations solutions for the forced oscillation of an airfoil are obtained with the euler and the navier stokes equations results are compared with experimental data

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

stochastic stability of the extended kalman filter with intermittent observations in this technical note we analyze the error behavior of the discrete time extended kalman filter for nonlinear systems with intermittent observations modelling the arrival of the observations as a random process we show that given a certain regularity of the system the estimation error remains bounded if the noise covariance and the initial estimation error are small enough we also study the effect of different measurement models on the bounds for the error covariance matrices

unscented kalman filter over unreliable communication networks with markovian packet dropouts the paper investigates the stability of the discrete time modified unscented kalman filter mukf in transmitting measurement outputs to the filter via a network since the communication channel states do not always vary in time the arrival of the observations is modeled as a two state time homogeneous markov process k the stability of the estimation error covariance matrices at packet reception times is analyzed sufficient conditions related to hk and the initial conditions for the peak covariance stability and the usual covariance stability are given also the relationship between the different types of stability notions is illustrated for systems with i i d observation dropouts numerical example is given to illustrate the effectiveness of the techniques developed

analysis of continuous time kalman filtering under incorrect noise covariances abstract the behavior of the continuous time kalman filter under incorrect noise covariances is analyzed the filter performance is quantified by the actual state error covariance through this quantity the characteristic of the filter is examined convergence and divergence analyses of the actual state error covariance are given the significance of the results presented in the paper is that they help one to understand and be able to predict certain behavior of the kalman filter when inexact values of noise covariances are used

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

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

brief paper derivative free estimation methods new results and performance analysis the derivative free nonlinear estimation methods exploiting the stirling s interpolation and the unscented transformation for discrete time nonlinear stochastic systems are treated the divided difference and unscented filters smoothers and predictors based on the methods are introduced in the unified framework the new relations among the first order stirling s interpolation the second order stirling s interpolation and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed the theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point gaussian sum filters given as a mixture of the derivative free filters

inequality based properties of detectability and stabilizability of linear time varying systems in discrete time well known properties of uniform detectability and uniform stabilizability are sharpened in terms of lyapunov and riccati inequalities for discrete time linear time varying systems in particular it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite path of present and future coefficients these results are applied to time varying systems where the system coefficients vary among a finite set and lead to precise and computable convex conditions for the stability and dynamic output feedback stabilizability of such systems

correspondence comments on performance evaluation of ukf based nonlinear filtering this note points out that the main result of the paper xiong k zhang h y chan c w 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of so called gaussian filters it justifies a practical countermeasure of the divergence i e adding small quantities to the noise covariance matrix to stabilize the filter

state estimation incorporating infrequent delayed and integral measurements this paper investigates the problem of state estimation incorporating infrequent delayed and integral measurements in chemical process there often exist two types of measurements on one hand the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously on the other hand the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved moreover due to the interval time taken by chemical sample collection the measurements for some quality variables have another important characteristic it is a function of the states of the compositions over a period of time this paper formulates the process with infrequent delayed and integral measurements as an equivalent variable dimension system whose measurements are both delay and integration free based on the new model a variable dimension unscented kalman filter vd ukf is proposed to estimate the states furthermore the stability of the proposed vd ukf is analyzed compared with the existing results the proposed stability condition is significantly relaxed and the invertibility condition of jacobian matrices is no longer needed finally a simulation example demonstrates the effectiveness of the proposed method

flutter computation of turbomachinery cascades using a parallel unsteady navier stokes code a quasi three dimensional multigrid navier stokes solver on single and multiple passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades the conventional direct store method is used for applying the phase shifted periodic boundary condition over a single blade passage a parallel version of the solver using the message passing interface standard is developed for multiple passage computations in parallel multiple passage computations the phase shifted periodic boundary condition is converted to a simple in phase periodic condition euler and navier stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel codes it is found that the parallel code offers almost linear speedup with a slope close to 1 on multiple cpus in addition significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple passage computations due to the use of the in phase periodic boundary conditions compared with that in the single passage computations with phase shifted periodic boundary conditions via the direct store method the parallel navier stokes code is also used to calculate the flow through an oscillating compressor cascade results are compared with experimental data and computations by other authors

limiting accuracy of segregated solution methods for nonsymmetric saddle point problems nonsymmetric saddle point problems arise in a wide variety of applications in computational science and engineering the aim of this paper is to discuss the numerical behavior of several nonsymmetric iterative methods applied for solving the saddle point systems via the schur complement reduction or the null space projection approach krylov subspace methods often produce the iterates which fluctuate rather strongly here we address the question whether large intermediate approximate solutions reduce the final accuracy of these two level inner outer iteration algorithms we extend our previous analysis obtained for symmetric saddle point problems and distinguish between three mathematically equivalent back substitution schemes which lead to a different numerical behavior when applied in finite precision arithmetic theoretical results are then illustrated on a simple model example

iterative residual generator for fault detection with linear time invariant state space models in this paper an iterative residual generator irg is proposed for discrete time invariant state space model with the aim of detecting faulty signals by minimizing the mean square errors subject to unbiasedness constraint a new filter with finite impulse response structure is derived the resulting irg is then obtained by extracting residual signal from the batch filter through several predictor corrector iterations it shows that irg can provide a zero mean gaussian process regardless of previous estimation errors more importantly it includes the residual generation process in the kalman filter as its special case with the chi square test a numerical example is simulated to demonstrate that irg can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults and the estimation horizon length in irg serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm

towards a link between the factorization approach and mimo robust adaptive control based on a doubly coprime factorization theorem nett et al 1984 an adaptive controller for discrete time mimo systems consisting of a not necessarily minimum phase modelled part and fraction type unmodelled dynamics which are not necessarily stable non linear and time varying is developed then by virtue of a stability result which is itself of interest it is shown that the adaptive closed loop system is bibo stable even in the presence of small but not necessarily stable unmodelled dynamics and arbitrarily bounded initial conditions consequently an initial but important step for applying the factorization approach to mimo robust adaptive control is completely established

analysis of kalman filter approximations for nonlinear measurements a theoretical analysis is presented of the correction step of the kalman filter kf and its various approximations for the case of a nonlinear measurement equation with additive gaussian noise the kf is based on a gaussian approximation to the joint density of the state and the measurement the analysis metric is the kullback leibler divergence of this approximation from the true joint density the purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the kf and its variants in nonlinear scenarios this is illustrated using a numerical example

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

recursive bayesian estimation using piece wise constant approximations abstract in bayesian estimation the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity this work considers recursive estimation of a nonlinear discrete time system state using successive observations the formal recursion for the density function is easily written but generally there is no closed form solution the numerical solution proposed here is obtained by modifying the recursion and using a simple piece wise constant approximation to the density functions the approach also allows detailed analysis of error propagation through the algorithm yielding a bound on the maximum error growth and a characterization of the situations with potential for large errors the stability of the algorithm is demonstrated by comparing its long term performance to a kalman filter for a linear system with gaussian noises comparison to the point mass algorithm shows improved estimation accuracy and for moderately dense grids faster computation as an example the algorithm is applied to a system identification problem and the results compared to a popular second order minimum variance estimator the optimal estimate derived from the approximate density is seen to be far superior

technical communique stochastic stability of the unscented kalman filter with intermittent observations in this paper the stochastic stability of the discrete time unscented kalman filter for general nonlinear stochastic systems with intermittent observations is proposed it is shown that the estimation error remains bounded if the system satisfies some assumptions and the statistical convergence property of the estimation error covariance is studied showing the existence of a critical value for the arrival rate of the observations an upper bound on this expected state error covariance is given a numerical example is given to illustrate the effectiveness of the techniques developed

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

performance evaluation of ukf based nonlinear filtering the performance of the modified unscented kalman filter ukf for nonlinear stochastic discrete time system with linear measurement equation is investigated it is proved that under certain conditions the estimation error of the ukf remains bounded furthermore it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm error behavior of the ukf is then derived in terms of mean square error mse and the cramer rao lower bound crlb is introduced as a performance measure the modified ukf is found to approach the crlb if the difference between the real noise covariance matrix and the selected one is small enough these results are verified by using monte carlo simulations on two example systems

brief paper optimal fault detection for linear discrete time varying systems this paper deals with the problem of observer based fault detection for linear discrete time varying ldtv systems a problem formulation is first proposed to address the optimization of the fault detection filter fdf design which is expressed in terms of maximizing a finite horizon h h or h h performance index this formulation can be applied to fdf design of ldtv systems subject to l 2 norm bounded unknown inputs or stochastic noise sequences it is shown that a unified optimal solution to the fdf can be obtained by solving the discrete time riccati equation and the optimal fdf is not unique a numerical example is given to illustrate the proposed method

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

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

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

anticausal stabilizing solution to discrete reverse time riccati equation abstract this paper is dealing with the problem of general conditions for the existence of the anticausal stabilizing solution to the discrete reverse time riccati equation the connection between the contracting property of the l2 input output operator of a linear internally stable system and the existence of the anticausal stabilizing solution to the above mentioned equation are pointed out

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

stabilizability of linear time varying systems abstract for linear time varying systems with bounded system matrices we discuss the problem of stabilizability by linear state feedback for example it is shown that complete controllability implies the existence of a feedback so that the closed loop system is asymptotically stable we also show that the system is completely controllable if and only if the lyapunov exponent is arbitrarily assignable by a suitable feedback for uniform exponential stabilizability and the assignability of the bohl exponent this property is known also dynamic feedback does not provide more freedom to address the stabilization problem the unifying tools for our results are two finite l 2 cost conditions the distinction of exponential and uniform exponential stabilizability is then a question of whether the finite cost condition is uniform in the initial time or not

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

exponential asymptotic stability of time varying inverse prediction error filters it is a classical result of linear prediction theory that as long as the minimum prediction error variance is nonzero the transfer function of the optimum linear prediction error filter for a stationary process is minimum phase and therefore its inverse is exponentially stable here extensions of this result to the case of nonstationary processes are investigated in that context the filter becomes time varying and the concept of transfer function ceases to make sense nevertheless we prove that under mild condition on the input process the inverse system remains exponentially stable we also consider filters obtained in a deterministic framework and show that if the time varying coefficients of the predictor are computed by means of the recursive weighted least squares algorithm then its inverse remains exponentially stable under a similar set of conditions

staggered finite volume scheme for solving cascade flow with a k omega turbulence model a k turbulence model by wilcox is applied to cascade flow calculations a staggered finite volume scheme is proposed to solve the compressible reynolds averaged navier stokes equations and the k equations are solved on staggered control volumes with k and defined at the cell vertices of the original grid by use of this combination of the cell centered and cell vertex schemes the method maintains a small stencil for all diffusion terms and closely couples the navier stokes and k equations

a strongly coupled time marching method for solving the navier stokes andk ω turbulence model equations with multigrid many researchers use a time lagged or loosely coupled approach in solving the navier stokes equations and two equation turbulence model equations in a time marching method the navier stokes equations and the turbulence model equations are solved separately and often with different methods in this paper a strongly coupled method is presented for such calculations the navier stokes equations and two equation turbulence model equations in particular thek equations are considered as one single set of strongly coupled equations and solved with the same explicit time marching algorithm without time lagging a multigrid method together with other acceleration techniques such as local time steps and implicit residual smoothing is applied to both the navier stokes and the turbulence model equations time step limits due to the source terms in thek equations are relieved by treating the appropriate source terms implicitly the equations are also strongly coupled in space through the use of staggered control volumes the method is applied to the calculation of flows through cascades as well as over isolated airfoils convergence rate is greatly improved by the use of the multigrid method with the strongly coupled time marching scheme

