the helmholtz equation least squares method and rayleigh hypothesis in near field acoustical holography in this paper we present a numerical investigation of reconstructing time harmonic acoustic pressure field in two dimensional space by using a series expansion the so called helmholtz equation least squares hels method series expansion methods or the rayleigh methods have been widely used in predicting the scattered acoustic pressure with regularization they can also be applied to reconstruction of acoustic pressure on the source surface from the measurements taken in the field and hels is the first such attempt for these problems in this paper we establish hels in the framework of the rayleigh methods and reveal its interrelationship with the rayleigh hypothesis in particular to regularize a reconstruction problem we use the method of quasisolutions i e a tikhonov regularization with an a posteriori choice of the regularization parameter it is shown that without regularization hels can still yield a satisfactory reconstruction of acoustic radiation from an arbitrary object when enough me

conformal generalized near field acoustic holography for axisymmetric geometries the normal velocity field on the boundary of a radiating source is reconstructed with high resolution by using pressure data measured in the very near field to include evanescent components fast decaying with the distance the measurement points belong to a surface conformal to the reconstruction is performed by identifying the boundary normal velocity distribution generating the pressure field best mean square fitting the measurement data the ensuing normal equations are solved by resorting to the singular value decomposition svd of the transformation from the boundary normal velocity to the pressure at the measurement points the reconstructed boundary normal velocity is represented as a linear combination of basis functions each associated with a singular value sv the errors in the estimation of the coefficients of the linear combination are proportional to the inverses of the corresponding svs to achieve robustness the svd is truncated to retain the terms corresponding to a limited dynamic range in turn related to the dynamic range of the measurement system for axisymmetric but otherwise general surfaces the numerical complexity is reduced because separate svds of greatly reduced dimensionality must be performed on a number of matrices each associated with one of the harmonics of the fourier expansion of the field around the symmetry axis in a numerical experiment making use of an available computer model by processing very near field pressure samples the normal velocity was reconstructed with excellent accuracy on the surface of a finite compliant cylinder with flat endcaps excited by point forces the viability of the method was then confirmed in a measurement tank experiment in which the distribution of the boundary normal velocity was reconstructed on a finite compliant cylinder driven by point shakers comparison with accelerometer data shows good agreement on a wide frequency band

robust identification in h abstract we consider system identification in the banach space h in the framework proposed by helmicki jacobson and nett it is shown that there is no robustly convergent linear algorithm for identifying exponentially stable systems in the presence of noise which is not tuned to prior information about the unknown system or noise various nonlinear algorithms some closely related to one of gu and khargonekar are analysed and results on trigonometric interpolation used to provide new error bounds an application of these techniques to approximation is given and finally some numerical results are provided for illustration

krylov subspace iterative methods for boundary element method based near field acoustic holography the reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods the solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements these methods will not require the calculation of the singular value decomposition which can be expensive when the matrix system is considerably large krylov subspace methods are iterative methods that have the phenomena known as semi convergence i e the optimal regularization solution is obtained after a few iterations if the iteration is not stopped the method converges to a solution that generally is totally corrupted by errors on the measurements for these methods the number of iterations play the role of the regularization parameter we will focus our attention to the study of the regularizing properties from the krylov subspace methods like conjugate gradients least squares qr and the recently proposed hybrid method a discussion and comparison of the available stopping rules will be included a vibrating plate is considered as an example to validate our results

notions of stabilizability and controllability for a class of uncertain linear systems abstract this paper investigates the relationship between stabilizability and certain notions of controllability for a class of uncertain linear systems containing time varying unknown but bounded uncertain parameters the paper introduces a notion of controllability invariance roughly speaking an uncertain system is controllability invariant if it is controllable in the usual sense for each fixed value of the uncertain parameters the paper describes a class of uncertain systems for which controllability invariance implies stabilizability

