a fast algorithm for prandtl s integro differential equation collocation and quadrature methods for singular integro differential equations of prandtl s type are studied in weighted sobolev spaces a fast algorithm basing on the quadrature method is proposed convergence results and error estimates are given

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

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

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

linear estimation for networked control systems with random transmission delays and packet dropouts in networked control systems random delays and packet dropouts are inevitable during data transmissions due to the limited communication capacity the phenomena of random delays and packet dropouts of both sides from a sensor to an estimator and from a controller to an actuator are modeled via employing two groups of bernoulli random variables by defining some new variables the original system with random delays and packet dropouts is equivalently transformed into a stochastic parameterized system the optimal linear filter predictor and smoother in the linear minimum variance sense are presented via the orthogonality projection approach they depend on the probabilities of the stochastic parameters the solutions to the optimal linear estimators are given by three equations including a riccati a lyapunov and a simple difference the stability of the proposed estimators is analyzed at last a sufficient condition for the existence of the steady state estimators is given for time invariant systems two examples are provided to verify the effectiveness of the proposed algorithms

on stability in the presence of analog erasure channel between the controller and the actuator consider a discrete time networked control system in which the controller has direct access to noisy measurements of the output of the plant however information flows from the controller to the actuator via a channel that features bernoulli erasure events if an erasure occurs the channel outputs an erasure symbol otherwise it transmits a real finite dimensional vector we determine necessary and sufficient conditions for the stabilizability of an unstable linear time invariant finite dimensional plant given a minimal state space representation for the plant the necessary and sufficient conditions for stabilizability are expressed in terms of the probability of erasure at the channel and of the spectral radius of the one step state transition matrix there are two main results in the technical note the first result shows that if the actuator has processing capabilities then the necessary and sufficient conditions for stabilizability remain unchanged with or without acknowledgements from the actuator to the controller the second result shows that the stabilizability conditions are identical for two types of actuators type i processing at the actuator has access to the plant s model type ii processing at the actuator uses a universal algorithm that does not depend on the model of the plant thus neither the knowledge of the model of the plant at the actuator nor the presence of acknowledgements from the actuator to the controller can be used to alter or relax the necessary and sufficient conditions for stabilizability

event based state estimation of discrete state hidden markov models the state estimation problem for hidden markov models subject to event based sensor measurement updates is considered in this work using the change of probability approach we assume the measurement updates are transmitted through wired or wireless communication networks for the scenarios with reliable and unreliable communication channels analytical expressions for the probability distributions of the states conditioned on all the past point and set valued measurement information are obtained also we show that the scenario with a lossy channel but without the event trigger can be treated as a special case of the reliable channel results based on these results closed form expressions for the estimated communication rates under the original probability measure are presented which are shown to be the ratio between a weighted 1 norm and the 1 norm of the unnormalized conditional probability distributions of the states under the new probability measures constructed implementation issues are discussed and the effectiveness of the results is illustrated by numerical examples and comparative simulations

numerical solution of systems of cauchy singular integral equations with constant coefficients abstract this paper deals with the numerical solution of a class of systems of cauchy singular integral equations with constant coefficients the proposed procedure consists of two basic steps the first one is to consider a modified problem equivalent to the original one under suitable conditions the second one is to approximate its solution by means of a vector of polynomial functions such array is constructed by applying a quadrature type method based on gaussian rules that leads to solve a determined and well conditioned linear system the convergence and stability of the method are proved in weighted l 2 spaces some numerical tests are also shown

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

invariant formulation for the minimum induced drag conditions of nonplanar wing systems under the hypotheses of linear potential flow and rigid wake aligned with the freestream a configuration invariant analytical formulation for the induced drag minimization of single wing nonplanar systems is presented following a variational approach the resulting euler lagrange integral equation in the unknown circulation distribution is obtained the kernel presents a singularity of the first order and an efficient computational method ideal for the early conceptual phases of the design is proposed munk s theorem on the normalwash and its relation with the geometry of the wing under optimal conditions is naturally obtained with the present method moreover munk s constant of proportionality not provided in his original work is demonstrated to be the ratio between the freestream velocity and the optimal aerodynamic efficiency the augmented munk s minimum induced drag theorem is then formulated additional induced drag theorems are demonstrated following the derivations of this invariant proced

