electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate we consider a two dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate the magnetic permeability is assumed to be a fixed positive constant in the media the material properties of the media are characterized completely by an index of refraction which is a bounded measurable function in the layer and a positive constant above the layer corresponding to a homogeneous dielectric medium in this paper we only examine the tm transverse magnetic polarization case a radiation condition is introduced and equivalence with a second kind lippmann schwinger type integral equation is shown with additional assumptions on the index of refraction in the layer uniqueness of solution is proved existence of solution is then established by employing a form of fredholm alternative using a general result on the solvability of integral equations on unbounded domains published earlier by chandler wilde and zhang an approximate analytic solution for the case of a thin inhomogeneous layer is obtained from the integral equation formulation and is used to show that if the index of refraction is appropriately chosen the scattered field can grow with distance from the plate

efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane this paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance the solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary and the discussion of the paper is motivated by this application the paper starts by deriving representations as laplace type integrals of the solution and its first partial derivatives the evaluation of these integral representations by gauss laguerre quadrature is discussed and theoretical bounds on the truncation error are obtained specific approximations are proposed which are shown to be accurate except in the very near field for all angles of incidence and a wide range of values of surface impedance the paper finishes with derivations of partial results and analogous laplace type integral representations for the case of a point source

on the derivation of the numerical permittivity and stability of the cds fdtd implementation of high order constitutive relations recently the derivation of the numerical permittivity and stability of the finite difference time domain fdtd implementation of a 4 pole complex rational function by using the central difference scheme cds have been studied in this communication the accuracy and the stability limitation of this scheme are investigated in addition alternative fdtd implementation based on the mobius transformation mt is presented it is observed that the cds implementation is less accurate and more stability restrictive than the mt counterpart

reflection of an acoustic line source by an impedance surface with uniform flow abstract an exact analytic solution is derived for the 2d acoustic pressure field generated by a time harmonic line mass source located above an impedance surface with uniform grazing flow closed form asymptotic solutions in the far field are also provided the analysis is valid for both locally reacting and nonlocally reacting impedances as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface the analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface the line source is found to excite surface waves on the impedance surface some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow the surface waves may be treated either correctly as unstable waves or artificially as stable waves enabling comparison with previous numerical or mathematical studies which make either of these assumptions the computer code for evaluating the analytic solution and far field asymptotics is provided in the supplementary material it is hoped this work will provide a useful benchmark solution for validating 2d numerical acoustic codes

fdtd dispersive modeling of human tissues based on quadratic complex rational function we propose a dispersive finite difference time domain fdtd suitable for the electromagnetic analysis of human tissues the dispersion relation of biological tissues is characterized by a quadratic complex rational function qcrf that leads to an accurate fdtd algorithm in 400 mhz 3 ghz qcrf coefficients are extracted by applying the complex curve fitting technique without initial guess numerical examples are used to illustrate the computational accuracy and stability of qcrf based fdtd

equations for finite difference time domain simulation of sound propagation in moving inhomogeneous media and numerical implementation finite difference time domain fdtd calculations are typically performed with partial differential equations that are first order in time equation sets appropriate for fdtd calculations in a moving inhomogeneous medium with an emphasis on the atmosphere are derived and discussed in this paper two candidate equation sets both derived from linearized equations of fluid dynamics are proposed the first which contains three coupled equations for the sound pressure vector acoustic velocity and acoustic density is obtained without any approximations the second which contains two coupled equations for the sound pressure and vector acoustic velocity is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure it is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere practical fdtd implementation of the second set of equations is discussed results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform high mach number flow and with fast field program calculations of sound propagation in a stratified moving atmosphere

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

a fast direct solver for quasi periodic scattering problems abstract we consider the numerical solution of the scattering of time harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium in two dimensions boundary integral formulations are ideal since they reduce the problem to n unknowns on the obstacle boundary however for complex geometries and or higher frequencies the resulting dense linear system becomes large ruling out dense direct methods and often ill conditioned despite being 2nd kind rendering fast multipole based iterative schemes also inefficient we present an integral equation based solver with o n complexity which handles such ill conditioning using recent advances in fast direct linear algebra to invert hierarchically the isolated obstacle matrix this is combined with a recent periodizing scheme that is robust for all incident angles including wood s anomalies based upon the free space green s function kernel the resulting solver is extremely efficient when multiple incident angles are needed as occurs in many applications our numerical tests include a complicated obstacle several wavelengths in size with n 10 5 and solution error of 10 10 where the solver is 66 times faster per incident angle than a fast multipole based iterative solution and 600 times faster when incident angles are chosen to share bloch phases