mixed time frequency domain based robust identification in this paper we propose a new robust identification framework that combines both frequency and time domain experimental data the main result of the paper shows that the problem of obtaining a nominal model consistent with the experimental data and bounds on the identification error can be recast as a constrained finite dimensional convex optimization problem that can be efficiently solved using linear matrix inequalities techniques this approach based upon a generalized interpolation theory contains as special cases the caratheodory fejer purely time domain and nevanlinna pick purely frequency domain problems the proposed procedure interpolates the frequency and time domain experimental data while restricting the identified system to be in an a priori given class of models resulting in a nominal model consistent with both sources of data thus it is convergent and optimal up to a factor of two with respect to central algorithms

the detection of the source of acoustical noise in two dimensions we consider the problem of detecting the source of acoustical noise inside the cabin of a midsize aircraft from measurements of the acoustical pressure field inside the cabin mathematically this field satisfies the helmholtz equation in this paper we consider the model two dimensional case we show that any regular solution of this equation admits a unique representation by a single layer potential so that the problem is reduced to the solution of a linear integral equation of the first kind we prove uniqueness of reconstruction and obtain a sharp stability estimate finally for two geometries and sources of noise simulating the cabin of the aircraft and two engines we give results of the numerical solution of this integral equation comparing regularization by the truncated singular value decomposition and the conjugate gradient method

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

thomson s heptagon a case of bifurcation at infinity abstract vortex modeling has a long history descartes 1644 used it as a model for the solar systems j j thomsom 1883 used it as a model for the atom we consider point vortex systems which can be regarded as discrete solutions of the euler equation their dynamics is described by a hamiltonian system of equations we are interested in polygonal configurations and how their stability depends upon various dynamical variables in the plane a polygon with seven vortices has been shown to be a special boundary case polygons with n 7 vortices are linearly and nonlinearly stable while polygons with n 7 vortices are unstable why should n 7 be special celestial mechanics helped us to simplify a problem that has been studied for over a century and to show that the case of thomson s heptagon is actually a case of bifurcation at infinity this becomes particularly clear when considering the corresponding problem of a ring on a sphere with two polar vortices of variable intensities n and s at the north and south pole respectively

a nearly interpolatory algorithm for h sub spl infin identification with mixed time and frequency response data a new algorithm is proposed for h sub spl infin identification with mixed time and frequency response data this algorithm shares similar properties to interpolatory algorithms and is nearly interpolatory meanwhile it greatly reduces the computational complexity of the interpolatory algorithm worst case identification error bounds are also characterized and derived for this nearly interpolatory algorithm a numerical example is used to illustrate the proposed identification algorithm

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

a parametric extension of mixed time frequency robust identification a parametric extension to the time frequency robust identification framework is presented the results can be applied to stable linear time invariant systems on which time and or frequency experiments have been performed the parametric portion of the model should be affine in the unknown parameters which includes practical applications such as flexible structures the consistency problem is cast as a constrained finite dimensional convex optimization problem that can be formulated as a linear matrix inequality the proposed procedure provides an interpolating identification algorithm convergent and optimal up to a factor of two with respect to central algorithms

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

a linear interpolatory algorithm for robust system identification with corrupted measurement data a linear robustly convergent interpolatory algorithm for system identification in the presence of bounded noise is presented the algorithm converges in the actual but unknown system in the frequency domain in the noise free case and maintains the robust convergence result in the face of bounded noise this robustness property distinguishes the algorithm from existing linear schemes a key idea of this robust linear algorithm is that the approximation is separated into real and imaginary parts and into fejer hermite interpolation because of the fejer interpolation the data points are required at the chebyshev points

the caratheodory fejer problem and h sub spl infin l sub 1 identification a time domain approach in this paper we study a worse case robust control oriented identification problem this problem is in the framework of h sub spl infin identification but the formulation here is more general the available a priori information in our problem consists 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 plant to be identified is assumed to lie in a certain subset in the space of h sub spl infin characterized by the assumed a priori information the available experimental information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input the proposed algorithm is in the class of interpolatory algorithms which are known to possess desirable optimality properties in reducing the identification error this algorithm is obtained by solving an extended caratheodory fejer problem via standard convex programming methods both the algorithm and error bounds ran be applied to l sub 1 identification problems as well

an operator marching method for inverse problems in range dependent waveguides abstract for large scale inverse problems in acoustics and electromagnetics numerical schemes based on direct methods e g fem and meshless methods often result in huge linear systems and thus are not feasible in terms of computing speed and memory storage this work proposes the inverse fundamental operator marching method based on the dirichlet to neumann map for solving large scale inverse boundary value problems in range dependent waveguides truncated singular value decomposition is employed to solve ill conditioned linear systems arising in marching process and the number of propagating modes in the waveguide assumes the role of a regularization parameter numerical results show that the method is computationally efficient highly accurate stable with respect to data noise for retrieving the propagating part of the starting field it particularly suits to long range wave propagation in slowly varying stratified waveguide