new error estimates for galerkin method to an airfoil equation in this paper we consider new error estimates under the weighted chebyshev norm for galerkin method to an airfoil equation galerkin discretisation is discussed the smoothness conditions of the input functions are improved i e they need to be holder continuous with 12 m 1

a numerical method and efficient preconditioner for generalized airfoil equations in this paper the generalized airfoil equations with cauchy algebraic singularity are researched by introducing the collocation method to conquer the singularity of the integral equation theoretical analysis and examples showed this method has accuracy o h m 1 with m the order of the interpolate polynomial in addition by separating the singular part into two so that they can offset against each other in the collocation points a new equivalent integrate function is also constructed moreover to accelerate the convergence of solving the obtained linear system a tridiagonal preconditioner is also presented for the singular integral operator by the operator splitting idea compared to the traditional tridiagonal preconditioner our method is more easily computed by an explicit inverse finally some numerical examples are presented to illustrate the behavior of the collocation method and this preconditioner

remarks on two integral operators and numerical methods for csie in this paper the author extends the mapping properties of some singular integral operators in zygmund spaces equipped with uniform norm as a by product quadrature methods for solving csie having indices 0 and 1 are proposed their stability and convergence are proved and error estimates in zygmund norm are given some numerical tests are also shown

global polynomial approximation for symm s equation on polygons summary to solve 1d linear integral equations on bounded intervals with nonsmooth input functions and solutions we have recently proposed a quite general procedure that is essentially based on the introduction of a nonlinear smoothing change of variable into the integral equation and on the approximation of the transformed solution by global algebraic polynomials in particular the new procedure has been applied to weakly singular equations of the second kind and to solve the generalized air foil equation for an airfoil with a flap in these cases we have obtained arbitrarily high orders of convergence through the solution of very well conditioned linear systems in this paper to enlarge the domain of applicability of our technique we show how the above procedure can be successfully used also to solve the classical symm s equation on a piecewise smooth curve the collocation method we propose applied to the transformed equation and based on chebyshev polynomials of the first kind has shown to be stable and convergent a comparison with some recent numerical methods using splines or trigonometric polynomials shows that our method is highly competitive

convergence of optimal linear estimator with multiplicative and time correlated additive measurement noises in this paper the problem of convergence for the optimal linear estimator of discrete time linear systems with multiplicative and time correlated additive measurement noises is studied by defining a new random vector that consists of the innovation error and part of the noise in the new measurement obtained from the measurement differencing method we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose it is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and moreover this fixed point can be obtained by solving a set of matrix equations

numerical analysis for one dimensional cauchy singular integral equations the paper presents a selection of modern results concerning the numerical analysis of one dimensional cauchy singular integral equations in particular the stability of operator sequences associated with different projection methods the aim of the paper is to show the main ideas and approaches such as the concept of transforming the question of the stability of an operator sequence into an invertibility problem in a certain banach algebra or the concept of certain scales of weighted besov spaces to prove convergence rates of the sequence of the approximate solutions moreover computational aspects in particular the construction of fast algorithms are discussed

a general framework for solving riemann hilbert problems numerically a new numerical framework for the approximation of solutions to matrix valued riemann hilbert problems is developed based on a recent method for the homogeneous painleve ii riemann hilbert problem we demonstrate its effectiveness by computing solutions to other painleve transcendents an implementation in mathematica is made available online

kalman filtering with intermittent observations convergence for semi markov chains and an intrinsic performance measure this technical note shows that the stationary distribution for the covariance of kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models semi markov chain these results are proved using the geometric properties of riccati recursions with respect to a particular riemannian distance moreover the riemannian mean induced by that distance is always bounded therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist other interesting properties of that mean include the symmetry between covariance and information matrices averaging covariances or their inverse gives the same result and its interpretation in information geometry as the natural mean for the manifold of gaussian distributions

modeling and estimation for networked systems with multiple random transmission delays and packet losses abstract in networked systems data packets are transmitted through networks from a sensor to a data processing center due to the unreliability of communication channels a packet may be delayed even lost during the transmission at each moment the data processing center may receive one or multiple data packets or nothing at all a novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of bernoulli distributed random variables it is transformed to a measurement model with multiple random delayed states and noises based on the model an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate it does not have a steady state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment so it needs to be computed online to reduce the online computational cost a suboptimal linear filter dependent on the probabilities of random variables is also proposed however it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities it can be computed offline since it has the steady state performance a sufficient condition of existence for the steady state performance is given a simulation example shows the effectiveness

