on the effectiveness of high gain observer based residuals for a class of non linear control systems the design of a high gain observer based residual is considered for a class of non linear systems input output maps are derived for use in residual design to increase design flexibility an invest

comparing classifiers when the misallocation costs are uncertain receiver operating characteristic roc curves are popular ways of summarising the performance of two class classification rules in fact however they are extremely inconvenient if the relative severity of the two different kinds of misclassification is known then an awkward projection operation is required to deduce the overall loss at the other extreme when the relative severity is unknown the area under an roc curve is often used as an index of performance however this essentially assumes that nothing whatsoever is known about the relative severity a situation which is very rare in real problems we present an alternative plot which is more revealing than an roc plot and we describe a comparative index which allows one to take advantage of anything that may be known about the relative severity of the two kinds of misclassification

the fast multipole method fmm for electromagnetic scattering problems the fast multipole method fmm developed by v rokhlin 1990 to efficiently solve acoustic scattering problems is modified and adapted to the second kind integral equation formulation of electromagnetic scattering problems in two dimensions the present implementation treats the exterior dirichlet problem for two dimensional closed conducting objects of arbitrary geometry the fmm reduces the operation count for solving the second kind integral equation from o n sup 3 for gaussian elimination to o n sup 4 3 per conjugate gradient iteration where n is the number of sample points on the boundary of the scatterer a sample technique for accelerating convergence of the iterative method termed complexifying k the wavenumber is also presented this has the effect of bounding the condition number of the discrete system consequently the operation count of the entire fmm all iterations becomes o n sup 4 3 computational results for moderate values of ka where a is the characteristic size of the scatterer are given

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

linear minimax regret estimation of deterministic parameters with bounded data uncertainties we develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties the estimator is designed to minimize the worst case regret over all bounded data vectors namely the worst case difference between the mean squared error mse attainable using a linear estimator that does not know the true parameters x and the optimal mse attained using a linear estimator that knows x we demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least squares estimator as well as several other least squares alternatives

robust detection filter design in the presence of time varying system perturbations this paper discusses the problem of designing detection filters for a class of linear time varying systems the basic contribution of the paper is that by applying a time invariant equivalent representation of the original time varying system it is possible to construct a detection filter such that the solution of the design problem can be solved using algebraic methods and geometric concepts similar to the case of time invariant situations

solution of electrically large problems with multilevel characteristic basis functions we present a multilevel version to the characteristic basis function method cbfm this technique extends the range of applicability of the conventional cbfm and allows a direct solution of problems even when they exceed 250 000 degrees of freedom in this paper it is shown how we can use the multilevel cbfm which is a natural extension of the conventional approach and which saves both time and memory and yet retains excellent accuracy in the computed far fields also the adaptive cross algorithm is used for fast calculation of the interaction between the blocks in the process of generating the reduced matrix

a competitive minimax approach to robust estimation of random parameters we consider the problem of estimating in the presence of model uncertainties a random vector x that is observed through a linear transformation h and corrupted by additive noise we first assume that both the covariance matrix of x and the transformation h are not completely specified and develop the linear estimator that minimizes the worst case mean squared error mse across all possible covariance matrices and transformations h in the region of uncertainty although the minimax approach has enjoyed widespread use in the design of robust methods we show that its performance is often unsatisfactory to improve the performance over the minimax mse estimator we develop a competitive minimax approach for the case where h is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst case regret namely the worst case difference between the mse attainable using a linear estimator ignorant of the signal covariance and the optimal mse attained using a linear estimator that knows the signal covariance the linear minimax regret estimator is shown to be equal to a minimum mse mmse estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region we demonstrate through examples that the minimax regret approach can improve the performance over both the minimax mse approach and a plug in approach in which the estimator is chosen to be equal to the mmse estimator with an estimated covariance matrix replacing the true unknown covariance we then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly gaussian is nonlinear we often do not lose much by restricting attention to linear estimators

combining the moment method with geometrical modelling by nurbs surfaces and bezier patches induced current distributions on conducting bodies of arbitrary shape modelled by nurbs non uniform rational b splines surfaces are obtained by using a moment method approach to solve an electric field integral equation efie the nurbs surfaces are expanded in terms of bezier patches by applying the cox de boor transformation algorithm this transformation is justified because bezier patches are numerically more stable than nurbs surfaces new basis functions have been developed which extend over pairs of bezier patches these basis functions can be considered as a generalization of rooftop functions the method is applied to obtain rcs values of several objects modelled with nurbs surfaces good agreement with results from other methods is observed the method is efficient and versatile because it uses geometrical modelling tools that are quite powerful