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

robust identification and interpolation in h abstract we consider system identification in h in the framework proposed by helmicki jacobson and nett an algorithm using the jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems it is shown that this and similar identification algorithms can be successfully combined with a model reduction procedure to produce low order models connections with the nevanlinna pick interpolation problem are explored and an algorithm is given in which the identified model interpolates the given noisy data some numerical results are provided for illustration finally the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions

on the time complexity of worst case system identification in this paper we treat a general worst case system identification problem this problem is worst case with respect to both noise and system modeling uncertainty we consider this problem under various a priori information structures we determine bounds on the minimum duration identification experiment that must be run to identify the plant to within a specified guaranteed worst case error bound our results are algorithm independent we show that this minimum duration is prohibitively long based on our results we suggest that worst case with respect to noise system identification requires unrealistic amounts of experimental data

prediction error identification of linear systems a nonparametric gaussian regression approach a novel bayesian paradigm for the identification of output error models has recently been proposed in which in place of postulating finite dimensional models of the system transfer function the system impulse response is searched for within an infinite dimensional space in this paper such a nonparametric approach is applied to the design of optimal predictors and discrete time models based on prediction error minimization by interpreting the predictor impulse responses as realizations of gaussian processes the proposed scheme describes the predictor impulse responses as the convolution of an infinite dimensional response with a low dimensional parametric response that captures possible high frequency dynamics overparameterization is avoided because the model involves only a few hyperparameters that are tuned via marginal likelihood maximization numerical experiments with data generated by armax and infinite dimensional models show the definite advantages of the new approach over standard parametric prediction error techniques and subspace methods both in terms of predictive capability on new data and accuracy in reconstruction of system impulse responses

robust identification and galois sequences abstract worst case l1 identification is studied for bibo stable linear shift invariant systems it is shown that the chebyshev identification method when used with galois input designs satisfies a certain robust convergence property and provides l1 model error bounds in worst case identification of bibo stable systems with a uniformly bounded noise set up the robust identification methodology developed is compatible with the modelling requirements of modern robust control design

worst case system identification in l 1 ne equation 1 optimal algorithms and error bounds abstract this paper analyses worst case identification of linear shift invariant systems with an l 1 error criterion the assumed apriori information on the plant are bounds on the system gain and decay rate of the impulse response of the unknown system and the experimental data is assumed to be a finite set of corrupted impulse or step response samples of the system

a class of algorithms for identification in h abs traet in this paper a class of algorithms for the problem of system identification in are investigated these algorithms are characterized by a two stage structure and involve a class of window functions some conditions in terms of properties of the window functions are derived which guarantee robust convergence of the algorithms identification errors are analyzed for several common window functions this leads to some insights into the trade off between the error induced by approximation and that due to noise

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

green s function for the laplace beltrami operator on a toroidal surface green s function for the laplacebeltrami operator on the surface of a three dimensional ring torus is constructed an integral ingredient of our approach is the stereographic projection of the toru

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

robust identification of strongly stabilizable systems for strongly stabilizable systems for which a strongly stabilizing controller is known approximately the authors consider system identification in the graph gap and chordal metrics using robust h sub infinity identification of the closed loop transfer function in the framework proposed by a j helmicki et al 1990 error bounds are derived showing that robust convergence is guaranteed and that the identification can be satisfactorily combined with a model reduction step two notions of robust identification of stable systems are compared and an alternative robust identification technique based on smoothing which can be used to yield polynomial models directly is developed

application of bem boundary element method based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries a method employing holograms that conform with arbitrarily shaped sources has been developed for enhancing conventional near field acoustic holography which has been limited to sources with simple geometries e g planar or cylindrical surfaces four holography transformation algorithms have been developed based on acoustic holography theory and the boundary element method bem singular value decomposition svd has been incorporated into the algorithms in order to alleviate the ill posed nature frequently encountered in backward reconstruction of a field a pulsating sphere a cylinder with spherical endcaps and a vibrating piston set in a rigid sphere have been adopted in a numerical simulation for verifying the algorithms satisfactory agreement has been achieved between the holographically transformed results and the analytical solutions

worst case system identification in h sub spl infin validation of a priori information essentially optimal algorithms and error bounds resolves several important open issues pertaining to a worst case control oriented system identification problem known as identification in h sub spl infin first a method is presented for developing confidence that certain a priori information available for identification is not invalid this method requires the solution of a certain nondifferentiable convex program second an essentially optimal identification algorithm is constructed this algorithm is worst case strongly optimal to within a factor of two finally new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm interestingly the development of each of these results draws heavily upon the classical nevanlinna pick interpolation theory as such the authors results establish a clear link between the areas of system identification and optimal interpolation theory both the formulation and techniques in this paper are applicable to problems where the frequency data available for identification may essentially be arbitrarily distributed

time domain identification for robust control abstract in this paper we are concerned with a problem of robust control oriented system identification in the time domain based on the well known schur takagi aak theorem we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by h norm it is also shown that in the model set defined by the nominal model and the uncertainty bound there exists at least one model which matches the prescribed input output data given in the time domain

on the stabilization of uncertain linear systems via bound invariant lyapunov functions this paper considers the problem of stabilizing a class of systems with an arbitrarily large uncertainty bounding set in particular the stabilization of linear uncertain systems via a bound invariant lyapunov function is examined necessary and sufficient conditions for the existence of a bound invariant lyapunov function are derived for systems with block structured uncertainty and a class of systems with scalar linear uncertainty

optimal nonparametric identification from arbitrary corrupt finite time series formulates and solves a worst case system identification problem for single input single output linear shift invariant distributed parameter plants the available a priori information in this problem consists of time dependent upper and lower bounds on the plant impulse response and the additive output noise the available a posteriori information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input signal the authors present a novel identification method for this problem this method maps the available a priori and a posteriori information into an uncertain model of the plant which comprises a nominal plant model a bounded additive output noise and a bounded additive model uncertainty the upper bound on the model uncertainty is explicit and expressed in terms of both the l sub 1 and h sub spl infin system norms the identification method and the nominal model possess certain well defined optimality properties and are computationally simple requiring only the solution of a single linear programming problem

reconstructing the vibro acoustic quantities on a highly non spherical surface using the helmholtz equation least squares method this paper presents helpful guidelines and strategies for reconstructing the vibro acoustic quantities on a highly non spherical surface by using the helmholtz equation least squares hels this study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces the key is to select the optimal origin of the coordinate system behind the planar surface choose a target structural wavelength to be reconstructed set an appropriate stand off distance and microphone spacing use a hybrid regularization scheme to determine the optimal number of the expansion functions etc the reconstructed vibro acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength and produce much more satisfactory results than a straight application of the original hels formulations experiment validations on a baffled square plate were conducted inside a fully anechoic chamber

optimal asymptotic identification under bounded disturbances the intrinsic limitation of worst case identification of linear time invariant systems using data corrupted by bounded disturbances when the unknown plant is known to belong to a given model set is studied this is done by analyzing the optimal worst case asymptotic error achievable by performing experiments using any bounded input and estimating the plant using any identification algorithm it is shown that under some topological conditions on the model set there is an identification algorithm which is asymptotically optimal for any input and the optimal asymptotic error is characterized as a function of the inputs these results which hold for any error metric and disturbance norm are applied to three specific identification problems identification of stable systems in the l sub 1 norm identification of stable rational systems in the h sub infinity norm and identification of unstable rational systems in the gap metric for each of these problems the general characterization of optimal asymptotic error is used to find near optimal inputs to minimize the error

suboptimal algorithms for worst case identification in h sup spl infin and model validation new algorithms based on convex programming are proposed for worst case system identification the algorithms are optimal within a factor of two asymptotically further model validation or data consistency is embedded in the identification process explicit worst case identification error bounds in the h sup spl infin norm are also derived for both uniformly and nonuniformly spaced frequency response samples

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

h sub spl infin identification of multivariable systems by tangential interpolation methods the purpose of this paper is to present an extension to some of the current work on worst case identification problems to multivariable systems we consider an h sub spl infin identification problem for a class of linear shift invariant multi input multi output systems our main results are an interpolatory algorithm and a number of bounds on the identification error this algorithm operates on available input and output data in the time domain and is constructed by solving an extended matrix tangential caratheodory fejer problem similar to its counterpart for scalar systems this interpolatory algorithm possesses certain desirable optimality properties and can be obtained via standard convex programming methods

brief paper multivariable pid control with set point weighting via bmi optimisation the paper focuses on the design of multivariable pid controllers with set point weighting the advantage of this pid structure is that the responses of the system to disturbances and to changes in the set point can be adjusted separately the proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback sof problem hence multivariable pid controllers can be designed by solving an optimisation problem with bilinear matrix inequalities bmis the paper addresses the design of both time invariant and gain scheduled robust controllers all of the tuning methods discussed through the paper are based on a pid structure with filtered derivative term thus guaranteeing the well posedness of the closed loop system

barrier certificates for nonlinear model validation methods for model validation of continuous time nonlinear systems with uncertain parameters are presented in this paper the methods employ functions of state parameter time termed barrier certificates whose existence proves that a model and a feasible parameter set are inconsistent with some time domain experimental data a very large class of models can be treated within this framework this includes differential algebraic models models with memoryless dynamic uncertainties and hybrid models construction of barrier certificates can be performed by convex optimization utilizing recent results on the sum of squares decomposition of multivariate polynomials

motion of three point vortices on a sphere abstract we solve the equations governing the relative motion of three point vortices of arbitrary strength moving on the surface of a sphere of radius r the system is more general than the corresponding one in the plane 1 3 5 19 28 33 34 37 38 and reduces to it in the limit r as long as the three vortices remain sufficiently close to each other during the course of their motion instead of using spherical coordinates we use cartesian coordinates in which the vector i points from the center of the sphere to the vortex with strength i an important conserved quantity is the center of vorticity vector c i i i which with no loss of generality we align with the z axis based on the size of this vector relative to the radius of the sphere we classify the motion into one of five types super radial radial sub radial degenerate or a limiting super radial case this categorization allows us to draw several conclusions about the qualitative motion of the vortices we then fully characterize all fixed and relative equilibria on the sphere for fixed equilibria the vortices must lie on great circles geodesics if the strengths are equal they form an equilateral triangle otherwise the triangle shape is specified once the strength of the vortices is given the relative equilibria are classified as either degenerate c 0 or non degenerate c 0 for each type the shape of the vortex triangle is described and the frequency of rotation is computed as in the planar problem it is possible to introduce trilinear coordinates and study the motion in a phase plane which allows us to locate all the equilibria as well as to characterize more complex relative dynamics we then describe self similar vortex collapse on the sphere stating necessary and sufficient conditions for collapse to occur computing the collapse times and vortex trajectories on the route towards collapse comparisons are made with the collapse formulas in the plane derived in 1 30

on the reconstruction of the vibro acoustic field over the surface enclosing an interior space using the boundary element method the vibrational velocity sound pressure and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures the singular value decomposition is used to obtain the inverse solution in the least square sense and to express the acoustic modal expansion between the measurement and source fields in general such an inverse operation has been considered an ill posed problem having a divergence phenomenon involved with extremely small measurement errors the ill conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components in order to minimize the singularity and to also reduce the number of measurement points optimal measurement positions are determined by the effective independence method regularization methods are used to stabilize the reconstructed field by suppressing nonradiating components resulting in the singular transfer

persistent identification of time varying systems identification of time varying systems especially slowly time varying systems is of importance in the development of a comprehensive theory of adaptation the persistent identification measures employed in this paper capture a main characterization in such identification problems namely one input signal must be used for identification of all possible observation windows this paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation 1 they have computable upper and lower bounds for typical classes of prior uncertainty sets 2 any full rank n periodic signals are optimal and the simple least squares estimates are optimal identification algorithms 3 optimal probing inputs can be approximately generated in a closed loop configuration when the plant and the controller are slowly time varying and 4 n periodic signals are asymptotically optimal for slowly time varying systems the main results of this paper have been successfully combined with a certain slow h sup spl infin design to derive an adaptive stabilization scheme