optimal periodic sensor schedule for steady state estimation under average transmission energy constraint we consider periodic sensor scheduling for remote state estimation under average transmission energy constraint the sensor decides whether or not to send its data to a remote estimator in order to meet the transmission energy constraint the transmitted data are likely to be dropped due to the imperfect communication an optimal periodic schedule is found via the tools from the markov chain furthermore a sufficient condition of the system dynamics energy budget and packet drop rate under which the remote estimator is guaranteed to be stable is derived examples are provided to show the effectiveness of results

stochastic link activation for distributed filtering under sensor power constraint we consider the problem of link activation for distributed estimation with power constraint to satisfy the requirement of power consumption we propose a stochastic link activation scheme where each sensor equipped with a distributed estimator sends data to its neighboring sensors according to different probabilities first we design the optimal estimator gain of each sensor to minimize the state estimation error covariance then we find an upper bound of the expected state estimation error covariance and provide a sufficient condition to guarantee the stability of the proposed estimator finally we formulate the link activation problem as an optimization problem and convert it to a convex optimization

optimal linear state estimator with multiple packet dropouts this technical note is concerned with the optimal linear estimation problem in the presence of multiple packet dropouts in both sensor to controller and controller to actuator channels the considered stochastic packet dropouts are independent and bernoulli distributed based on a linear packet dropout model with stochastic parameters a linear minimum variance lmv filter is proposed using the orthogonality principle a sufficient condition for convergence of the steady state lmv filter under a dc controller output is also given simulation results show the effectiveness of the proposed filter

stochastic consensus over noisy networks with markovian and arbitrary switches this paper considers stochastic consensus problems over lossy wireless networks we first propose a measurement model with a random link gain additive noise and markovian lossy signal reception which captures uncertain operational conditions of practical networks for consensus seeking we apply stochastic approximation and derive a markovian mode dependent recursive algorithm mean square and almost sure i e probability one convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition subsequently we consider a model with arbitrary random switching and a common stochastic lyapunov function technique is used to prove convergence finally our method is applied to models with heterogeneous quantizers and packet losses and convergence results are proved

on error bounds for orthogonal polynomial expansions and gauss type quadrature this paper presents new asymptotics on the coefficients of f x expanded in forms of ultraspherical or jacobi polynomial series which imply the rate of the decay of the coefficients and derive the truncated error bounds moreover we show that the chebyshev coefficient alpha n decays a factor of sqrt n faster than the legendre coefficient u n by using the chebyshev expansion for f x of finite regularity we give new error bounds for a gauss type quadrature and present the aliasing error between the coefficients which shows the equal accuracy of these quadratures for nonanalytic functions

cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution cauchy singular integral equations on an interval are studied in weighted spaces of continuous functions convergence rates for a general method for their numerical solution are proved in weighted uniform norms applications of these results to the collocation method and the quadrature method are given

optimal scheduling of scalar gauss markov systems with a terminal cost function in this technical note we consider the problem of optimal measurement scheduling for a particular class of gauss markov systems these type of scheduling problems arise in applications such as multi target tracking and sensor management general solutions to such problems in the gauss markov framework are still the subject of ongoing research here for the first time we present a set of results for scalar systems where we consider optimality in the context of minimizing a terminal cost complete proofs are given in each case in some cases proof outlines have been previously available other cases are presented here for the first time for the class of problems considered we demonstrate that simple index policies are optimal we further examine practical problems in which suboptimal solutions may suffice numerical examples are presented for each case

optimal estimation over the collision channel consider a distributed sensing system that comprises two sensors each observing a random variable and a remote estimator the goal of the remote estimator is to produce estimates of the random variables based on information transmitted to it by the sensors the random variables are independent and information is transferred from the sensors to the estimator via a collision channel which can only convey a single packet each sensor has the authority to decide what and when to transmit and simultaneous transmissions result in a collision event to be detected at the estimator in our formulation there is no communication between the sensors which precludes the use of coordinated strategies our results characterize the structure of policies at the sensors and the remote estimator that are optimal with respect to a mean squared error criterion more specifically we show that there exist optimal policies at the sensors that use deterministic threshold strategies to decide when to transmit this structural result is independent of the distributions of the observed random variables in our analysis we prove that the computation of a person by person optimal threshold policy can be recast as a one bit optimal quantization problem for which the cost is nonuniform across representation symbols based on that observation we provide an iterative procedure akin to the lloyd max algorithm that can be used to compute locally optimal solutions in the gaussian case our iterative method converged to an optimal solution in all numerical examples we have tried we provide several examples that show the optimality of asymmetric threshold policies even when the overall framework is symmetric such as when both random variables are gaussian with zero mean and the same variance