fast preconditioned conjugate gradient algorithms for wiener hopf integral equations in this paper the authors study circulant approximations of finite sections of a wiener hopf integral equation on the half line such circulant operators are defined by periodic kernel functions they approximate finite sections of the wiener hopf operator within a sum of a small operator and an operator with fixed finite rank constructions are given of two such circulant operators and their use as preconditioners for the conjugate gradients algorithm is explained numerical examples are included to illustrate the results

a generalized recursive convolution method for time domain propagation in porous media an efficient numerical method referred to as the auxiliary differential equation ade method is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media for this purpose the relaxation functions are approximated in the frequency domain by rational functions the time variation of the convolution is thus governed by first order differential equations which can be straightforwardly solved the accuracy of the method is first investigated and compared to that of recursive convolution methods it is shown that while recursive convolution methods are first or second order accurate in time the ade method does not introduce any additional error the ade method is then applied for outdoor sound propagation using the equations proposed by wilson et al in the ground 2007 appl acoust 68 173 200 a first one dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications finally the ade method is used to compute sound propagation in a three dimensional geometry over an absorbing ground results obtained with wilson s equations are compared to those obtained with zwikker and kosten s equations and with an impedance surface for different flow resistivities

sound radiation by a moving line source above an impedance plane with frequency dependent properties abstract an analytic solution for the problem of sound radiation by a harmonic line source moving at a uniform subsonic speed parallel to an impedance plane is proposed the main originality of this work is that the variation of the impedance with the frequency is taken into account compared to the case of a constant impedance the reflection coefficient and the location of its poles in the complex plane are modified a uniform asymptotic expression is then developed for moderate mach numbers and a closed form expression corresponding to a weyl van der pol formula is proposed for a grazing incidence for hard grounds and for low mach numbers unlike previous analytical solutions derived in the literature for a point source the impedance is evaluated at the doppler frequency instead of at the source frequency the analytical solution and asymptotic expressions are then compared satisfactorily to a numerical solution obtained from a time domain solver of the linearized euler equations finally a parametric study is carried out showing that the assumption of a constant impedance is valid if the source mach number remains small typically less than 0 2 and if the source is not too close to the ground

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

efficient calculation of two dimensional periodic and waveguide acoustic green s functions new representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane and for the green s function for sound propagation in the canyon formed by two infinitely high parallel rigid or sound soft walls and an impedance ground surface the infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a laplace type integral a pole subtraction technique is used to remove poles in the integrand which lie near the path of integration obtaining a smooth integrand more suitable for numerical integration and a specific numerical integration method is proposed numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types it is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts and for problems of scattering by periodic surfaces

numerical analysis of graded mesh methods for a class of second kind integral equations on the real line abstract in this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form s s r s t z t t dt s r where l 1 r z l r and bc r the space of bounded continuous complex valued functions on r are assumed known and the function bc r is to be determined we introduce some new graded meshes for the collocation method of the integral equation which are different from those used previously for the wiener hopf integral equation in the case when the solution decays exponentially at infinity and establish optimal local and global l norm error estimates under the condition that the solution decays only polynomially at infinity

fdtd dispersive modeling with high order rational constitutive parameters in this work we present a dispersive finite difference time domain fdtd algorithm using a four pole complex rational function crf for the sake of a better curve fitting of the four pole crf dispersion model we use a particle swarm optimization technique we also discuss an efficient memory storage strategy using a state space approach the numerical aspects of four pole crf fdtd the numerical accuracy and the numerical stability are investigated in detail numerical examples are used to validate four pole crf fdtd and numerical stability issues are discussed in detail we also discuss the computational accuracy and the computational efficiency of an arbitrary n pole crf fdtd

fractional calculus based fdtd algorithm for ultrawideband electromagnetic characterization of arbitrary dispersive dielectric materials a novel finite difference time domain algorithm for modeling ultrawideband electromagnetic pulse propagation in arbitrary multirelaxed dispersive media is presented the proposed scheme is based on a general yet computationally efficient series representation of the fractional derivative operators associated with the permittivity functions describing the frequency dispersion properties of a given dielectric material dedicated uniaxial perfectly matched layer boundary conditions are derived and implemented in combination with the basic time marching scheme moreover a total field scattered field formulation is adopted in order to analyze the material response under plane wave excitation compared with alternative numerical methodologies available in the scientific literature the proposed technique features a significantly enhanced accuracy in the solution of complex electromagnetic propagation problems involving higher order dispersive dielectrics such as the ones typically encountered in geoscience and bioengineering applications

