robust kalman bucy filter development of a robust estimator for uncertain stochastic systems under persistent excitation is presented the given continuous time stochastic formulation assumes norm bounded parametric uncertainties and excitations when there are no system uncertainties the performance of the proposed robust estimator is similar to that of the kalman bucy filter and the proposed approach asymptotically recovers the desired optimal performance in the presence of uncertainties and or persistent excitation

the existence of asymptotically stable solutions for a nonlinear functional integral equation with values in a general banach space abstract motivated by the recent known results about the solvability and existence of asymptotically stable solutions for nonlinear functional integral equations in spaces of functions defined on unbounded intervals with values in the n dimensional real space we establish asymptotically stable solutions for a nonlinear functional integral equation in the space of all continuous functions on r with values in a general banach space via a fixed point theorem of krasnosel skii type in order to illustrate the result obtained here an example is given

a polynomial approach to robust estimation of uncertain discrete time systems the robust estimation problem for uncertain discrete time systems is treated in this paper considering parametric uncertainties in the polynomial framework the estimator is the minimiser of a cost function written in a epsilon contaminated form uncertainties are not formally modelled it is shown that in the present context the proposed approach can be connected to stochastic modelling of uncertainties the optimal robust estimator is obtained by computing a spectral factorisation and by solving a single diophantine equation an example shows the efficiency of the proposed method

an explicit form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids this paper presents an analytical approach to solve the plane elasticity and thermoelasticity problems for inhomogeneous orthotropic planes half planes and strips solution of the problems is reduced to the governing volterra integral equation formulated for the key function and accompanied by the corresponding integral conditions by making use of the resolvent kernel technique the governing equation is solved and the solution to the original problem is presented in explicit form

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

model quality evaluation in h sub 2 identification model quality evaluation in set membership identification is investigated in the recent literature two main approaches have been used to investigate this problem based on the concepts of n width and of radius of information in this paper it is shown that the n width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements upper and lower bounds of the conditional radius of information are derived for the h sub 2 identification of exponentially stable systems using approximating n dimensional models linear in the parameters in the presence of power bounded measurement errors the derived bounds are shown to be convergent to the radius for a large number of data and model dimensions moreover a formula for computing the worst case identification error for any linear algorithm is given in particular it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension peaking effect an almost optimal linear algorithm is presented that is not affected by this peaking effect and indeed is asymptotically optimal

control oriented system identification a worst case deterministic approach in h sub infinity the authors formulate and solve two related control oriented system identification problems for stable linear shift invariant distributed parameter plants in each of these problems the assumed a priori information is minimal consisting only of a lower bound on the relative stability of the plant an upper bound on a certain gain associated with the plant and an upper bound on the noise level the first of these problems involves identification of a point sample of the plant frequency response from a noisy finite output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest this problem leads naturally to the second problem which involves identification of the plant transfer function in h sub infinity from a finite number of noisy point samples of the plant frequency response concrete plans for identification algorithms are provided for each of these two problems

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

two dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties abstract a multi layered model for frictionless contact analysis of functionally graded materials fgms with arbitrarily varying elastic modulus under plane strain state deformation has been developed based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves the fgm is divided into several sub layers and in each sub layers the shear modulus is assumed to be linear function while the poisson s ratio is assumed to be a constant with the model the frictionless contact problem of a functionally graded coated half space is investigated by using the transfer matrix method and fourier integral transform technique the problem is reduced to a cauchy singular integral equation the contact pressure contact region and indentation are calculated for various indenters by solving the equations numerically

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

conditional central algorithms for worst case set membership identification and filtering this paper deals with conditional central estimators in a set membership setting the role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering in contexts in which disturbances are described through norm bounds are reducible to the computation of conditional central algorithms the conditional chebyshev center problem is solved for the case when energy norm bounded disturbances are considered a closed form solution is obtained by finding the unique real root of a polynomial equation in a semi infinite interval

structure identification for gene regulatory networks via linearization and robust state estimation abstract inferring causal relationships among cellular components is one of the fundamental problems in understanding biological behaviours the well known extended kalman filter ekf has been proved to be a useful tool in simultaneously estimating both structure and actual gene expression levels of a gene regulatory network grn first order approximations however unavoidably result in modelling errors but the ekf based method does not take either unmodelled dynamics or parametric uncertainties into account which makes its estimation performances not very satisfactory to overcome these problems a sensitivity penalization based robust state estimator is adopted in this paper for revealing the structure of a grn based on the specific structure of the estimation problem it has been proved that under some weak conditions both the ekf based method and the method suggested in this paper provide a consistent estimate but the suggested method has a faster convergence speed compared with both the ekf and the unscented kalman filter ukf based methods simulation results and real data based estimations consistently show that both convergence speed and parametric estimation accuracy can be appreciably improved these lead to significant reductions in both false positive errors and false negative errors and may imply helpfulness of the suggested method in better understanding the structure and dynamics of actual grns

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

hukuhara kneser property for a nonlinear dirichlet problem abstract the purpose of this paper is to show that the set of solutions of a nonlinear dirichlet problem satisfies the usual hukahara kneser property for ordinary differential equations

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

modeling method for a crack problem of functionally graded materials with arbitrary properties piecewise exponential model abstract a new model piecewise exponential model pe model is developed to investigate the crack problem of the functionally graded materials fgms with arbitrary properties in the pe model the functionally graded material is divided into some nonhomogeneous layers along the gradient direction of the properties with each layer s properties varying exponentially by this way the real material properties can be approached by a series of exponential functions since the real material properties are used on both surfaces of each nonhomogeneous layer the nature of continuously varying properties of fgms can be approached accurately the influences of the local nonhomogeneity on the crack tip fields can be fully considered by using the new model the fracture problem of a functionally graded strip with arbitrary properties and a crack vertical to the free surfaces is studied the integral transform method the theory of residues and the theory of singular integral equation are applied some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding stress intensity factors sifs are presented it is shown that the pe mode is effective for investigating the crack problems of the fgms with arbitrary properties

remark on krasnoselskii s fixed point theorem abstract a well known result due to krasnoselskii ensures the existence of a fixed point for an operator k a b which is defined on a non empty bounded closed convex subset s of a banach space x where i a is a contraction ii b is a compact operator and iii a s b s s in the present note an easy sufficient condition for fulfilling iii in the case of a locally convex space is given an application to the existence of solutions of a nonlinear integral equation illustrates this result

worst case conditional system identification in a general class of norms we consider optimality of identification of linear systems by reduced complexity models which belong to a subspace of possibly low dimension of a system space identification is based on the a priori knowledge that an unknown system belongs to a certain class and a posteriori information given by its nonexact output measurements measurement errors are assumed unknown but norm bounded the analysis is not restricted to specific norms in system and measurement spaces generic norms are considered we derive tight upper and lower bounds on the minimal local worst case identification error and define an algorithm whose error is within the derived bounds the results are specified for product norms which include l p norms email protected email protected in the system space the bounds are expressed in terms of the model error which measures a quality of representing systems by a model subspace and the diameter of information reflecting the size of a model uncertainty set the model error is further splitted into truncated model error and residual error which controls tail properties of the unknown system examples of model and input selection in some special cases are given and numerical experiments showing the behavior of the estimates reported

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter

optimal robust filtering for systems subject to uncertainties in this paper we deal with an optimal filtering problem for uncertain discrete time systems parametric uncertainties of the underlying model are assumed to be norm bounded we propose an approach based on regularization and penalty function to solve this problem the optimal robust filter with the respective recursive riccati equation is written through unified frameworks defined in terms of matrix blocks these frameworks do not depend on any auxiliary parameters to be tuned simulation results show the effectiveness of the robust filter proposed

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

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half space abstract this paper addresses an axisymmetric quasi static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate to solve the formulated boundary value problem the technique of hankel s integral transformation is used using the bilateral asymptotic method an approximate analytical numerical solution is constructed for the heat flux boundary displacements of the half space and contact stress under the punch numerical implementation is performed for different dependences of the material properties on the depth of the half space

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

periodically time varying cal h _ infty memory filter design for discrete time lti systems with polytopic uncertainty this technical note focuses on the development of a general periodically time varying memory filter ptvmf to improve the robust h filtering performance for discrete time linear time invariant lti systems with polytopic parameter uncertainties a sufficient condition to design the h ptvmf is given in terms of convex optimizations expressed as linear matrix inequalities lmis finally examples demonstrate its potential less conservatism

analytical solution of the spherical indentation problem for a half space with gradients with the depth elastic properties the contact problem for the impression of spherical indenter into a non homogeneous both layered and functionally graded elastic half space is considered analytical methods for solving this problem have been developed it is assumed that the lame coefficients vary arbitrarily with the half space depth the problem is reduced to dual integral equations the developed methods make it possible to find the analytical asymptotically exact problem solution suitable for a pc the influence of the lame coefficients variation upon the contact stresses and size of the contact zone with different radius of indenter as well as values of the impressing forces are studied the effect of the non homogeneity is examined the developed method allows to construct analytical solutions with presupposed accuracy and gives the opportunity to do multiparametric and qualitative investigations of the problem with minimal computation time expenditure

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

generalizations of the krasnoselskii fixed point theorem abstract we obtain new generalized forms of the krasnoselskii theorem on fixed points for a sum of two operators and show that our new results encompass a number of previously known generalizations of the theorem

the hukuhara kneser property for quasilinear parabolic equations on etudie le probleme de dirichlet quasilineaire u t a x t u lu f x t u x t q t u x t t t ou a est une matrice diagonale et l un operateur elliptique on demontre un resultat d invariance pour un ensemble convexe borne d la limitation de l ensemble d donne une borne a priori que l on utilise avec une application de la theorie du degre de leray schauder et un theoreme de structure pour montrer l existence de solutions et la propriete de hukuhara kneser

event based state estimation with time synchronous updates to reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than at each synchronous sample instant however this complicates estimation problems considerably especially in the situation when no measurement is received anymore the goal of this paper is therefore to develop a state estimator that can successfully cope with event based measurements and attains an asymptotically bounded error covariance matrix to that extent a general mathematical description of event sampling is proposed this description is used to set up a state estimator with a hybrid update i e when an event occurs the estimated state is updated using the measurement while at synchronous instants the update is based on knowledge that the sensor value lies within a bounded subset of the measurement space furthermore to minimize computational complexity of the estimator the algorithm is implemented using a sum of gaussians approach the benefits of this implementation are demonstrated by an illustrative example of state estimation with event sampling

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

on the controllability and observability of networked dynamic systems some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant lti dynamics the topology of this system is fixed but arbitrary and every subsystem is permitted to have different dynamics these conditions essentially depend only on transmission zeros of every subsystem and the subsystem connection matrix which makes them attractive in the analysis and synthesis of a large scale networked system as an application these conditions are utilized to characterize systems whose steady estimation accuracy with the distributed predictor of zhou 2013 is equal to that of the lumped kalman filter it has been made clear that to guarantee this equivalence the steady update gain matrix of the kalman filter must be block diagonal

regularized robust filters for time varying uncertain discrete time systems this note develops robust filters for time varying uncertain discrete time systems the developed filters are based on a data regularization solution and they enforce a minimum state error variance property simulation results confirm their superior performance over other robust filter designs

axisymmetric frictionless contact of a functionally graded piezoelectric layered half space under a conducting punch abstract this paper studies the axisymmetric frictionless contact of a functionally graded piezoelectric layered half space subjected to three typical rigid punches i e flat circular punch spherical punch and conical punch the punch is assumed as a perfect conductor with a constant electric potential the electro mechanical properties of the functionally graded piezoelectric materials fgpms vary exponentially along the thickness direction by employing the hankel integral transform technique the problem is reduced to a set of singular integral equations of the first kind these equations are then discretized and solved numerically to determine the unknown normal contact pressure and electric charge the effects of the gradient index and punch geometry on the surface electro mechanical contact behaviors are discussed in detail