h filtering of networked discrete time systems with random packet losses this paper studies the h filtering problem for networked discrete time systems with random packet losses the general multiple input multiple output mimo filtering system is considered the multiple measurements are transmitted to the remote filter via distinct communication channels and each measurement loss process is described by a two state markov chain both the mode independent and the mode dependent filters are considered and the resulting filtering error system is modelled as a discrete time markovian system with multiple modes a necessary and sufficient condition is derived for the filtering error system to be mean square exponentially stable and achieve a prescribed h noise attenuation performance the obtained condition implicitly establishes a relation between the packet loss probability and two parameters namely the exponential decay rate of the filtering error system and the h noise attenuation level a convex optimization problem is formulated to design the desired filters with minimized h noise attenuation level bound finally an illustrative example is given to show the effectiveness of the proposed results

the convergence of a collocation method for a class of cauchy singular integral equations in several recent papers we have studied the numerical solution of cauchy singular integral equations of the first kind by a polynomial collocation method 4 61 this technique has proved to be quite efftcient for many problems even when the kernel but not the right hand side is discontinuous 4 61 the l convergence and stability was established in s and 6 in 121 ioakimidis extended this method to solve cauchy singular integral equations of the second kind with constant coefficients although some discussion of convergence was given it appears at least to this author that the proof is incomplete and the conditions on the kernel and the right hand side are somewhat more restrictive than necessary in this paper we will show that the convergence analysis given in 5 6 can be generalized to establish the l convergence of collocation under rather mild restrictions on the data although a variety of numerical techniques such as galerkin s method and direct quadrature have been used extensively to solve cauchy singular equations they seem to be generally suited for problems with smooth kernels for problems with discontinuous kernels collocation methods appear to be a reasonable compromise between time consuming galerkin methods 2 and direct quadrature methods which require the evaluation of the kernel at pairs of points where the kernel may become unbounded 3 131 it is well known that for fredholm equations collocation is related to product integration quadrature methods 11 since such methods seem not to have been developed for the solution of cauchy singular equations collocation appears to be a good way of dealing with fairly general integral equations of this type 4 71

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

collocation quadrature methods and fast summation for cauchy singular integral equations with fixed singularities abstract basing on recent results on the stability of collocation methods applied to cauchy singular integral equations with additional fixed singularities we give necessary and sufficient conditions for the stability of collocation quadrature methods for such equations these methods have the advantage that the respective system of equations has a very simple structure and allows to apply fast summation methods which results in a fast algorithm with o n log n complexity we present numerical results of the application of the proposed collocation quadrature methods to the notched half plane problem of two dimensional elasticity theory

new error bounds for the quadrature method for the solution of cauchy singular integral equations the quadrature method for singular integral equations with cauchy kernels on the arc 1 1 is investigated and a comprehensive theory of this method s convergence in the continuous maximum norm is presented this approach is based on new results in the theory of orthogonal polynomials on a regularity property for the solution of some singular integral equations and on the concept of regular convergent operator sequences new and improved estimates for the rates of convergence are obtained

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

on the integral equation formulations of some 2d contact problems two integral equations representing the mechanical response of a 2d infinite plate supported along a line and subject to a transverse concentrated force are examined the kernels of the integral operators are of the type x y ln x y and x y 2ln x y in spite of the fact that these are only weakly singular the two equations are studied in a more general framework which allows us to consider also solutions having non integrable endpoint singularities the existence and uniqueness of solutions of the equations are discussed and their endpoint singularities detected since the two equations are of interest in their own right some properties of the associated integral operators are examined in a scale of weighted sobolev type spaces then new results on the existence and uniqueness of integrable solutions of the equations that in some sense are complementary to those previously obtained are derived