analytical redundancy relations for fault detection and isolation in algebraic dynamic systems this paper extends the analytical redundancy techniques well developed for linear systems to fdi in non linear dynamic systems modeled by polynomial differential algebraic equations the residual evaluation form is developed for sensor actuator and process component faults fault detectability and isolability conditions are given and the design of robust structured residuals is addressed

on the structure of strict sense bayesian cost functions and its applications in the context of classification problems the paper analyzes the general structure of the strict sense bayesian ssb cost functions those having a unique minimum when the soft decisions are equal to the posterior class probabilities we show that any ssb cost is essentially the sum of a generalized measure of entropy which does not depend on the targets and an error component symmetric cost functions are analyzed in detail our results provide a further insight on the behavior of this family of objective functions and are the starting point for the exploration of novel algorithms two applications are proposed first the use of asymmetric ssb cost functions for posterior probability estimation in non maximum a posteriori map decision problems second a novel entropy minimization principle for hybrid learning use labeled data to minimize the cost function and unlabeled data to minimize the corresponding entropy measure

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

linear embedding via green s operators a modeling technique for finite electromagnetic band gap structures we propose a modular electromagnetic modeling procedure for large finite electromagnetic band gap ebg structures called linear embedding via green s operators it is a diakoptic method based on the huygens schelkunoff principle involving equivalent boundary current sources that electromagnetically characterize the enclosed domain of arbitrary shapes as if it were a multiport system in a cascade of embedding steps separate reusable domains are combined to form larger domains device design often involves tuning local medium properties in a compact designated domain with a large environment through an additional embedding step the equivalent sources describing the environment can be transferred to the boundary of the designated domain rendering subsequent design steps very fast this two stage optimization process is applied in the design of an ebg power splitter

brief paper robust fault detection based on observers for bilinear systems the design of a residual generator for robust fault detection in bilinear systems is considered two methods are presented the first one is based on a linear time invariant observer up to output injection while the second one relies on a so called kalman like observer it is shown via examples that the approach based on a kalman like observer allows one to handle a larger class of bilinear systems than the other observer based methods presented in the literature

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

minimax regret classifier for imprecise class distributions the design of a minimum risk classifier based on data usually stems from the stationarity assumption that the conditions during training and test are the same the misclassification costs assumed during training must be in agreement with real costs and the same statistical process must have generated both training and test data unfortunately in real world applications these assumptions may not hold this paper deals with the problem of training a classifier when prior probabilities cannot be reliably induced from training data some strategies based on optimizing the worst possible case conventional minimax have been proposed previously in the literature but they may achieve a robust classification at the expense of a severe performance degradation in this paper we propose a minimax regret minimax deviation approach that seeks to minimize the maximum deviation from the performance of the optimal risk classifier a neural based minimax regret classifier for general multi class decision problems is presented experimental results show its robustness and the advantages in relation to other approaches

fast analysis of a dual band reflectarray using two different numerical approaches based on the moment method this communication presents two efficient approaches for the electromagnetic field analysis of complex 3d bodies the first method can provide a fast and accurate analysis of arbitrary metallic and dielectric magnetic structures and combines the moment method mm the multilevel fast multipole algorithm mlfma physics optics po and the characteristic basis function method cbfm to solve very large scattering problems the second technique is based on a domain decomposition approach that divides the geometry into several parts to minimize the vast computational resources required when applying the mm a parallelization process was carried out by using the message passing interface mpi algorithm to minimize the memory and time requirements for each simulation a dual band reflectarray was successfully analyzed to compare the performance of both codes

generation of characteristic basis functions defined over large surfaces by using a multilevel approach an efficient procedure for the generation of characteristic basis functions cbfs over large arbitrary surfaces is presented in this work the first step is to partition the original object into subdomains and then derive the cbfs for these domains by solving for the currents induced by a set of components of the planewave spectrum pws next we aggregate the adjacent domains to obtain enlarged cbfs by expanding the original ones in terms of the weighted planewaves used to compute them this process can be performed iteratively and involves fast non expensive matrix manipulation we obtain a progressive decrease of the number of unknowns as we increase the domain size by following the procedure described above