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

a meshless method for the numerical solution of the cauchy problem associated with three dimensional helmholtz type equations in this paper the application of the method of fundamental solutions to the cauchy problem associated with three dimensional helmholtz type equations is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for under equally and over determined cauchy problems in a piecewise smooth geometry the convergence accuracy and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

iterative svd based methods for ill posed problems very large matrices with rapidly decaying singular values commonly arise in the numerical solution of ill posed problems the singular value decomposition svd is a basic tool for both the analysis and computation of solutions to such problems in most applications it suffices to obtain a partial svd consisting of only the largest singular values and their corresponding singular vectors in this paper two separate approaches one based on subspace iteration and the other based on the lanczos method are considered for the efficient iterative computation of partial svds in the context of ill posed problems an analytical and numerical comparison of these two methods is made and the role of the regularization operator in convergence acceleration is explored

a convex relaxation approach to set membership identification of lpv systems identification of linear parameter varying models is considered in this paper under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise first the problem of computing parameter uncertainty intervals is formulated in terms of nonconvex optimization then on the basis of the analysis of the regressor structure we present an ad hoc convex relaxation scheme for computing parameter bounds by means of semidefinite optimization

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

on the choice of expansion functions in the helmholtz equation least squares method this paper examines the performance of helmholtz equation least squares hels method in reconstructing acoustic radiation from an arbitrary source by using three different expansions namely localized spherical waves lsw distributed spherical waves dsw and distributed point sources dps under the same set of measurements the reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 hz reconstruction is obtained by using tikhonov regularization or its modification with the regularization parameter selected by error free parameter choice methods the impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated results demonstrate that dsw leads to a better conditioned transfer matrix yields more accurate reconstruction than both lsw and dps and is not affected as much by the change in measurement points also it is possible to obtain optimal locations of the auxiliary sources for dsw lsw and dps by taking an independent layer of measurements use of these auxiliary sources and an optimal combination of regularization and error free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost effective manner

an lmi approach to control oriented identification and model in validation of lpv systems this note proposes a control oriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on time varying parameters as well as the possible existence of a nonparametric component the main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems moreover as the information is completed the algorithm is shown to converge in the l sub 2 induced topology to the actual plant additional results include deterministic bounds on the identification error these results are illustrated with a practical example arising in the context of active vision

optimal constant i o similarity scaling for full information and state feedback control problems abstract in robust control problems capturing all robustness and performance objectives in a single h norm cost function is impossible an alternative approach still untilizing the h norm involves diagonal similarity scaling of certain closed loop transfer functions the set of allowable diagonal scalings is problem dependent and reflects assumptions about the uncertainty and desired performance objectives the scaling set considered here is a prescribed convex set of positive definite matrices we consider the optimal constant scaling problem for the full information h control problem the solution is obtained by transforming the original problem into a convex feasibility problem specifically a structured linear matrix inequality in special cases solvability of the full information problem is equivalent to solvability of the state feedback problem

a time domain approach to model validation in this paper we offer a novel approach to control oriented model validation problems the problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input output data our approach directly uses time domain input output data to validate uncertainty models the algorithms we develop are computationally tractable and reduce to generally nondifferentiable convex feasibility problems or to linear programming problems in special cases we give analytical solutions to these problems

iterative tikhonov regularization for the cauchy problem for the helmholtz equation abstract the cauchy problem for the helmholtz equation appears in various applications the problem is severely ill posed and regularization is needed to obtain accurate solutions we start from a formulation of this problem as an operator equation on the boundary of the domain and consider the equation in h 1 2 spaces by introducing an artificial boundary in the interior of the domain we obtain an inner product for this hilbert space in terms of a quadratic form associated with the helmholtz equation perturbed by an integral over the artificial boundary the perturbation guarantees positivity property of the quadratic form this inner product allows an efficient evaluation of the adjoint operator in terms of solution of a well posed boundary value problem for the helmholtz equation with transmission boundary conditions on the artificial boundary in an earlier paper we showed how to take advantage of this framework to implement the conjugate gradient method for solving the cauchy problem in this work we instead use the conjugate gradient method for minimizing a tikhonov functional the added penalty term regularizes the problem and gives us a regularization parameter that can be used to easily control the stability of the numerical solution with respect to measurement errors in the data numerical tests show that the proposed algorithm works well

convex certificates for model in validation of switched affine systems with unknown switches checking validity of a model is a crucial step in the process of system identification this is especially true when dealing with switched affine systems since in this case the problem of system identification from noisy data is known to be generically np hard and can only be solved in practice by using heuristics and relaxations therefore before the identified models can be used for instance for controller design they should be systematically validated against additional experimental data in this paper we address the problem of model in validation for multi input multi output switched affine systems in output error form with unknown switches as a first step we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems in principle these problems involve increasingly large matrices however as we show in the paper by exploiting recent results from semialgebraic geometry the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the a priori information in addition this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden the effectiveness of the proposed method is illustrated using both academic examples and a non trivial problem arising in computer vision activity monitoring

an accelerated alternating procedure for the cauchy problem for the helmholtz equation in this paper we study the cauchy problem for the helmholtz equation this problem appears in various applications and is severely ill posed the modified alternating procedure has been proposed by

estimation of model quality this paper provides an introduction to recent work on the problem of quantifying errors in the estimation of models for dynamic systems this is a very large field we therefore concentrate on approaches that have been motivated by the need for reliable models for control system design this will involve a discussion of efforts that go under the titles of estimation in th worst case estimation estimation in l1 and stochastic embedding of undermodelling a central theme of this survey is to examine these new methods with reference to the classic bias variance tradeoff in model structure selection

vortex motion on surfaces with constant curvature vortex motion on two dimensional riemannian surfaces with constant curvature is formulated by way of the stereographic projection the relation and difference between the vortex motion on a sphere s 2 and on a hyperbolic plane h 2 can be clearly analysed the hamiltonian formalism is presented for the motion of point vortices on s 2 and h 2 the set of first integrals for each hamiltonian shows a corresponding algebraic property in terms of the poisson bracket defined respectively for s 2 and h 2 as an example of analytic solutions the motion of a vortex pair dipole is considered it is shown that a dipole draws a geodesic curve as its trajectory on s 2 and h 2

comparison of regularization methods for solving the cauchy problem associated with the helmholtz equation in this paper several boundary element regularization methods such as iterative conjugate gradient tikhonov regularization and singular value decomposition methods for solving the cauchy problem associated to the helmholtz equation are developed and compared regularizing stopping criteria are developed and the convergence as well as the stability of the numerical methods proposed are analysed the cauchy problem for the helmholtz equation can be regularized by various methods such as the general regularization methods presented in this paper but more accurate results are obtained by classical methods such as the singular value decomposition and the tikhonov regularization methods copyright 2004 john wiley sons ltd

marching schemes for inverse scattering problems in waveguides with curved boundaries abstract a marching scheme is developed for inverse scattering problems of the helmholtz equation in waveguides with curved boundaries we implement a local orthogonal transform to transform the irregular waveguide in physical plane into a regular rectangle in computing plane then the modified helmholtz system in computational domain is piecewise solved through a second order numerical marching scheme and we propose a spectral projector based on the truncated local propagating eigenfunction expansion to regularize the marching scheme in the end the marching scheme is verified by extensive numerical experiments and it is shown that the scheme is efficient stable and accurate in rapidly varying waveguides with curved boundaries even when the number of propagating modes in the main propagation direction is variable

the sample complexity of worst case identification of fir linear systems we consider the problem of identification of linear systems in the presence of measurement noise which is unknown but bounded in magnitude by some 0 we focus on the case of linear systems with a finite impulse response it is known that the optimal identification error is related within a factor of 2 to the diameter of a so called uncertainty set and that the latter diameter is upper bounded by 2 if a sufficiently long identification experiment is performed we establish that for any k 1 the minimal length of an identification experiment that is guaranteed to lead to a diameter bounded by 2k behaves like 2nf 1k when n is large where n is the length of the impulse response and is a positive function known in closed form while the framework is entirely deterministic our results are proved using probabilistic tools

implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography two integral equation methods are considered which can be inverted to provide the surface velocity and or pressure given a measurement of the pressure on an imaginary surface in the nearfield of a vibrating or scattering body this problem is central to nearfield acoustical holography nah the integral equations are discretized using boundary element methods bems the integral equation methods considered are 1 an indirect formulation method based on the single layer integral equation and 2 a direct formulation method based on a system of equations derived from the helmholtz kirchhoff integral equation the formation of integral equations from the mentioned methods will not involve the explicit inversion of matrices but instead will require this inversion to be done implicitly since these methods back track the sound field from the measurement surface to the surface of the source vibrator they are ill posed in nature and tikhonov regularization are used to stabilize the reconstruction problems a

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

dual reciprocity boundary element method solution of the cauchy problem for helmholtz type equations with variable coefficients in this paper the application of the dual reciprocity boundary element method drbem to the cauchy problem for helmholtz type equations with variable coefficients is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for cauchy problems in smooth and piecewise smooth geometries as well as simply and doubly connected domains the accuracy convergence and stability of the proposed numerical method with respect to various approximating functions various drbem discretizations and various levels of noise added in the boundary data respectively are also analysed

gain scheduling dynamic linear controllers for a nonlinear plant abstract for a general type of nonlinear tracking problem we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points a necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented using this condition the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed and ad hoc approaches to scheduling can be analyzed

identification in h using pick s interpolation the problem of system identification in h is studied using the pick interpolation theorem a tuned nonlinear interpolation algorithm is proposed and the resulting error bound in h norm is derived an example is used to illustrate the use of the interpolation algorithm

relative equilibria of point vortices on the sphere we prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non rotating sphere the proofs use the rotational symmetry group so 3 and the resulting conservation laws the time reversing reflectional symmetries in o 3 and the finite symmetry group of permutations of identical vortices results include both global existence theorems and local results on bifurcations from equilibria a more detailed study is made of relative equilibria which consist of two parallel rings with n vortices in each rotating about a common axis the paper ends with discussions of the bifurcation diagrams for systems of 3 6 identical vortices

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

the motion of point vortices on closed surfaces we develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere when the sum of the vortex circulations is non ze

fading regularization mfs algorithm for the cauchy problem associated with the two dimensional helmholtz equation abstract in this paper we combine the fading regularization method with the method of fundamental solutions mfs and investigate its application to the cauchy problem for the two dimensional helmholtz equation we present a numerical reconstruction of the missing data on an inaccessible part of the boundary from the knowledge of overprescribed noisy data taken on the remaining accessible boundary part for both smooth and piecewise smooth two dimensional geometries the accuracy convergence stability and efficiency of the proposed numerical algorithm as well as its capability to deblur the noisy data are validated by three numerical examples

guaranteed properties of gain scheduled control for linear parameter varying plants abstract gain scheduling has proven to be a successful design methodology in many engineering applications however in the absence of a sound theoretical analysis these designs come with no guarantees on the robustness performance or even nominal stability of the overall gain scheduled design this paper presents such an analysis for one type of gain scheduled system namely a linear parameter varying plant scheduling on its exogenous parameters conditions are given which guarantee that the stability robustness and performance properties of the fixed operating point designs carry over to the global gain scheduled design these conditions confirm and formalize popular notions regarding gain scheduled design such as the scheduling variable should vary slowly

reconstructing interior acoustic pressure fields via helmholtz equation least squares method this paper extends the helmholtz equation least squares hels method previously developed by wang and wu j acoust soc am 102 2020 2032 1997 to reconstruction of acoustic pressure fields inside the cavity of a vibrating object the acoustic pressures are reconstructed through an expansion of the acoustic modes generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation such an expansion is uniformly convergent because the selected acoustic modes consist of a uniformly convergent series of legendre functions the coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method numerical examples of partially vibrating spheres and cylinders with various half length to radius aspect ratios subject to different frequency excitations are demonstrated the recon