scheduling parallel kalman filters for multiple processes in this paper we investigate the problem of scheduling parallel kalman filters for multiple processes where each process is observed by a kalman filter and at each time step only one kalman filter could obtain observation due to practical constraints to solve the problem two novel notions permissible consecutive observation loss pcol and least consecutive observation lco are introduced as criteria to describe feasible observation sequences for a process ensuring desired estimation qualities then two methods namely the threshold method and the periodic method are proposed to calculate pcol and lco for each process based on the derived pcol and lco requirements we develop two algorithms that are applicable to different situations sxy algorithm from the pinwheel problem for the case of lco 1 and tree search algorithm for general cases also to reduce the computational complexity of tree search algorithm several useful pruning conditions are obtained

consensusability of discrete time linear multi agent systems over analog fading networks this paper studies the consensusability problem of discrete time linear multi agent systems over analog fading networks it aims to decide whether there exists a distributed controller such that the underlying multi agent system can achieve mean square consensus over analog fading channels conditions to ensure mean square consensus are derived for the scenarios of undirected communication topologies with identical fading networks balanced directed communication topologies with identical fading networks and undirected communications topologies with non identical fading networks respectively for scalar systems the sufficient condition is shown to be necessary the results indicate that the effect of fading networks on consensusability is determined by the statistics of channel fading finally simulations are conducted to validate the theoretical results

the classical collocation method for singular integral equations first of all a method of collocation which we call classical collocation is described for the approximate solution of complete singular integral equations with cauchy kernel taken over the arc 1 1 secondly we demonstrate that under reasonable conditions the approximate solutions converge to the solution of the original equation

submodularity and greedy algorithms in sensor scheduling for linear dynamical systems this paper focuses on sensor scheduling for state estimation which consists of a network of noisy sensors and a discrete time linear system with process noise as an energy constraint only a subset of sensors can take a measurement at each time step these measurements are fused into a common state estimate using a kalman filter and the goal is to schedule the sensors to minimize the estimation error at a terminal time a simple approach is to greedily choose sensors at each time step to minimize the estimation error at the next time step recent work has shown that this greedy algorithm outperforms other well known approaches results have been established to show that the estimation error is a submodular function of the sensor schedule submodular functions have a diminishing returns property that ensures the greedy algorithm yields near optimal performance as a negative result we show that most commonly used estimation error metrics are not in general submodular functions this disproves an established result we then provide sufficient conditions on the system for which the estimation error is a submodular function of the sensor schedule and thus the greedy algorithm yields performance guarantees

on energy to peak filtering for nonuniformly sampled nonlinear systems a markovian jump system approach this paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by takagi sugeno t s fuzzy systems the sampling periods of the measurements are time varying and the nonuniform observations of the outputs are modeled by a homogenous markov chain a mode dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs the nonlinear systems are discretized with the fast sampling period by using an augmentation technique the corresponding stochastic estimation error system is obtained by studying the stochastic stability and the energy to peak performance of the estimation error system we derive the linear matrix inequality based sufficient conditions the parameters of the mode dependent estimator can be calculated by using the proposed iterative algorithm two examples are used to demonstrate the design procedure and the efficacy of the proposed design method

a collocation method for the generalized airfoil equation for an airfoil with a flap we are concerned with the numerical solution of the generalized airfoil equation for an airfoil with a flap by means of global algebraic polynomial approximants this problem has been considered in a recent paper by monegato and sloan siam j numer anal 34 1997 pp 2288 2305 where the authors proved the stability and convergence of a galerkin method based on high order polynomials they also presented very promising numerical results for the corresponding collocation method but left the theoretical results of stability and convergence as an open problem we have succeeded in proving the stability and convergence properties of this collocation method by slightly modifying it in the neighborhood of the flap the rate of convergence we have derived for our collocation method is very similar to that of the above galerkin method

error bounds for gauss kronrod quadrature formulae of analytic functions we consider the gauss kronrod quadrature formula for the legendre weight function on certain spaces of analytic functions its error term is a continuous linear functional we derive easy to compute estimates for the norm of the error functional which lead to bounds for the error functional itself the efficiency of these bounds is illustrated with some numerical examples