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

a moment method approach using frequency independent parametric meshes a moment method mm formulation using nonuniform rational b splines nurbs parametric surfaces is introduced to analyze radiation and scattering from arbitrarily shaped conducting bodies a feature of the technique presented is the independence of the geometrical model from the frequency which avoids the regeneration of the geometry model when the frequency changes this feature is obtained by defining new sets of basis and testing functions that extend over subpatches in each nurbs the proposed approach is accurate flexible and efficient

application of the characteristic basis function method utilizing a class of basis and testing functions defined on nurbs patches a novel implementation of the characteristic basis function method cbfm is given in which the high level basis functions called characteristic basis functions cbfs are represented in terms of curved rooftops generated from nonuniform rational b splines nurbs in the parametric u v domain the associated macro testing functions are defined by using curved razor blade functions corresponding to each rooftop the underlying objective of the cbfm is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments mom the result is therefore an approach which can handle many complex cases via direct solvers without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill conditioned matrices as a result of the combination of the cbfm with the special class of low level basis and testing functions directly located over nurbs surfaces complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the cpu time as well as required memory resources

scattering analysis of a large body with deep cavities a numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body coated with inhomogeneous composite materials with large and deep cavities this numerical scheme employs the higher order vector finite element method fem to discretize the fields inside the cavities and coatings and the higher order boundary integral bi method to terminate the fem computational domain a highly efficient special solver is designed to eliminate the unknowns inside the cavities which yields a computed relation cr matrix over the cavity s aperture between the tangential electric and magnetic fields this cr matrix is then combined with the finite element boundary integral fe bi matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain the resulting system is solved iteratively using a novel preconditioner derived by replacing the bi with a corresponding absorbing boundary condition abc

universal composite hypothesis testing a competitive minimax approach a novel approach is presented for the long standing problem of composite hypothesis testing in composite hypothesis testing unlike in simple hypothesis testing the probability function of the observed data given the hypothesis is uncertain as it depends on the unknown value of some parameter the proposed approach is to minimize the worst case ratio between the probability of error of a decision rule that is independent of the unknown parameters and the minimum probability of error attainable given the parameters the principal solution to this minimax problem is presented and the resulting decision rule is discussed since the exact solution is in general hard to find and a fortiori hard to implement an approximation method that yields an asymptotically minimax decision rule is proposed finally a variety of potential application areas are provided in signal processing and communications with special emphasis on universal decoding

a dynamic recurrent neural network based adaptive observer for a class of nonlinear systems abstract an adaptive observer for a class of single input single output siso nonlinear systems is proposed using a generalized dynamic recurrent neural network drnn the neural network nn weights are tuned on line with no off line learning required no exact knowledge of non linearities in the observed system is required furthermore no linearity with respect to unknown system parameters is assumed the drnn observer does not assume that nonlinearities in the system are restricted to the system output only the overall adaptive observer scheme is shown to be uniformly ultimately bounded simulation results have verified the performance of the drnn observer

minimax classifiers based on neural networks the problem of designing a classifier when prior probabilities are not known or are not representative of the underlying data distribution is discussed in this paper traditional learning approaches based on the assumption that class priors are stationary lead to sub optimal solutions if there is a mismatch between training and future real priors to protect against this uncertainty a minimax approach may be desirable we address the problem of designing a neural based minimax classifier and propose two different algorithms a learning rate scaling algorithm and a gradient based algorithm experimental results show that both succeed in finding the minimax solution and it is also pointed out the differences between common approaches to cope with this uncertainty in priors and the minimax classifier

a fast impedance and pattern computation scheme for finite antenna arrays a fast numerical method well suited to the analysis of moderate size arrays made of complex elements is presented it combines macro basis functions and multipole approaches without an iterative procedure this method is exploited to estimate the impedance matrix and active element patterns for the latter an efficient formulation is provided as a series of pattern multiplication problems examples are shown for arrays of broadband dipoles the computational gain obtained for the reduction of the original method of moments system of equations is briefly described

generation of excitation independent characteristic basis functions for three dimensional homogeneous dielectric bodies the aim of this paper is the development of characteristic basis functions cbfs for homogeneous dielectric bodies that are modeled with the surface equivalence principle this approach contributes to generalize the characteristic basis function method cbfm for any kind of material the foundations for the generation of these new basis functions are widely revised and the cbfm is adapted for this purpose the validity of the method is illustrated with the systematic analysis of canonical geometries as well as with the computation of the specific absorption rate inside a head like geometry in all the cases the error in the current distribution as well as in the near and far field is considered in addition a detailed comparison of the generation of the cbfs using plane waves and spherical waves is also carried out

wave field interaction with complex structures using equivalence principle algorithm a domain decomposition scheme based on the equivalence principle similar to huygens principle for integral equation solvers and the method of moments is introduced the equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume it also allows the dissociation of the solution of one region from that of another region in this manner problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns it can aid in parallel algorithms reusability of solutions as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed the challenge arises when an equivalence surface intercepts a current carrying conductor because the breakup of the current into separate pieces gives rise to charge singularity a junction basis can be used to mitigate this singularity however a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces using this scheme the current continuity is conserved and the singularity of the charges is avoided the solution is shown to be accurate

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature