robust state estimation and unknown inputs reconstruction for a class of nonlinear systems multiobjective approach we consider a novel method to design h h observers for a class of uncertain nonlinear systems subject to unknown inputs first the main system dynamics are rewritten as an augmented system with state vector including both the state vector of the main system and the unknown inputs then we design a h h reduced order observer to estimate both state variables and unknown inputs simultaneously based on a lyapunov functional we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality to facilitate the observer design the achieved condition is formulated in terms of a set of linear matrix inequalities lmi by extending the proposed method to a multiobjective optimization problem the maximum bound of the uncertainty and the minimum value of the disturbance attenuation level are found finally the proposed observer is illustrated with an example

localization of laplacian eigenfunctions in circular spherical and elliptical domains we consider laplacian eigenfunctions in circular spherical and elliptical domains in order to discuss three kinds of high frequency localization whispering gallery modes bouncing ball modes and focusing modes although the existence of these modes has been known for a class of convex domains the separation of variables for circular spherical and elliptical domains helps us to better understand the mechanism of localization i e how an eigenfunction is getting distributed in a small region of the domain and decays rapidly outside this region using the properties of bessel and mathieu functions we derive inequalities which imply and clearly illustrate localization moreover we provide an example of a nonconvex domain an elliptical annulus for which the high frequency localized modes are still present at the same time we show that there is no localization in most rectangle like domains this observation leads us to formulate an open problem of localization in polygonal domains and more ge

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

fixed point smoothing of scalar diffusions i an asymptotically optimal smoother the problem of nonlinear estimation of the initial value of a given diffusion process given its noisy measurements as a function of time is the fixed point smoothing problem a zakai type equation is derived for the time evolution of an unnormalized version of the conditional probability density function cpdf of the initial value given the measurements up to time t the equation for the epdf of the initial value is coupled to a zakai equation for the filtering problem with a singular initial condition an asymptotic solution to both equations is constructed under the assumption of small measurements noise and small initial error from this solution an asymptotically optimal four dimensional fixed point smoother is obtained the leading order approximation to the optimal fixed point smoother turns out to be the four dimensional extended kalman smoother if the initial error is not small the error of the optimal smoother can be expected to equal that of the optimal filter as in the linear case

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

solution to sylvester equation associated to linear descriptor systems abstract this paper presents the solution of the constrained sylvester equation associated to linear descriptor systems this problem has been recently studied in castelan and da silva on the solution of a sylvester equation appearing in descriptor systems control theory systems control lett 54 2005 109 117 where sufficient conditions for the existence of the solution are given in the present paper a simple and direct method is developed to solve this problem this method shows that the conditions given in castelan and da silva on the solution of a sylvester equation appearing in descriptor systems control theory systems control lett 54 2005 109 117 are necessary and sufficient

numerical solution of an inverse problem of imaging of antipersonnel land mines by the globally convergent convexification algorithm the globally convergent convexification algorithm has been successfully applied to some coefficient inverse problems in this paper a new numerical implementation of this algorithm is presented and applied to a model problem of imaging of antipersonnel plastic land mines using electric signal propagation a smoothing technique is introduced to smooth out the spikes on the image for the reconstructed unknown coefficient some artifacts of resulting images are explained based on numerical evidences with the new implementation the convexification algorithm is computationally efficient and is feasible to be applied in real time to detect and image antipersonnel land mines in the field

applicability of music type imaging in two dimensional electromagnetic inverse problems the behavior of the multiple signal classification music algorithm is investigated when used to locate small dielectric cylinders of specific characteristics in noise free and noisy scenarios using the te incidence we have made three observations regarding the performance of music in the two dimensional te scenario which reveal the significance of the choice of signal subspace while employing music and the shortcoming of traditional music when used to detect degenerate cylinders which might be so due to the material or geometry of the cylinders the detailed analysis of the sources induced on a cylinder and their linear dependency on each other gives a distinct insight into the use of music algorithm to locate it a non iterative retrieval algorithm is provided that is based on the least squares method which retrieves the electric and magnetic polarization tensors of the small cylinders the algorithm proposed here is mathematically a simple and direct representation of the physical principles and is applicable to degenerate cylinders as well

music imaging and electromagnetic inverse scattering of multiple scattering small anisotropic spheres the foldy lax equation is used to derive a multiple scattering model for the multiple scattering small anisotropic spheres by this model if the number of the non zero singular values of the multistatic response msr matrix is smaller than the number of the antennas the range space of the msr matrix is found to be spanned by the background green s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer which indicates that the multiple signal classification music method could be implemented to obtain the locations of the scatterers after estimating the positions of the scatterers a non iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer two numerical simulations show that the music method and the non iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple scattering small anisotropic spheres such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres

direct sampling method for retrieving small perfectly conducting cracks abstract in this paper direct sampling method is considered for determining the location of a set of small linear perfectly conducting cracks from the collected far field data corresponding to an incident field to show the feasibility of the direct sampling method this study proves that the indicator function of the direct sampling method can be represented by the bessel function of order zero and the crack lengths the results of the numerical simulations are shown to support the fact that the imaging performance is highly dependent on the crack lengths to explain the fact that the imaging performance is highly dependent on the rotation of the cracks the direct sampling method is further analyzed by establishing a representation using bessel functions of orders zero and one based on the derived representation of indicator function we design improved direct sampling methods by applying incident fields with multiple directions and multiple frequencies corresponding analysis of indicator functions and simulation results are shown for demonstrating the effectiveness and improvements

music type electromagnetic imaging of a collection of small three dimensional inclusions in this paper we consider the localization of a collection of small three dimensional bounded homogeneous inclusions via time harmonic electromagnetic means typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization s at some distance from the collection possibly also lying in the far field the inclusions somewhat apart or closely spaced are buried within a homogeneous medium and are of arbitrary contrast of permittivity conductivity and permeability vis ag vis this embedding medium the problem is formulated as an inverse scattering problem for the full maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix no specific application is studied at this stage but characterization of obstacles in subsoils nondestructive evaluation of man made structures and medical imaging are primary fields of application envisaged the proposed approach uses a music multiple signal classification type algorithm and it yields fast numbering accurate localization and estimates of the electromagnetic and geometric parameters polarization tensors of the inclusions the mathematical machinery is detailed first some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes for the latter known results are retrieved then the viability of this algorithm which would be easily extended to planarly layered environments by introduction of their green s functions is documented by a variety of numerical results from synthetic noiseless and severely noisy field data

observers and observer based control for descriptor systems revisited this technical note is devoted to the observers and observer based control for linear descriptor systems first the complete proof of necessary and sufficient conditions for the existence of luenberger observers for an arbitrary order is given then the existence conditions for the controller based on these observers are presented in the lmi formulation the design approach is simple and based on the new study of the constrained generalized sylvester equations it unifies all the observers and observer based controllers of different orders a numerical example is presented to illustrate our approach

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

multi frequency topological derivative for approximate shape acquisition of curve like thin electromagnetic inhomogeneities abstract in this paper we investigate a non iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and or magnetic permeability differ from those in the embedding homogeneous space the main objective is the imaging of crack like thin inclusions but the algorithm can be applied to arbitrarily shaped inclusions for this purpose we apply multiple time harmonic frequencies and normalize the topological derivative imaging function by its maximum value in order to verify its validity we apply it for the imaging of two dimensional crack like thin electromagnetic inhomogeneities completely hidden in a homogeneous material corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm

topological derivative strategy for one step iteration imaging of arbitrary shaped thin curve like electromagnetic inclusions in this manuscript a fast imaging of thin curve like electromagnetic inclusions completely hidden in the homogeneous domain with smooth boundaries is considered by creating an electromagnetic inclusion of a small diameter and applying the asymptotic expansion formula in the existence of such an inclusion the topological derivative is successfully derived based on this derivative a one step iteration imaging algorithm is designed by solving an adjoint problem various numerical experiments of single and multiple inclusions demonstrate the viability and limitation of the designed algorithm

enhanced multilevel linear sampling methods for inverse scattering problems we develop two enhanced techniques for the multilevel linear sampling method mlsm proposed in 32 for inverse scattering problems under some practical situations the mlsm suffers certain undesirable breakage cells problem we propose to avoid the curse of breakage cells by incorporating expanding and searching techniques the new techniques are shown to significantly improve the robustness of the mlsm and meanwhile they possess the same optimal computational complexity as the mlsm numerical experiments are presented to illustrate the promising features of the enhanced mlsms

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

focusing and imaging using eigenfunctions of the scattering operator an inverse scattering method that uses eigenfunctions of the scattering operator is presented this approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media scattered acoustic fields are described using a compact normal operator the eigenfunctions of this operator are shown to correspond to the far field patterns of source distributions that are directly proportional to the position dependent contrast of a scattering object conversely the eigenfunctions of the scattering operator specify incident wave patterns that focus on these effective source distributions these focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions a regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities the corresponding linearized problem is solved analytically resulting in a simple formula for the low pass filtered scattering potential the linear formula is analytically equivalent to known filtered backpropagation formulas for born inversion and at least in the case of small scattering objects has advantages of computational simplicity and efficiency a similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions inverse scattering in an inhomogeneous background medium and reconstructions for data corrupted by noise

electromagnetic music type imaging of perfectly conducting arc like cracks at single frequency we propose a non iterative music multiple signal classification type algorithm for the time harmonic electromagnetic imaging of one or more perfectly conducting arc like cracks found within a homogeneous space r 2 the algorithm is based on a factorization of the multi static response msr matrix collected in the far field at a single nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition followed by the calculation of a music cost functional expected to exhibit peaks along the crack curves each half a wavelength numerical experimentation from exact noiseless and noisy data shows that this is indeed the case and that the proposed algorithm behaves in robust manner with better results in the tm mode than in the te mode for which one would have to estimate the normal to the crack to get the most optimal results

a time domain sampling method for inverse acoustic scattering problems this work concerns the inverse scattering problems of imaging unknown inaccessible scatterers by transient acoustic near field measurements based on the analysis of the migration method we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time dependent scattered data due to incident impulsive point sources though the inverse scattering problems are known to be nonlinear and ill posed the proposed imaging algorithms are totally direct involving only integral calculations on the measurement surface theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods in particular the proposed static imaging functionals enhance the performance of the total focusing method tfm and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time dependent wave equations

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

new unified h dynamic observer design for linear systems with unknown inputs in this paper a unified h dynamic observer uo is proposed for a class of linear systems in the presence of unknown inputs and disturbances it generalizes the existing results on the proportional observer po the proportional integral observer pio and the dynamic observer do the design approach of the uo is derived from the solution of the linear matrix inequality lmi based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error a numerical example is provided to show the applicability and the performance of our results

the generalized polarization tensors for resolved imaging part ii shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements this paper deals with the problem of reconstructing the electromagnetic parameters and the shape of a target from multi static response matrix measurements at a single frequency the target is of characteristic size less than the operating wavelength using long wavelength asymptotic expansions of the measurements of high order we show how the electromagnetic parameters and the equivalent ellipse of the target can be reconstructed the asymptotic expansions of the measurements are written in terms of the new concept of frequency dependent polarization tensors moreover we extend the optimization approach proposed in part i 9 to image geometric details of an electromagnetic target that are finer than the equivalent ellipse the equivalent ellipse still provides a good initial guess for the optimization procedure however compared to the conductivity case in 9 the cost functional measures the discrepancy between the computed and measured high order frequency dependent polarization tensors rather than between the generalized polarization tensors the main reason for such a modification of the cost functional is the fact that the measured frequency dependent polarization tensors can be easily obtained from multistatic measurements by solving a linear system while the derivation of the generalized polarization tensors from measurements requires more delicate treatment the proposed methods are numerically implemented to demonstrate their validity and efficiency mathematics subject classification msc2000 35r30 35b30

asymptotic analysis of the optimal filtering problem for two dimensional diffusions measured in a low noise channel we consider the problem of filtering one dimensional diffusions with nonlinear drift coefficients transmitted through a nonlinear fow noise channel we construct an asymptotic solution to zakai s equation for the unnormalized conditional probability density of the signal given the noisy measurements this expansion is used to find the asymptotic expansion of the minimum error variance filter and its mean square estimation error msee we construct approximate filters whose msee agrees with that of the optimal one to a given degree of accuracy the dimension of the approximate filter increases with the required degree of accuracy similarly we expand the maximum a posteriori probability estimator and the minimum energy estimator and compare their performance we also discuss some extended kalman filters and present some examples

a new solution to the generalized sylvester matrix equation av evf bw abstract this note deals with the problem of solving the generalized sylvester matrix equation av evf bw with f being an arbitrary matrix and provides complete general parametric expressions for the matrices v and w satisfying this equation the primary feature of this solution is that the matrix f does not need to be in any canonical form and may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems in control systems theory

h_ infty unbiased filtering for linear descriptor systems via lmi this note concerns the optimal h infin unbiased filtering problem for linear descriptor systems it unifies the design of reduced order minimal order and full order filters for continuous and discrete time systems necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of linear matrix inequalities lmis the parametrization of all h infin unbiased filters is presented application to standard systems with or without unknown inputs is given a numerical example is given to show the applicability of the presented approach

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

a direct impedance tomography algorithm for locating small inhomogeneities impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface in its most general form impedance tomography is quite ill posed but when additional a priori information is admitted the situation changes dramatically in this paper we consider the case where the goal is to find a number of small objects inhomogeneities inside an otherwise known conductor taking advantage of the smallness of the inhomogeneities we can use asymptotic analysis to design a direct i e non iterative reconstruction algorithm for the determination of their locations the viability of this direct approach is documented by numerical examples

music algorithm for location searching of dielectric anomalies from s parameters using microwave imaging abstract motivated by the biomedical engineering used in early stage breast cancer detection we investigated the use of multiple signal classification music algorithm for location searching of small anomalies using s parameters we considered the application of music to functional imaging where a small number of dipole antennas are used our approach is based on the application of born approximation or physical factorization we analyzed cases in which the anomaly is respectively small and large in relation to the wavelength and the structure of the left singular vectors is linked to the nonzero singular values of a multi static response msr matrix whose elements are the s parameters using simulations we demonstrated the strengths and weaknesses of the music algorithm in detecting both small and extended anomalies

imaging small three dimensional elastic inclusions by an enhanced multiple signal classification method in this paper an enhanced multiple signal classification music algorithm is introduced to retrieve small three dimensional elastic inclusions first the multistatic response msr matrix is built by two different ways depending on considering the multiple scattering effect or not the eigenvalue structure of the msr matrix is analyzed to identify the degenerate case of inclusions second the pseudo spectrum function is built with an optimal test direction on each node where a balancing technique is employed to ensure the numerical stability benefitting from this music indicator the degenerate inclusions can be located with a good performance against noise numerical simulations show the proposed method has wider applicability better resolution and more robust in the presence of noise than the standard music methods

design of observers for descriptor systems in this note simple and straightforward methods to design full and reduced order observers for linear time invariant descriptor systems are presented the approach for the reduced order observer design is based on the generalized sylvester equation sufficient conditions for the existence of the observers are given an illustrative example is included

brief paper h observers design for a class of nonlinear singular systems the present paper is devoted to the h observer or filter design problem for a class of lipschitz nonlinear singular systems the approach is based on the parameterization of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given the method also unifies the design for the full order reduced order minimal order observers for continuous time systems it can be seen that the obtained conditions when applied to linear systems are also necessary a numerical example is given to show the applicability of our results

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

on the accuracy of the numerical detection of complex obstacles from far field data using the probe method we deal with the acoustic inverse scattering problem for detecting an obstacle with mixed boundary conditions from the far field map we show how the geometrical properties and the material parameter distributed on the surface are involved in the obstacle reconstruction numerically the main advance of this research is the numerical analysis and implementation of our recent theoretical work j j liu and m sini how to make the reconstruction of obstacles more or less accurate from exterior measurements ricam preprint 2008 04 johann radon institute for computational and applied mathematics linz austria 2008 regarding the higher order asymptotic expansion of the probe indicator function and the introduction of complex valued surface impedance an efficient numerical implementation scheme is proposed based on the properties of minimum norm solutions precisely using the relation between the surface impedance and the obstacle curvature contained in the higher order expansion of the indicators we reveal how the obstacle curvature and the surface impedance on the coated part influence the blowing up behavior using this theoretical result we can specify the complex surface impedance in terms of the obstacle curvature to make the reconstruction more or less accurate by establishing properties of the minimum norm solution for approximating the singular sources efficient realizations for approximating the multipoles by the herglotz wave function and therefore the implementations of the probe methods are developed with an error estimate we finally show extensive numerical tests explaining how and to what extent the coupling relation between the curvature and the surface impedance changes the accuracy of the reconstruction of the obstacles

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

robust h output feedback control of systems with time delay abstract the problem of designing robust dynamic output feedback controllers for linear continuous time invariant systems with uncertain time delay in the measured output and or the control input and with polytopic type parameter uncertainties is considered given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges an appropriate not necessarily minimal state space model of the system is described which permits reconstruction of its states the resulting retarded model incorporates the uncertain parameters of the transfer function matrix in the state space matrices and the uncertain time delay that occurs in the control channel to this model the recent theory of robust h state feedback control for retarded systems is applied the theory is used to solve a benchmark problem of distillation column robust control design

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

mutual information and minimum mean square error in gaussian channels this paper deals with arbitrarily distributed finite power input signals observed through an additive gaussian noise channel it shows a new formula that connects the input output mutual information and the minimum mean square error mmse achievable by optimal estimation of the input given the output that is the derivative of the mutual information nats with respect to the signal to noise ratio snr is equal to half the mmse regardless of the input statistics this relationship holds for both scalar and vector signals as well as for discrete time and continuous time noncausal mmse estimation this fundamental information theoretic result has an unexpected consequence in continuous time nonlinear estimation for any input signal with finite power the causal filtering mmse achieved at snr is equal to the average value of the noncausal smoothing mmse achieved with a channel whose snr is chosen uniformly distributed between 0 and snr

multi frequency subspace migration for imaging of perfectly conducting arc like cracks in full and limited view inverse scattering problems multi frequency subspace migration imaging techniques are usually adopted for the non iterative imaging of unknown electromagnetic targets such as cracks in concrete walls or bridges and anti personnel mines in the ground in the inverse scattering problems it is confirmed that this technique is very fast effective robust and can not only be applied to full but also to limited view inverse problems if a suitable number of incidents and corresponding scattered fields are applied and collected however in many works the application of such techniques is heuristic with the motivation of such heuristic application this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two dimensional full and limited view inverse scattering problems when the unknown targets are arbitrary shaped arc like perfectly conducting cracks located in the two dimensional homogeneous space in contrast to the statistical approach based on statistical hypothesis testing our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the bessel functions of integer order of the first kind this is based on the structure of the multi static response msr matrix collected in the far field at nonzero frequency in either transverse magnetic tm mode dirichlet boundary condition or transverse electric te mode neumann boundary condition the investigation of the expression of imaging functionals gives us certain properties of subspace migration and explains why multi frequency enhances imaging resolution in particular we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident fields are applied consequently we introduce a weighted multi frequency imaging functional and confirm that it is an improved version of subspace migration in tm mode various results of numerical simulations performed on the far field data affected by large amounts of random noise are similar to the analytical results derived in this study and they provide a direction for future studies

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

mathematical analysis of plasmonic resonances for nanoparticles the full maxwell equations abstract in this paper we use the full maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles we mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size shape and arrangement of the nanoparticles using the layer potential techniques associated with the full maxwell equations we present an effective medium theory for resonant plasmonic systems and derive a condition on the volume fraction under which the maxwell garnett theory is valid at plasmonic resonances

multistatic response matrix of a 3 d inclusion in half space and music imaging recent work on the retrieval of 3 d bounded dielectric and or magnetic inclusions in free space is extended to burial in a half space though emphasis is on the case of a single inclusion enabling the derivation of closed form mathematical results in illuminating fashion the approach extends to the case of an unknown number of well separated inclusions within an asymptotic field formulation derived from exact contrast source vector integral formulations satisfied by the time harmonic fields and using proper reciprocity relationships of the dyadic green s functions the multistatic response matrix of the inclusion is constructed from the leading order term of the fields its singular value structure is analyzed in detail for a dielectric or a magnetic contrast or both contrasts this is performed in the case of a unique electric dipole array operated in the transmit receive mode at a single frequency a multiple signal classification type algorithm follows from the decomposition yielding a cost functional the magnitude of which peaks at the inclusion center numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data as well as of two inclusions embedded within a non conductive or conductive half space

a sliding mode observer for infinitely unobservable descriptor systems in existing work of sliding mode observers smos for descriptor systems a necessary condition is that the system must be infinitely observable this paper presents a scheme that circumvents that condition by reformulating the system as a reduced order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs following that an smo is implemented on the reduced order system where state and fault estimation can be achieved necessary and sufficient conditions of this scheme are also presented finally a simulation example shows the effectiveness of the proposed scheme

adaptive eigenspace for multi parameter inverse scattering problems abstract a nonlinear optimization method is proposed for inverse scattering problems in the frequency domain when the unknown medium is characterized by one or several spatially varying parameters the time harmonic inverse medium problem is formulated as a pde constrained optimization problem and solved by an inexact truncated newton type method combined with frequency stepping instead of a grid based discrete representation each parameter is projected to a separate finite dimensional subspace which is iteratively adapted during the optimization each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori the small and slowly increasing finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard tikhonov type regularization numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi parameter problems including the well known marmousi model from geosciences

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem we propose a method for computing the scattering of a time harmonic electromagnetic wave in a medium with a locally perturbed refractive index we prove that it converges of arbitrarily high order depending on the smoothness of the refractive index and that the time complexity is o n 3log n as an application we solve the corresponding inverse problem using a preconditioned newton method and discuss how to compute the frechet derivative of the solution operator and its adjoint by the proposed method the performance of both the forward and the inverse solver is illustrated in a number of numerical experiments

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

numerical solution of an inverse medium scattering problem for maxwell s equations at fixed frequency consider a time harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in r 3 in this paper well posedness of the variational problem for the direct scattering is examined an energy estimate for the scattered field is obtained on which the born approximation is based a regularized recursive linearization method for the inverse medium scattering which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered field is developed the algorithm requires only single frequency data using an initial guess from the born approximation each update is obtained via continuation on the spatial frequency of a two parameter family of plane waves by solving one direct problem and one adjoint problem of the maxwell equation

h sub spl infin filtering for singular systems this note considers the h sub spl infin filtering problem for linear continuous singular systems the purpose is the design of a linear filter such that the resulting error system is regular impulse free and stable while the closed loop transfer function from the disturbance to the filtering error output satisfies a prescribed h sub spl infin norm bound constraint without decomposing the original system matrices a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given finally an illustrative example is presented to demonstrate the applicability of the proposed approach

on the solution of a sylvester equation appearing in descriptor systems control theory the solution of a generalized sylvester equation associated to a linear descriptor system and subject to some rank and regional pole placement constraints is studied in this paper under the hypothesis of strong detectability of the descriptor system a sequence of coordinate transformations is proposed such that the considered problem can be solved through a sylvester equation associated to a detectable reduced order normal system thus solutions to this equation can be found either by eigenstructure assignment or by regional pole placement in lmi type regions of the complex plane the proposed results are motivated from its use for designing minimal order observers and for computing output feedback control laws by a particular technique some numerical results are reported and possible extensions for the proposed approach are commented

correction of order three for the expansion of two dimensional electromagnetic fields perturbed by the presence of inhomogeneities of small diameter the derivation of the correction of order 3 for the expansion of 2 dimensional electromagnetic fields perturbed by the presence of dielectric inhomogeneities of small diameter was completed in 3 however previous numerical work such as that in 6 and in 14 do not corroborate the existence of these correcting terms the inhomogeneities used in all those numerical simulations were collections of ellipses in this paper we propose to elucidate this discrepancy we prove that the correction of order 3 is zero for any inhomogeneity that has a center of symmetry we present numerical experiments for asymmetric inhomogeneities they illustrate the importance of the correction of order 3 finally we prove that numerical schemes based on the usual quadrature for solving mixed linear integral equations on a smooth contour with smooth integration kernels and kernels involving logarithmic singularities preserve at the discrete level the fact that correcting terms of order 3 are zero for inhomogeneities that are symmetric about their center

observation of nonlinear differential algebraic systems with unknown inputs a method to carry out the state estimation is proposed for a class of nonlinear systems with unknown inputs whose dynamics is governed by differential algebraic equations dae we achieve under suitable conditions to replace the original dae for a system with differential equations only by using a zeroing manifold algorithm inducing a state space dimension reduction observability conditions can be checked using the original system parameters the state estimation is done using a sliding mode high order differentiator

fixed point smoothing of scalar diffusions ii the error of the optimal smoother the problem of fixed point smoothing of a scalar diffusion process consists of estimating the initial value of the process given its noisy measurements as a function of time an asymptotic expansion of the joint filtering smoothing conditional density function is constructed in the limit of small measurements noise the approximate optimal nonlinear fixed point smoother of part i siam j appl math 54 1994 pp 833 853 is rederived from the expansion a detailed analysis of the conditional mean square estimation error cmsee of the optimal fixed point smoother and of its leading order approximation is presented it is shown that if the initial error is small e g if asymptotically optimal filtering is used first the leading order approximation to the optimal smoother is three dimensional and thus simpler than the four dimensional extended kalman smoother furthermore nonlinear fixed point smoothing can reduce the cmsee relative to that of filtering by a factor of frac 1 2 within smoothin

music algorithm for two dimensional inverse problems with special characteristics of cylinders a multiple signal classification music algorithm is proposed to determine the positions of small cylinders which have some special characteristics that may lend traditional music unsuccessful the tm case is discussed in detail up to three independent currents are induced on each cylinder in the tm case however for a cylinder if the material property is the same as the background medium in one or two of the principal axes or if the geometry makes one or two of the induced currents very small with respect to the others so as to be negligible in noisy scenario the number of significant sources may be less than three and the traditional music may fail in locating the cylinder in such event knowledge of the direction of the induced source becomes mandatory to locate the cylinder the proposed method determines the direction of the induced source and uses the background green s function corresponding to it as music s test function the method uses minimization of the analytical expressions and gives good results in noise free as well as noisy scenarios

observers for a class of nonlinear singular systems this technical note considers the observers design for a class of nonlinear singular systems the approach is based on the new parameterization of the generalized sylvester equations solutions the conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities lmis formulation reduced order minimal order and full order observers are designed by a unified method a numerical example is presented to demonstrate the effectiveness of the developed method

identification of small inhomogeneities asymptotic factorization we consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions we give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential the location of the inhomogeneities and their geometry as the size of the inhomogeneities tends to zero such asymptotic expansions have already been used to design direct i e noniterative reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary e g music type methods our derivation of the asymptotic formulas is based on integral equation methods it demonstrates the strong relation between factorization methods and music type methods for the solution of this inverse problem

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

on the generalized sylvester mapping and matrix equations general parametric solution to a family of generalized sylvester matrix equations arising in linear system theory is presented by using the so called generalized sylvester mapping which has some elegant properties the solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution the results provide great convenience to the computation and analysis of the solutions to this family of equations and can perform important functions in many analysis and design problems in linear system theory it is also expected that this so called generalized sylvester mapping tool may have some other applications in control system theory