an algebraic study of gauss kronrod quadrature formulae for jacobi weight functions we study gauss kronrod quadrature formulae for the jacobi weight function w d t 1 t a 1 t and its special case a f a of the gegenbauer weight function we are interested in delineating regions in the a f plane resp intervals in a for which the quadrature rule has a the interlacing property i e the gauss nodes and the kronrod nodes interlace b all nodes contained in 1 1 c all weights positive d only real nodes not necessarily satisfying a and or b we determine the respective regions numerically for n 1 1 20 4 40 in the gegenbauer case and for n 1 1 10 in the jacobi case where n is the number of gauss nodes algebraic criteria in particular the vanishing of appropriate resultants and discriminants are used to determine the boundaries of the regions identifying properties a and d the regions for properties b and c are found more directly a number of conjectures are suggested by the numerical results finally the gauss kronrod formula for the weight w al 2 is obtained from the one for the weight w ca and similarly the gauss kronrod formula with an odd number of gauss nodes for the weight function w t itlv 1 t2 c is derived from the gauss kronrod formula for the weight w a l y 2

state estimation over a lossy network in spatially distributed cyber physical systems in this paper we analyze stochastic stability of kalman filter kf based state estimation over a lossy network in spatially distributed cyber physical systems we study a practical scenario in which sensors are arbitrarily deployed over an area to jointly sense the state of underlying physical system the sensors directly communicate observations to a central state estimation unit over a network resulting in random loss in measurements and partial observation updates in kf we analyzed stability of state estimation process in this scenario by establishing conditions under which steady state error covariance matrix is bounded in contrast to previous work on gathered measurement scenario with intermittent loss we considered a dispersed measurement scenario and established bounds on critical probability of receiving measurements over individual sensor communication links our analysis later exploited possible existence of spatial correlation among states in the filtering process and characterized its impact on the bounds we further extended our analysis by considering correlated loss among sensor measurements the overall analysis quantifies the trade off between state estimation accuracy and the quality of underlying communication network in addition our analysis demonstrates that by exploiting spatial correlation among states a higher degree of information loss or lower network quality can be tolerated to achieve a certain estimation accuracy since estimation accuracy directly impacts the stability of control operation this analysis is critical for architecture and network planing design of cyber physical systems

numerical solution of the generalized airfoil equation for an airfoil with a flap in this paper we are concerned with the generalized airfoil equation which governs the pressure across an airfoil oscillating in a wind tunnel in particular we examine the case of an airfoil which contains a flap so that the input function has a simple jump at a point x0 1 x0 1 this generates a logarithmic singularity in the solution u at the same point x0 and considerably complicates the problem of the numerical approximation of u by introducing a nonlinear transformation of the independent variable in the integral equation we improve the behavior of the unknown function u through incorporation of the jacobian of the transformation the price is that the kernel of the new integral equation becomes more complicated nevertheless we are able to show that a galerkin method based on high order polynomials is both stable and convergent we also present some promising numerical results for the corresponding collocation method for which we have not succeeded in proving stability and convergence although those results seem to suggest that it is indeed stable and has a rate of convergence similar to that we have derived for the galerkin method

rates of convergence for the method of classical collocation for solving singular integral equations the method of classical collocation for the approximate solution of the complete singular integral equation with cauchy kernel taken over the arc 1 1 has been described previously by the author in siam j numer anal 19 1982 pp 816 832 in this paper we consider in greater detail the urates of convergence for both discrete and global errors in the approximate solution of this equation this analysis gives a better convergence theorem than that given in the earlier paper the paper concludes with a discussion on the necessity of a particular condition for discrete convergence

distributing the kalman filter for large scale systems this paper presents a distributed kalman filter to estimate the state of a sparsely connected large scale n dimensional dynamical system monitored by a network of n sensors local kalman filters are implemented on nl dimensional subsystems nl lt n obtained by spatially decomposing the large scale system the distributed kalman filter is optimal under an lth order gauss markov approximation to the centralized filter we quantify the information loss due to this lth order approximation by the divergence which decreases as l increases the order of the approximation l leads to a bound on the dimension of the subsystems hence providing a criterion for subsystem selection the approximated centralized riccati and lyapunov equations are computed iteratively with only local communication and low order computation by a distributed iterate collapse inversion dici algorithm we fuse the observations that are common among the local kalman filters using bipartite fusion graphs and consensus averaging algorithms the proposed algorithm achieves full distribution of the kalman filter nowhere in the network storage communication or computation of n dimensional vectors and matrices is required only nl lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors in other words knowledge of the state is itself distributed

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

stability conditions for multi sensor state estimation over a lossy network this paper studies a networked state estimation problem for a spatially large linear system with a distributed array of sensors each of which offers partial state measurements a lossy communication network is used to transmit the sensor measurements to a central estimator where the minimum mean square error mmse state estimate is computed under a markovian packet loss model we provide necessary and sufficient conditions for the stability of the estimator for any diagonalizable system in the sense that the mean of the state estimation error covariance matrix is uniformly bounded in particular the stability conditions for the second order systems with an i i d packet loss model are explicitly expressed as simple inequalities in terms of the largest open loop pole and the packet loss rate

detection thresholds for tracking in clutter a connection between estimation and signal processing in the kalman bucy filter and other trackers the dependence of tracking performance upon the quality of the measurement data is well understood in terms of the measurement noise covariance matrix which specifies the uncertainty in the values of the measurement inputs the measurement noise and process noise covariances determine via the riccati equation the state estimation error covariance when the origin of the measurements is also uncertain one has the widely studied problem of data association or data correlation and tracking performance depends critically on signal processing parameters primarily the probabilities of detection and false alarm in this paper we derive a modified riccati equation that quantifies approximately the dependence of the state error covariance on these parameters we also show how to use a receiver operating characteristic roc curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors the approach presented in this paper provides a feedback mechanism from the information processing tracking subsystem to the signal processing subsystem so as to optimize the overall performance in clutter

a numerical method for the generalized airfoil equation based on the de la vallee poussin interpolation the authors consider the generalized airfoil equation in some weighted holder zygmund spaces with uniform norms using a projection method based on the de la vallee poussin interpolation they reproduce the estimates of the l2 case by cutting off the typical extra log m factor which seemed inevitable to have dealing with the uniform norm because of the unboundedness of the lebesgue constants the better convergence estimates do not produce a greater computational effort the proposed numerical procedure leads to solve a simple tridiagonal linear system the condition number of which tends to a finite limit as the dimension of the system tends to infinity whatever natural matrix norm is considered several numerical tests are given

a note on peano constants of gauss kronrod quadrature schemes abstract for the error r 2 n 1 gk of the gauss kronrod quadrature formula q 2 n 1 gk we prove the precise asymptotic value of the low order peano constants c s r 2 n 1 gk where s is fixed for increasing n the result is applied for comparisons of the gauss kronrod formula q 2 n 1 gk with the gauss formula q n g and with the gauss formula q 2 n 1 g with respect to this often used quality measure

condition numbers for singular integral equations in weighted l 2 spaces the convergence and stability of a discrete collocation method for cauchy singular integral equations in some weighted besov spaces are studied this numerical method results in solving a linear system in order to determine the unknown coefficients of the approximate solution the author proves that this linear system is well conditioned

on a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage in this note we consider the following problem suppose a set of sensors is jointly trying to estimate a process one sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors what is the sensor schedule that results in the minimum error covariance we describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable the problem described above comes up in many domains out of which we discuss two in the sensor selection problem there are multiple sensors that cannot operate simultaneously e g sonars in the same frequency band thus measurements need to be scheduled in the sensor coverage problem a geographical area needs to be covered by mobile sensors each with limited range thus from every position the sensors obtain a different view point of the area and the sensors need to optimize their trajectories the algorithm is applied to these problems and illustrated through simple examples

uniform convergence of a fast algorithm for cauchy singular integral equations abstract error estimates for a fast algorithm applied to a cauchy singular integral equation are proved in weighted uniform norms this algorithm is essentially based on the application of discrete sine transformations numerical results are presented

galerkin solution of a singular integral equation with constant coefficients galerkin methods are used to approximate the singular integral equation email protected x email protected 1 email protected t email protected 1 1k t x f t dt f x 10 are constants in this case f is decomposed as f x 1 x a 1 x bu x where email protected 0 0 is a small enough constant

minimax estimation with intermittent observations this paper considers a problem of minimax or h state estimation with intermittent observations in this setting the disturbance in the dynamical system and the sensor noise are controlled by adversaries and the estimator receives the sensor measurements only sporadically with the availability governed by an independent and identically distributed bernoulli process we cast this problem within the framework of stochastic zero sum dynamic games we first obtain a corresponding stochastic minimax state estimator smse and an associated generalized stochastic riccati equation gsre whose evolutions depend on two parameters one that governs the random measurement arrivals and another one that quantifies the level of h disturbance attenuation we then analyze the asymptotic behavior of the sequence generated by the gsre in the expectation sense and its weak convergence specifically we obtain threshold type conditions above which the sequence generated by the gsre can be bounded both below and above in the expectation sense moreover we show that under some conditions the norm of the sequence generated by the gsre converges weakly to a unique stationary distribution finally we prove that when the disturbance attenuation parameter goes to infinity our asymptotic results are equivalent to the corresponding results from the literature on kalman filtering with intermittent observations we provide simulations to illustrate the results

team optimal control of stochastically switched systems with local parameter knowledge this paper considers the optimal decentralized control of linear systems with stochastically switched cost and system matrices depending on local parameters two types of dynamic switched problems are considered with partially nested and one step delayed sharing information structures for the former case parameters and measurements follow a partially nested structure with the parameters possibly being correlated across all stages for the latter case parameters are assumed to be markov processes with their values along with measurements available instantaneously to local controllers but with a one time step delay to others the solution to both these problems rely on the optimal solution to a static one stage stochastic parameter problem with local type dependent gaussian measurements and for this purpose the static quadratic team problem is examined in some generality using an operator theoretic framework it is shown that the sequential update scheme always converges to the team optimal strategy for general static quadratic team setups this when applied to the static stochastic parameter problem yields the team optimal strategy the corresponding strategy is affine in the measurements with the parameter dependent coefficients obtained by solving a set of linear equations these equations are immediately solvable when the total number of parameter values is finite however for the case of infinite parameter values the update scheme also provides a mechanism to determine an approximation to the team optimal strategy

lqg control for mimo systems over multiple erasure channels with perfect acknowledgment this technical note concerns control applications over lossy data networks sensor data is transmitted to an estimation control unit over a network and control commands are issued to subsystems over the same network sensor and control packets may be randomly lost according to a bernoulli process in this context the discrete time linear quadratic gaussian lqg optimal control problem is considered in schenato a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively here a nontrivial generalization for mimo systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet no aggregation in such a framework it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver moreover the optimal lqg control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels such a dependence is not present in the single channel case considered in mean square in the infinite horizon case stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities lmis

probability of error analysis for hidden markov model filtering with random packet loss this paper studies the probability of error for maximum a posteriori map estimation of hidden markov models where measurements can be either lost or received according to another markov process analytical expressions for the error probabilities are derived for the noiseless and noisy cases some relationships between the error probability and the parameters of the loss process are demonstrated via both analysis and numerical results in the high signal to noise ratio snr regime approximate expressions which can be more easily computed than the exact analytical form for the noisy case are presented

a fast algorithm for solving the generalized airfoil equation abstract the present paper is devoted to the quadrature method for cauchy type singular integral equations on 1 1 with an additional logarithmic singularity of the kernel an algorithm being based on this method is given whose realization only requires a computational work of o n ln n operations in order to determine n unknown coefficients of the approximate solution furthermore in a scale of weighted sobolev like spaces on 1 1 having analogous properties like the classical sobolev spaces on the unit circle the order of convergence is optimal

a new h_ bm infty stabilization criterion for networked control systems this note is concerned with robust hinfin control of linear networked control systems with time varying network induced delay and data packet dropout a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the time varying network induced delay is proposed to drive a new delay dependent hinfin stabilization criterion the criterion is formulated in the form of a non convex matrix inequality of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequalities in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no slack variable is introduced finally two numerical examples are given to show the effectiveness of the proposed design method

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

error bounds for rational quadrature formulae of analytic functions we study the error of rational quadrature rules when functions which are analytic on a neighborhood of the set of integration are considered a computable upper bound of the error is presented which is valid for a broad range of rational quadrature formulae and a comparison is made with the exact error for a number of numerical examples

on kalman filtering for detectable systems with intermittent observations we consider the problem of kalman filtering when observations are available according to a bernoulli process it is known that there exists a critical probability pc such that if measurements are available with probability greater than pc then the expected prediction covariance is bounded for all initial conditions otherwise it is unbounded for some initial conditions we show that when the system observation matrix restricted to the observable subspace is invertible the known lower bound on pc is in fact the exact critical probability this result is based on a novel decomposition of positive semidefinite matrices