model quality evaluation in set membership identification abstract identification from corrupted input output measurements of systems that do not necessarily belong to the model class used is investigated this leads to a nonstandard set membership sm identification problem the goodness of different model classes is measured by the conditional radius of information a generalization of the radius in standard sm identification theory giving a measure of the minimal worst case modeling error upper and lower bounds on the radius are derived for linearly parameterized model classes specific formulas for the upper and lower bounds are given for the case of h 2 identification of exponentially stable systems in the presence of powerbounded noise the bounds are shown to coincide with the conditional radius when the model space dimension is equal to the number of output measurements an almost optimal identification algorithm is derived giving identification error within the range of the derived bounds

robust filtering for linear time invariant continuous systems the problem of robust filtering for linear time invariant lti continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations and then in the state space domain the basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv contaminated model the general solution to the problem is given in the transfer function representation while in the polynomial framework the causal estimator is obtained by means of a spectral factorization and a diophantine equation the state space realization of the causal estimator is discussed examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty

approximate optimal periodic scheduling of multiple sensors with constraints a constrained periodic multiple sensor scheduling problem is considered in this paper for each sensor constraints on dwell time and activation times are imposed at each time instant only one sensor can update its measurement with the estimator and the objective is to minimize the average state estimation error an approximation framework is proposed to calculate the objective function which transforms the original scheduling problem into an approximate optimal scheduling problem aosp an upper bound on the approximation error is presented to evaluate the performance of the framework to solve the aosp a necessary condition is first proposed on the optimal schedules when no constraints on activation times exist a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity when activation time constraints exist we show that the aosps can be solved by solving traveling salesman problems examples are provided to illustrate the proposed results

the hukuhara kneser property for a nonlinear integral equation abstract applying a structure theorem of krasnosel skii and perov we show that the solution set of a nonlinear integral equation satisfies the classical hukuhara kneser property

h sub spl infin identification and model quality evaluation set membership h sub spl infin identification is investigated using time domain data and mixed parametric and nonparametric models as well as supposing power bounded measurement errors the problem of optimally estimating the unknown parameters and evaluating the minimal worst case identification error called radius of information is solved for classes of models affine in the parameters the radius of information is obtained as function of the h sub spl infin norm of the unmodeled dynamics a method is given for estimating this norm from the available data and some general a priori information on the unmodeled dynamics thus allowing the actual evaluation of the radius of information the radius represents a measure of the predictive ability of the considered class of models and it is then used for comparing the quality of different classes of models and for the order selection of their parametric part the effectiveness of the proposed procedure is tested on some numerical examples and compared with standard statistical criteria for model order selection

the hukuhara kneser property for parabolic systems with nonlinear boundary conditions the domain of the problem is a cylinder qt r x 0 7 1 the parabolic operator l is the same for each component of u and the nonlinearity f may be strongly coupled the purpose of this paper is to develop some of the fundamental theory for this problem we allow conditions general enough for nonunique solutions and start by giving a set of conditions that requires all the solutions to remain in an invariant region using these conditions we show the existence of at least one such solution and that the problem satisfies the hukuhara kneser property these results are thus extensions of berbernes and schmitt 5 to nonlinear boundary conditions a set d c rm is said to be invariant for the above problem if w g c d implies u q c d let n u denote an outer normal at a point u in the boundary of a nonempty open convex set d in theorem 3 1 the maximum principle is used to show that if the strong tangent inequality

optimal induced norm and set membership state smoothing and filtering for linear systems with bounded disturbances in this paper a unified framework founded on information based complexity is introduced to study set membership and optimal induced norm state estimation problems for linear systems subject to norm bounded process noise and measurement errors the proposed approach leads to a clean geometric picture of the problem allowing for a straightforward derivation of several existing results moreover it permits to tackle new estimation problems in which both induced norm optimization and consistency of the estimate with the noise bound are required