scattering by infinite one dimensional rough surfaces we consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane this problem models time harmonic electromagnetic scattering by a one dimensional infinite rough perfectly conducting surface the same problem arises in acoustic scattering by a sound soft surface chandler wilde and zhang have suggested a radiation condition for this problem a generalization of the rayleigh expansion condition for diffraction gratings and uniqueness of solution has been established recently an integral equation formulation of the problem has also been proposed and in the special case when the whole boundary is both lyapunov and a small perturbation of a flat boundary the unique solvability of this integral equation has been shown by chandler wilde and ross by operator perturbation arguments in this paper we study the general case with no limit on surface amplitudes or slopes and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers as an important corollary we prove that for a variety of incident fields including the incident plane wave the dirichlet boundary value problem for the scattered field has a unique solution

composite learning from adaptive dynamic surface control in the conventional adaptive control a stringent condition named persistent excitation pe must be satisfied to guarantee parameter convergence this technical note focuses on adaptive dynamic surface control for a class of strict feedback nonlinear systems with parametric uncertainties where a novel technique coined composite learning is developed to guarantee parameter convergence without the pe condition in the composite learning online recorded data together with instantaneous data are applied to generate prediction errors and both tracking errors and prediction errors are utilized to update parametric estimates the proposed approach is also extended to an output feedback case by using a nonlinear separation principle the distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval excitation condition which is much weaker than the pe condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability an illustrative example is used for verifying effectiveness of the proposed approach

stability and exponential stability of an adaptive control scheme for plants of any relative degree relying on a new adaptive pole assignment control scheme for plants with unknown relative degree and uncertain order which can be made minimum phase by means of a relative degree one first order parallel compensator a new adaptation mechanism is proposed in this note in order to tackle with the problem of the attainment of an exponentially stable behavior of the output error in particular the connection between exponential stability and persistent excitation is outlined and a complete stability analysis is performed

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

brief paper composite adaptive control for euler lagrange systems with additive disturbances in a typical adaptive update law the rate of adaptation is generally a function of the state feedback error ideally the adaptive update law would also include some feedback of the parameter estimation error the desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback in all previous composite adaptive controllers the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters lp uncertainty the presence of additive disturbances that are not lp would destroy the prediction error formulation and stability analysis arguments in previous results in this paper a new prediction error formulation is constructed through the use of a recently developed robust integral of the sign of the error rise technique the contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the lp assumption e g additive bounded disturbances a composite adaptive controller is developed for a general mimo euler lagrange system with mixed structured i e lp and unstructured uncertainties a lyapunov based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi global asymptotic tracking experimental results are presented to illustrate the approach

heuristic approximations for sound fields produced by spherical waves incident on locally and non locally reacting planar surfaces the classic weyl van der pol wvdp formula is a well known asymptotic solution for accurately predicting sound fields above a locally reacting ground surface however the form of the wvdp formula is inadequate for predicting sound fields in the vicinity of non locally reacting surfaces a correction term is often required in the formula to provide accurate numerical solutions even with this correction there is a singularity in the diffraction wave term when the source is located directly above or below the receiver this paper explores a heuristic method to remove this singularity and suggests an analytical form comparable to the wvdp formula this improved formula offers a physically interpretable solution and allows for accurate predictions of the total sound field above locally and non locally reacting surfaces for all geometrical configurations

stability considerations for the direct fdtd implementation of the dispersive quadratic complex rational function models in this communication detailed stability considerations for the direct finite difference time domain implementation of the dispersive quadratic complex rational function models are investigated it is shown that the time step stability limit of this numerical scheme is more restrictive than the previously published constrain in addition it is found that by using high spatial resolution the stability limit tends to retain the classical courant friedrichs lewy constrain numerical examples are included to verify these results

preconditioners for wiener hopf equations with high order quadrature rules we consider solving the wiener hopf equations with high order quadrature rules by preconditioned conjugate gradient pcg methods we propose using convolution operators as preconditioners for these equations we will show that with the proper choice of kernel functions for the preconditioners the resulting preconditioned equations will have clustered spectra and therefore can be solved by the pcg method with superlinear convergence rate moreover the discretization of these equations by high order quadrature rules leads to matrix systems that involve only toeplitz or diagonal matrix vector multiplications and hence can be computed efficiently by ffts numerical results are given to illustrate the fast convergence of the method and the improvement on accuracy by using higher order quadrature rule we also compare the performance of our preconditioners with the circulant integral operators

some new discretization and adaptation and multigrid methods for 2 d 3 t diffusion equations in the simulation of laser driven implosion of a fuel capsule in inertial confinement fusion experiments a system of two dimensional diffusion equations coupled with electron iron and photon temperature are widely used to approximately describe the process of energy across multiple materials and the exchange of energy among electrons irons and photons the numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces in this article we design a symmetric finite volume method develop the corresponding preconditioning technique and propose a mesh adaptation algorithm based on hessian matrix and a two grid method using these new methods we demonstrate that the energy conservation error and computation efficiency of the integrated algorithm are much better than classical method

sound propagation above an inhomogeneous plane boundary integral equation methods abstract a boundary integral equation method is used to compute the sound pressure emitted by a harmonic source above an inhomogeneous plane first the theoretical aspects of the problem behaviour of the pressure around the discontinuities are studied then a comparison between theoretical levels and experimental levels obtained in an anechoic room is presented it shows that the boundary integral equation bie method is quite convenient for solving this kind of problem two interesting results are pointed out i if only a prediction of maximum sound levels is needed the attenuation is the same for a cylindrical source a spherical source and n spherical sources and so it is possible to transform some three dimensional problems into two dimensional ones ii a numerical method of computation of the sound field above an inhomogeneous plane does not provide a correct prediction if each part of the plane is not accurately described by the boundary condition chosen

modular adaptive control of uncertain euler lagrange systems with additive disturbances a novel adaptive nonlinear control design is developed which achieves modularity between the controller and the adaptive update law modularity between the controller update law design provides flexibility in the selection of different update laws that could potentially be easier to implement or used to obtain faster parameter convergence and or better tracking performance for a general class of linear in the parameters lp uncertain euler lagrange systems subject to additive bounded non lp disturbances the developed controller uses a model based feedforward adaptive term in conjunction with the recently developed robust integral of the sign of the error rise feedback term modularity in the adaptive feedforward term is made possible by considering a generic form of the adaptive update law and its corresponding parameter estimate this generic form of the update law is used to develop a new closed loop error system and stability analysis that does not depend on nonlinear damping to yield the modular adaptive control result

a two grid discretization method for decoupling systems of partial differential equations in this paper we propose a two grid finite element method for solving coupled partial differential equations e g the schrodinger type equation with this method the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid it is shown both theoretically and numerically that the resulting solution still achieves asymptotically optimal accuracy

energy based approach to sliding composite adaptive control for rigid robots with finite error convergence time in this paper a terminal sliding mode adaptive control scheme for robotic manipulators designed following an energybased approach is presented the control comprises two basic terms a composite adaptive term which implements a feedback law for compensating the modelled dynamics and a non linear sliding mode term for overcoming the unmodelled dynamics and perturbations the resulting closed loop system is proved to be stable and it is also shown that the trajectory tracking error converges to zero in finite time moreover an upper bound of this error convergence time is calculated finally the design is evaluated by means of simulations

full wave modeling of therapeutic ultrasound efficient time domain implementation of the frequency power law attenuation for the simulation of therapeutic ultrasound applications a method including frequency dependent attenuation effects directly in the time domain is highly desirable this paper describes an efficient numerical time domain implementation of the power law attenuation model presented by szabo szabo j acoust soc am 96 491 500 1994 simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time domain fdtd algorithm for nonlinear ultrasound propagation ginter et al j acoust soc am 111 2049 2059 2002 szabo implemented the empirical frequency power law attenuation using a causal convolutional operator directly in the time domain equation though a variety of time domain models has been published in recent years no efficient numerical implementation has been presented so far for frequency power law attenuation models solving a convolutional integral with standard time domain techniques requires enormous computational ef

acoustic scattering by an inhomogeneous layer on a rigid plate the problem of scattering of time harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in r 2 is considered the density is assumed to be unity in the media within the layer the sound speed is assumed to be an arbitrary bounded measurable function the problem is modelled by the reduced wave equation with variable wavenumber in the layer and a neumann condition on the plate to formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced a generalization of the rayleigh expansion condition for diffraction gratings with the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate under additional assumptions on the wavenumber in the layer uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established general results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

brief paper adaptive inverse dynamics control of robots with uncertain kinematics and dynamics it has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties however not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution this adaptive controller belongs to passivity based control though passivity based controllers have many attractive properties in general they are not able to guarantee the uniform performance of the robot over the entire workspace even in the ideal case of perfect knowledge of the manipulator parameters the closed loop system remains nonlinear and coupled thus the closed loop tracking performance is difficult to quantify while the inverse dynamics controllers can overcome these deficiencies therefore in this work we will develop a new adaptive jacobian tracking controller based on the inverse manipulator dynamics using the lyapunov approach we have proved that the end effector motion tracking errors converge asymptotically to zero simulation results are presented to show the performance of the proposed controller

monte carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the bmia canonical grid method scattering of a te incident wave from a perfectly conducting one dimensional random rough surface is studied with the banded matrix iterative approach canonical grid bmia cag method the bmia cag is an improvement over the previous bmia the key idea of bmia cag is that outside the near field interaction the rest of the interactions can be translated to a canonical grid by taylor series expansion the use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast fourier transform for nonnear field interaction the method can be used for monte carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface we illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns the method is also applied to study scattering from random rough surfaces at near grazing incidence the numerical examples illustrate the importance of using a large surface length for some backscattering problems

adaptive vision based control of a motor toggle mechanism simulations and experiments the dynamic motion of an adaptive visual servoing feedback controlled punching machine which is made up by a toggle mechanism driven by a permanent magnet pm synchronous servomotor is studied numerically and experimentally first hamilton s principle lagrange multiplier geometric constraints and partitioning method are employed to derive its dynamic equations for numerical simulations to satisfy the demand of the machine performance adaptive controller by using stability analysis with inertia related lyapunov function is designed to control the slider responses different from the previous studies the vision servo system of a non contact measurement of a charge coupled device ccd camera is employed to measure the shape patterns as output states instead of using the expensive linear scale or encoder of the motor mechanism system finally the stable and robust control performances of an adaptive controller by the lyapunov stable theory for a motor toggle mechanism with external disturbances are proposed a combination of the visual servoing measurement system and the motion control system are established experimentally for the motor toggle mechanism system from the agreements between numerical simulations and experimental results it is demonstrated that the proposed controller by use of machine vision is robust to external disturbances for a punching machine system

homography based visual servo control with imperfect camera calibration in this technical note a robust adaptive uncalibrated visual servo controller is proposed to asymptotically regulate a robot end effector to a desired pose a homography based visual servo control approach is used to address the six degrees of freedom regulation problem a high gain robust controller is developed to asymptotically stabilize the rotation error and an adaptive controller is developed to stabilize the translation error while compensating for the unknown depth information and intrinsic camera calibration parameters a lyapunov based analysis is used to examine the stability of the developed controller

a fast two grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half plane we consider the numerical treatment of second kind integral equations on the real line of the form phi s psi s int infty infty k s t z t phi t dt s in mathbb r abbreviated k z in which l 1 z l and bc the space of bounded continuous functions on are assumed known and bc is to be determined we first derive sharp error estimates for the finite section approximation reducing the range of integration to a a via bounds on i k z 1 as an operator on spaces of weighted continuous functions numerical solution by a simple discrete collocation method on a uniform grid on is then analysed in the case whenz is compactly supported this leads to a coefficient matrix which allows a rapid matrix vector multiply via the fft to utilise this possibility we propose a modified two grid iteration a feature of which is that the coarse grid matrix is approximated by a banded matrix and analyse convergence and computational cost in cases wherez is not compactly supported a combined finite section and two grid algorithm can be applied and we extend the analysis to this case as an application we consider acoustic scattering in the half plane with a robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied our final result is that ifz related to the boundary impedance in the application takes values in an appropriate compact subsetq of the complex plane then the difference between s and its finite section approximation computed numerically using the iterative scheme proposed is c 1 khlog 1 kh 1 1 2 ka 1 2 in the interval a a 1 forkh sufficiently small wherek is the wavenumber andh the grid spacing moreover this numerical approximation can be computed in c 2 n logn operations wheren 2a h is the number of degrees of freedom the values of the constantsc 1 andc 2 depend only on the setq and not on the wavenumberk or the support ofz

an improved dynamic neurocontroller based on christoffel symbols in this paper a dynamic neurocontroller for positioning of robots based on static and parametric neural networks nns has been developed this controller is based on christoffel symbols of first kind in order to carry out coriolis centripetal matrix structural properties of robots and kronecker product has been taken into account to develop nns to approximate nonlinearities the weight updating laws have been obtained from a nonlinear strategy based on lyapunov energy that guarantees both stability and boundedness of signals and weights the nn weights are tuned online with no offline learning phase and are initialized to zero the neurocontroller improves the implementation with respect to other dynamic nns used in the literature

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

an indirect adaptive robot controller abstract indirect adaptive control of robot manipulators represents an approach parallel to direct and composite adaptive methods this paper develops a new globally convergent indirect adaptive controller which requires neither measurements of joint acceleration nor inversion of the estimated inertia matrix several aspects of this paper such as new parameter estimators with desirable properties and a physically based technique for guaranteeing the uniform positive definiteness of the estimated inertia matrix along with the related convexity proof are also of interest in their own right

wavenumber explicit analysis for the helmholtz h bem error estimates and iteration counts for the dirichlet problem we consider solving the exterior dirichlet problem for the helmholtz equation with the h version of the boundary element method bem using the standard second kind combined field integral equations we prove a new sharp bound on how the number of gmres iterations must grow with the wavenumber k to have the error in the iterative solution bounded independently of k as k rightarrow infty when the boundary of the obstacle is analytic and has strictly positive curvature to our knowledge this result is the first ever sharp bound on how the number of gmres iterations depends on the wavenumber for an integral equation used to solve a scattering problem we also prove new bounds on how h must decrease with k to maintain k independent quasi optimality of the galerkin solutions as k rightarrow infty when the obstacle is nontrapping

adaptive control for robot manipulators using discrete time identification an adaptive control scheme is proposed for rigid link robots where the control signal computations are performed continuously and the control coefficient computations are performed in discrete time a global boundedness result is established for the resulting scheme independent of the sampling rate it is also shown that the position velocity and acceleration tracking errors are of the order of the sampling period furthermore it is shown that if the reference trajectory is persistently exciting in a continuous time sense then for a sufficiently fast sampling rate the tracking errors decay to zero

pade approximants for the acoustical characteristics of rigid frame porous media in this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media especially those involving ratios of bessel functions of complex argument can be accurately approximated and greatly simplified by the use of pade approximation techniques in the case of the model of attenborough j acoust soc am 81 93 102 1987 rational approximations are produced for the characteristic impedance propagation constant dynamic compressibility and dynamic density as a function of frequency and the material parameters the model proposed by stinson and champoux j acoust soc am 91 685 695 1992 is approximated via rational approximation for the viscosity correction function

on the solvability of a class of second kind integral equations on unbounded domains we consider integral equations of the form x x k x y z y y dy in operator form kz where is some subset ofrn n 1 the functionsk z and are assumed known withz l and y the space of bounded continuous functions on the function yis to be determined the class of domains and kernelskconsidered includes the case rnandk x y x y with l1 rn in which case ifzis the characteristic function of some setg the integral equation is one of wiener hopf type the main theorems proved using arguments derived from collectively compact operator theory are conditions on a setw l which ensure that ifi kzis injective for allz wtheni kzis also surjective and moreover the inverse operators i kz 1onyare bounded uniformly inz these general theorems are used to recover classical results on wiener hopf integral operators of21and19 and generalisations of these results and are applied to analyse the lippmann schwinger integral equation

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

solvability and spectral properties of integral equations on the real line i weighted spaces of continuous functions abstract we consider in this paper the solvability of linear integral equations on the real line in operator form k where c and k is an integral operator we impose conditions on the kernel k of k which ensure that k is bounded as an operator on x bc r let xa denote the weighted space x a x s o s a as s our first result is that if additionally k s t s t with l 1 r and s o s b as s for some b 1 then the spectrum of k is the same on xa as on x for 0 k k k w which ensure that if 0 and kk has only the trivial solution in x for all k w then for 0 a b k has exactly one solution xa for every k w and xa these conditions ensure further that k 1 x a x a is bounded uniformly in k w for 0 a b as a particular application we consider the case when the kernel takes the form k s t s t z t with l 1 r z l r and s o s b as s for some b 1 as an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the helmholtz equation in a half plane

sound propagation above an inhomogeneous impedance plane abstract boundary integral equation bie methods are described for the prediction of sound propagation in particular from a line source over a flat plane of inhomogeneous impedance approximate methods which satisfy reciprocity for the calculation of the wave field over a two impedance plane are proposed these approximations applied to propagation from a line source give results agreeing well with those of the bie method when they are applied to propagation from a point source agreement with experiment is shown

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

adaptive visual servoing scheme free of image velocity measurement for uncertain robot manipulators this work addresses the visual tracking problem of robot manipulators with non negligible dynamics using a fixed camera when the camera robot system parameters are uncertain an adaptive strategy is developed for visual servoing systems based on the image based look and move structure to allow the tracking of a 2d reference trajectory without using image velocity measurements the adaptive visual servoing problem free of image velocity information is formulated as a relative degree two mimo adaptive control problem as a solution we employ a recently proposed lyapunov passivity based adaptive control scheme based on the sdu factorization method from a cascade control strategy the resulting online camera calibration scheme is combined with a direct adaptive motion controller for the robot manipulator which takes into account its uncertain nonlinear dynamics the overall stability of the adaptive visual servoing system can be proved thanks to the explicit lyapunov like functions of both adaptation schemes