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

computation of mistuning effects on cascade flutter a computational method is described for predicting eutter of turbomachinery cascades with mistuned blades themethodsolves theunsteadyeuler navier stokesequationsformultiple bladepassageson aparallel computer usingthemessagepassinginterface asecond orderimplicit schemewithdualtime steppingand multigrid isused each individual blade is capable of moving with its own independent frequency and phase angle thus modeling a cascade with mistuned blades flutter predictions are performed through the energy method both phase angle and frequency mistuning are studied it is found that phase angle mistuning has little effect on stability whereas frequencymistuningsignie cantlychanges theaerodynamicdamping theimportant effectoffrequencymistuning is to average out the aerodynamic damping of the tuned blade row over the whole range of interbladephase angles ibpa if a tuned blade row is stable over most of the ibpa range the blades can be stabilized for the complete ibpa range through appropriate frequency mistuning nomenclature ch coefecient of aerodynamic force in h direction cw aerodynamic work coefe cient c blade chord length e total energy per unit mass h translational blade displacement p static pressure t e utter period t time u v e ow velocity components in x and y directions ub vb grid velocity components in x and y directions u v relative velocity components u i ub v i vb a rotational blade displacement h stream tube thickness ratio in x direction n e utter damping coefe cient q density r interblade phase angle x e utter frequency

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

improved cubature kalman filter for gnss ins based on transformation of posterior sigma points error tightly coupled gnss ins has been widely approved as a promising substitute for standalone gnss in urban areas navigation however due to the frequent gnss signal outages the filter used in gnss ins should be insensitive to the less informative observations in this paper a novel sigma points update method is proposed to enhance the robustness of cubature kalman filter ckf under the circumstance of unavailable observations first the problems of existing sampling based filters are analyzed then by transforming the posterior sigma points error matrix from prediction phase of filtering to the posterior domain of update the updated sigma points are expected to capture the covariance more precisely than traditional sigma points finally an improved ckf ickf is developed by embedding these points into the bayesian estimation framework and the upper bounds of error covariance matrices are analyzed theoretically signal outages with different durations are simulated and results demonstrate that ickf outperforms state of the art methods

nonlinear estimation applying an unscented transformation in systems with correlated uncertain observations an approximation to the least squares filter is proposed for discrete signals whose evolution is governed by nonlinear functions when the estimation is based on nonlinear observations with additive noise which can consist only of random noise this uncertainty in the observation process is modelled by bernoulli random variables which are correlated at consecutive time instants and are otherwise independent the proposed recursive approximation is based on the unscented principle successive applications of the unscented transformation to a suitable augmented state vector enable us to approximate the one stage state and observation predictors from the state filter at the previous time instant the performance of the proposed algorithm is compared with that of an extended algorithm in a numerical simulation example

on the numerical behavior of matrix splitting iteration methods for solving linear systems we study the numerical behavior of stationary one step or two step matrix splitting iteration methods for solving large sparse systems of linear equations we show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic for a general stationary matrix splitting iteration method we analyze two mathematically equivalent implementations and discuss the conditions when they are componentwise or normwise forward or backward stable we distinguish two different forms of matrix splitting iteration methods and prove that one of them is significantly more accurate than the other when employing inexact inner solves the theoretical results are illustrated by numerical experiments with an inexact one step and an inexact two step splitting iteration method

robust recursive estimation in the presence of heavy tailed observation noise a first order approximation is derived for the conditional prior distribution of the state of a discrete time stochastic linear dynamic system in the presence of contaminated normal observation noise this distribution is then used to derive a first order approximation of the conditional mean minimum variance estimator if the observation noise distribution can be represented as a member of the e contaminated normal neighborhood then the conditional prior is also to first order an analogous perturbation from a normal distribution whose first two moments are given by the kalman filter moreover the perturbation is itself of a special form combining distributions whose parameters are given by banks of parallel kalman filters and optimal smoothers

an extended kalman filter frequency tracker for high noise environments the problem of constructing a frequency tracker for weak narrowband signals with slowly varying frequency is considered an extended kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal to noise ratios

on stability of constrained receding horizon control with finite terminal weighting matrix in this paper a new stabilizing receding horizon control based on a finite input and state horizon cost with a finite terminal weighting matrix is proposed for time varying discrete linear systems with constraints we propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints we show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality lmi in the case of constrained time invariant systems an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints using the invariant ellipsoid constraints a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control

simplified rapid switching gain scheduling for a class of lpv systems a limitation of the original gain scheduling approaches is that the closed loop stability can only be assured when the underlying parameters vary sufficiently slowly a remedy exists but requires for its implementation the possible solution of asymptotic riccati equations are for an infinite number of different parameter values and the on line solution of a riccati differential equation rde with time varying coefficient matrices our method avoids solving the rde online and instead uses an explicit transient formula that looks up the predetermined solutions of the associated ares at a finite set of given system operating points furthermore only a finite number of ares are solved to determine a finite set of controller gains

design and implementation of gaussian filter for nonlinear system with randomly delayed measurements and correlated noises abstract in this paper we focus on the nonlinear state estimation problem with both one step randomly delayed measurements and correlated noises firstly a general framework of gaussian filter is designed under gaussian assumption on the conditional density furthermore the implementation of gaussian filter is transformed into the computation of the nonlinear numerical integrals in the proposed framework secondly a new cubature kalman filtering ckf algorithm is developed on the basis of the spherical radial cubature rule for approximating such nonlinear integrals finally the performance of the modified ckf is verified by a numerical simulation example

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

a spectral test for observability and reachability of time varying systems a spectral test for the observability and reachability of linear time invariant systems the popov belevitch hautus test is well known and serves as a powerful characterization of these properties in this paper it is shown that similar tests exist for linear time varying systems the test presented here involves a check over a subset of the spectrum of the weighted block shift known as the set of almost eigenvalues

a new continuous discrete particle filter for continuous discrete nonlinear systems abstract the continuous discrete version of particle filter cd pf for continuous discrete nonlinear systems is proposed in this paper firstly the continuous discrete extended kalman filter cd ekf and the cd pf are described in detail then some comparisons of these two methods are carried out the simulation results show that the performance of the cd pf is better than that of the cd ekf then higher order stochastic runge kutta schemes are proposed to improve the stability and precision of the filter furthermore the cd pf is applied to nonlinear systems with nongaussian noise finally some simulations are provided to illustrate the effectiveness of the proposed filter

reynolds stress model dual time stepping computation of unsteady three dimensional flows an efficient and robust implicit methodology for the integration of the unsteady three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynolds stress closure is developed the five mean flow and seven turbulence transport equations are discretized on a structured deforming grid using an o x 3 finite volume upwind biased muscl scheme time integration uses an implicit o t 2 dual time stepping procedure with alternating direction implict subiterations with approximate jacobians designed to minimize the computing time requirements of the implicit phase for the reynolds stresses so that the computational overhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration based on a dynamic criterion of subiterative convergence grid deformation velocities associated with solid wall displacement are computed using a laplacian operator the method is validated by comparison with experimental data for 1 two dimensional pitching oscillations of a naca 0012 airfoil and 2 three dimensional shock wave oscillation in a transonic channel the influence of the various parameters of the method is analyzed in detail

brief paper adaptive divided difference filtering for simultaneous state and parameter estimation a novel adaptive version of the divided difference filter ddf applicable to non linear systems with a linear output equation is presented in this work in order to make the filter robust to modeling errors upper bounds on the state covariance matrix are derived the parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality lmi constraint which ensures that the predicted output error covariance is larger than the observed output error covariance the resulting sub optimal high gain filter is applied to the problem of joint state and parameter estimation simulation results demonstrate the superior performance of the proposed filter as compared to the standard ddf

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

stability of a random riccati equation with markovian binary switching this paper is concerned with the boundedness of the solution of a random riccati difference equation arising from kalman filtering with observation losses characterized by a markovian binary jump parameter a new sufficient condition for stability in the peak covariance sense is obtained which has a simpler form and is shown to be less conservative for systems with the observability index of two than existing works meanwhile we give some conditions under which the covariance matrix is bounded or unbounded in the usual sense then the equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and independent and identically distributed i i d observation losses