prediction of the attenuation of road traffic noise with distance abstract a method is described of calculating the sound pressure level received from single representative light and heavy vehicles after propagation over terrain composed of various combinations of hard ground and grass land these results are then used to derive correction contours for the attenuation with distance of the leq level received from streams of each class of vehicle the results apply to conditions where the boundary between the soft and hard areas is parallel to the traffic stream and the soft ground is on the receiver side various positions of the boundary are considered a simple prediction method for leq is developed incorporating the distance corrections similar calculations are carried out for the attenuation with distance of the l10 noise index for a representative stream of vehicles based on these results simple prediction equations for the excess attenuation are proposed in terms of the receiver position and the proportion of soft ground below the propagation path

pade approximation in time domain boundary conditions of porous surfaces formulation and implementation of time domain boundary conditions tdbcs at the surface of a reactive porous material are made challenging by the slow decay complexity or noncausal nature of many commonly used models of porous materials in this paper approaches are described that improve computational efficiency and enforce causality one approach involves approximating the known tdbc for the modified zwikker kosten impedance model as a summation of decaying exponential functions a second approach which can be applied to any impedance model involves replacing the characteristic admittance with its pade approximation then approximating fractional derivatives with decaying exponentials a causal and recursive tdbc is formulated

the algorithm for computing nonmonic second order multivariable systems abstract an efficient method for computing impulse response matrices of nonmonic multivariable second order systems is proposed a procedure has been developed which uses some properties of regular matrix polynomials p s s 2 a 2 sa 1 a 0 with a 2 identically singular an algorithm suitable for computer use is established and its applications can be effectively controlled via the newly introduced special graphical scheme it produces simultaneously the adjoint and determinant of the matrix polynomial p s and avoids the inversion of any matrix moreover all computations can be performed on constant matrices and coefficients only it is shown that substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many physical plants and engineering structures

second order consensus of networked thrust propelled vehicles on directed graphs this technical note addresses the second order consensus problem of multiple underactuated thrust propelled vehicles tpvs on directed graphs containing a directed spanning tree we propose an adaptive control approach to resolve this problem and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the tpvs in addition the resultant complexity is reduced and the requirement on the interaction graph is relaxed using an input output analysis we show that the proposed controller realizes second order consensus of the tpvs i e the position and velocity consensus errors between the tpvs converge to zero and moreover the velocities of the tpvs converge to the weighted average of their initial values the performance of the proposed control approach is shown by a numerical simulation

brief paper adaptive jacobian vision based control for robots with uncertain depth information this paper presents a simple vision based setpoint controller with adaptation to uncertainty in depth information depth uncertainty plays a special role in vision based control as it appears nonlinearly in the overall jacobian matrix and hence cannot be adapted together with other uncertain kinematic parameters we propose a novel parameter update law to update the uncertain parameters of the depth it is proved that system stability can be guaranteed for the vision regulation task in presence of uncertainties in depth information robot kinematics and dynamics simulation results are presented to illustrate the performance of the proposed controller

dealing with time varying parameter problem of robot manipulators performing path tracking tasks using the properties of the element by element or hadamard product of matrices the authors obtain the robot dynamics in parameter isolated form from which a new control scheme is developed the controller proposed yields zero asymptotic tracking errors when applied to robotic systems with time varying parameters by using a switching type control law the results obtained are global in the initial state of the robot and can be applied to rapidly varying systems

brief paper tracking and disturbance rejection for fully actuated mechanical systems in this paper we solve the tracking and disturbance rejection problem for fully actuated passive mechanical systems we assume that the reference signal r and its first two derivatives r r are available to the controller and the disturbance signal d can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an arbitrary l 2 signal we combine the internal model principle with the ideas behind the slotine li adaptive controller the internal model based adaptive controller that we propose causes the closed loop state trajectories to be bounded and the tracking error and its derivative to converge to zero without any prior knowledge of the plant parameters an important part of our results is that we prove the existence and uniqueness of the state trajectories of the closed loop system

composite model reference adaptive control with parameter convergence under finite excitation a new parameter estimation method is proposed in the framework of composite model reference adaptive control for improved parameter convergence without persistent excitation the regressor filtering scheme is adopted to perform the parameter estimation with signals that can be obtained easily a new framework for residual signal construction is proposed the incoming data are first accumulated to build the information matrix and then its quality is evaluated with respect to a chosen measure to select and store the best one the information matrix is built to have full rank after sufficient but not persistent excitation in this way the exponential convergence of both tracking error and parameter estimation error can be guaranteed without persistent oscillation in the external command which drives the system numerical simulations are performed to verify the theoretical findings and to demonstrate the advantages of the proposed adaptation law over the standard direct adaptation law

a wavenumber independent boundary element method for an acoustic scattering problem in this paper we consider the impedance boundary value problem for the helmholtz equation in a half plane with piecewise constant boundary data a problem which models for example outdoor sound propagation over inhomogeneous flat terrain to achieve good approximation at high frequencies with a relatively low number of degrees of freedom we propose a novel galerkin boundary element method using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that on each element the approximation space contains polynomials of degree nu multiplied by traces of plane waves on the boundary we prove stability and convergence and show that the error in computing the total acoustic field is cal o n nu 1 log 1 2 n where the number of degrees of freedom is proportional to n log n this error estimate is independent of the wavenumber and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity

prediction error based adaptive jacobian tracking of robots with uncertain kinematics and dynamics in this note we have proposed a prediction error based adaptive jacobian controller to solve the problem of concurrent adaptation to both uncertain kinematics and dynamics this controller is composed of a modified computed torque controller and two cushion floor least square estimators and in ideal case of perfect knowledge of the robot parameters it leads to linear and decoupled error dynamics the kinematic and dynamic parameters adaptations are driven by prediction errors using input output stability analysis we show that the end effector motion tracking errors converge asymptotically we have also derived an alternative adaptive jacobian controller that does not require the invertibility of the estimated inertia matrix simulation results are presented to show the performance of the proposed controllers

hybrid adaptive fuzzy identification and control of nonlinear systems we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller and adaptive fuzzy identification model parameters first using adaptive fuzzy building blocks with a common set of parameters we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems we then propose a hybrid adaptive ha law for adjusting the parameters the ha law utilizes two types of errors in the adaptive system the tracking error and the modeling error performance analysis using a lyapunov synthesis approach proves the superiority of the ha law over the direct adaptive da method in terms of faster and improved tracking and parameter convergence furthermore this is achieved at negligible increased implementation cost or computational complexity we prove a theorem that shows the properties of this hybrid adaptive fuzzy control system i e bounds for the integral of the squared errors and the conditions under which these errors converge asymptotically to zero are obtained finally we apply the hybrid adaptive fuzzy controller to control a chaotic system and the inverted pendulum system

a uniformly valid far field asymptotic expansion of the green function for two dimensional propagation above a homogeneous impedance plane abstract a generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived the expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance including the limiting cases of zero and infinite impedance the technique used is a rigorous application of the modified steepest descent method of ott 1

green s function for a plane three dimensional fluid layer at small horizontal distances from the source the green s function for a plane three dimensional layer in its common form is usually determined as an infinite series of the waveguide s normal modes the slow convergence of the series close to the source limits the applicability of green s function to solving sound generation and scattering problems in waveguides especially if near field effects are significant in the present work a more convenient form of green s function for such a waveguide is obtained as a sum of two quickly converging series the first series is a difference between the green s functions for helmholtz and laplace equations whereas the second series is green s function for the laplace equation determined as a sum of the mirror images of the source in the waveguide boundaries the behaviour of the obtained function close to the source is investigated numerical experiments show significantly better convergence for the obtained function as compared with the green s function in its common form it is also shown that the obtained function can be easily calculated at the points directly underneath or above the source where the terms of the green s function series in the common form are singular

lyapunov design for convergence rate improvement in adaptive control this note deals with the improvement of the convergence rate and robust properties in an adaptive error model a new adaptive control algorithm is presented which includes both the estimate of the prediction error to drive the parameter adaptation and the proportional integral or integral relay adjustment law to prevent unbounded growth of feedback gains a least squares gain update is used the adaptive controller is constructed using measurements of state variables only the design is based on the lyapunov function method and a new general form of the lyapunov function was found as a result exponential convergence of the lyapunov function in the presence of persistent excitation is obtained

the convergence of nystrom methods for wiener hopf equations we consider second kind integral equations on the half line where the integral operator is a compact perturbation of a convolution operator it is shown that these may be solved numerically by nystrom methods based on composite quadrature rules provided the underlying mesh is graded to correctly match the behaviour of the solution we prove the same rates of convergence that occur when the methods are applied to equations on finite intervals numerical examples are given

adaptive visual tracking for robotic systems without image space velocity measurement in this paper we investigate the visual tracking problem for robotic systems without image space velocity measurement simultaneously taking into account the uncertainties of the camera model and the manipulator kinematics and dynamics we propose a new image space observer that exploits the image space velocity information contained in the unknown kinematics upon which we design an adaptive controller without using the image space velocity signal where the adaptations of the depth rate independent kinematic parameter and depth parameter are driven by both the image space tracking errors and observation errors the major superiority of the proposed observer based adaptive controller lies in its simplicity and the separation of the handling of multiple uncertainties in visually servoed robotic systems thus avoiding the overparametrization problem of the existing work using lyapunov analysis we demonstrate that the image space tracking errors converge to zero asymptotically the performance of the proposed adaptive control scheme is illustrated by a numerical simulation

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized