robust inversion of seismic data using the huber norm the huber function or huber norm is one of several robust error measures which interpolates between smooth l2 treatment of small residuals and robust l1 treatment of large residuals since the huber function is differentiable it may be minimized reliably with a standard gradient based optimizer we propose to minimize the huber function with a quasi newton method that has the potential of being faster and more robust than conjugate gradient methods when solving nonlinear problems tests with a linear inverse problem for velocity analysis with both synthetic and field data suggest that the huber function gives far more robust model estimates than does a least squares fit with or without damping

integral sliding manifold design for linear systems with additive unmatched disturbances this note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances system sensitivity upon an unmatched disturbance vector is assessed by the steady state dependent criterion function the derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion applicability of this method in case of slowly varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance the proposed approach has been demonstrated on a numerical example and verified by simulations

sliding mode control design based on ackermann s formula the sliding mode control methods are developed to design systems which have the desired dynamic behavior and are robust with respect to perturbations it is shown that the discontinuity plane for sliding mode control may be found in an explicit form using ackermann s formula two design procedures are derived first static controllers are designed to enforce sliding modes with the desired dynamic properties after a finite time interval then dynamic controllers are designed that exhibit the desired dynamic properties during the entire control process

sliding mode control of linear systems with mismatched uncertainties abstract it is well known that sliding mode control is robust to matched uncertainties that lie in the range space of the input matrix however many systems are affected by mismatched uncertainties and yet do not enjoy the matching conditions it is the purpose of this paper to present a new dynamical approach of sliding variable formulation which when the system is in sliding mode can explicitly deal with mismatched uncertainties our first step is to treat certain states as inputs to a reduced order system and use adaptive techniques to design fictitious controllers for these inputs which can then tackle the mismatched uncertainties the second step is to use sliding control to realize the adaptive fictitious controllers the design is systematic modular and intuitively simple

fuzzy output tracking control of semi linear first order hyperbolic pde systems with matched perturbations abstract this paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi linear first order hyperbolic partial differential equations pdes firstly a t s fuzzy hyperbolic pde model is assumed to be used to accurately represent the semi linear first order hyperbolic pde system subsequently based on the t s fuzzy pde model the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi linear pde system exponentially tracks a desired reference and the state of the system is uniformly bounded in the filippov sense by constructing a strict lyapunov function the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities lmis in space with an equality constraint it has been shown that when these algebraic lmis with an equality constraint are feasible fuzzy tracking control design can be obtained via the existing convex optimization techniques finally the developed design methodology is successfully applied to the control of a semi linear lotka volterra pde system and the achieved results illustrate its effectiveness

comparison of source independent methods of elastic waveform inversion in this paper we investigate several source independent methods of nonlinear full waveform inversion of multicomponent elastic wave data this includes iterative estimation of source signature ies standard trace normalization stn and average trace normalization atn inversion methods all are based on the finite element method in the frequency domain one synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature kss inversion method the numerical experiments show that the ies method is superior to both stn and atn methods in two component elastic wave inversion in the frequency domain when the source signature is unknown the stn and atn methods have limitations associated with near zero amplitudes or polarity reversals in traces from one of the components which destroy the energy balance in the normalized traces and cause a loss of frequency information but the atn method is somewhat superior to the stn method in suppressing random noise and improving stability as the developed formulas and the numerical experiments show we suggest the ies method as a practical procedure for multicomponent seismic inversion

sliding mode control design for nonlinear systems using probability density function shaping in this paper we propose a sliding mode based stochastic distribution control algorithm for nonlinear systems where the sliding mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function kullback leibler divergence is introduced to the stochastic distribution control and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode it is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank condition which is much weaker than the persistent excitation condition the effectiveness of the proposed algorithm is illustrated by simulation

source independent time domain waveform inversion using convolved wavefields application to the encoded multisource waveform inversion full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion this is especially true for an encoded multisource time domain implementation which conventionally requires separate source modeling as well as the fourier transform of wavefields as an alternative we have developed the source independent time domain waveform inversion using convolved wavefields specifically the misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefield plus the convolution of the modeled wavefields with a reference trace from the observed wavefield in this case the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function and thus the effects of the source wavelets are eliminated furthermore because the modeled wavefields play a role of low pass filtering the observed wavefields in the misfit function the frequency selection stra

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

robust source independent elastic full waveform inversion in the time domain abstractaccurate estimation of source wavelet is crucial in a successful full waveform inversion fwi however it cannot be guaranteed in the case of real seismic data we have developed time domain source independent elastic fwi using the convolution based objective function that was originally developed for acoustic fwi we have applied a new time window on the reference traces in the objective function to suppress the noises induced by the convolution and crosscorrelation operations also we have adopted l1 huber and hybrid norm objective functions to improve the antinoise ability of our algorithm we implemented a multiscale inversion strategy to conduct the tests with a quasi newton limited memory broyden fletcher goldfarb shanno l bfgs method to reduce the sensitivity to initial models and to improve the quality of inversion results synthetic tests verified that the new added time window can not only improve the inversion results but also accelerate the convergence rate our method can be

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

nonliner inversion of seismic reflection data in a laterally invariant medium interpretation of seismic waveforms can be expressed as an optimization problem based on a non linear least squares criterion to find the model which best explains the data an initial model is corrected iteratively using a gradient method conjugate gradient at each iteration computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse time propagation of the residuals misfit between the data and the synthetics the two wave fields thus obtained are then correlated an extra forward propagation is required to compute the amplitude of the perturbation along the conjugate gradient direction the number of propagations to be simulated numerically in each iteration equals three times the number of shots since a 2 d finite difference code is employed to solve forward and backward propagation problems the method is general and can handle arbitrary 2 d source receiver configurations and lateral heterogeneities using conventional velocity

source receiver compression scheme for full waveform seismic inversion we have developed a source receiver compression approach for reducing the computational time and memory usage of the acoustic and elastic full waveform inversions by detecting and quantifying the extent of redundancy in the data we assembled a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey because the numbers of these simultaneous sources and receivers could be significantly less than those of the physical sources and receivers the computational time and memory usage of any gradient type inversion method such as steepest descent nonlinear conjugate gradient contrast source inversion and quasi newton methods could be reduced the scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data reduction is done through the elimination of the small eigenvalues consequently this would suppress the effect of noise in the data moreover taking advantage

source independent full waveform inversion of seismic data a set of seismic trace data is collected in an input data set that is first fourier transformed in its entirety into the frequency domain a normalized wavefield is obtained for each trace of the input data set in the frequency domain normalization is done with respect to the frequency response of a reference trace selected from the set of seismic trace data the normalized wavefield is source independent complex and dimensionless the normalized wavefield is shown to be uniquely defined as the normalized impulse response provided that a certain condition is met for the source this property allows construction of the inversion algorithm disclosed herein without any source or source coupling information the algorithm minimizes the error between data normalized wavefield and the model normalized wavefield the methodology is applicable to any 3 d seismic problem and damping may be easily included in the process

2d frequency domain elastic full waveform inversion using time domain modeling and a multistep length gradient approach abstractto decouple the parameters in elastic full waveform inversion fwi we evaluated a new multistep length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction to perform wavefield extrapolations for the inversion we used parallelized high precision finite element fe modeling in the time domain the inversion was implemented in the frequency domain the data were obtained at every subsurface grid point using the discrete fourier transform at each time domain extrapolation step we also used frequency selection to reduce cycle skipping time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data and source wavelet estimation at the receivers over the full frequency spectrum by using a fast fourier transform in the inversion the velocity and density reconstructions behaved differently as a low wavenumber tomography for v

layer oscillations in reaction diffusion systems this paper considers a two component system of reaction diffusion equations involving two parameters varepsilon and tau varepsilon tau u 1 varepsilon 2 u xx f u v qquad v

multiscale seismic waveform inversion iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models e g the marmousi model the primary difficulty being the presence of numerous local minima in the objective function the presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum the multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale at long scales there are fewer local minima and those that remain are further apart from each other thus at long scales iterative methods can get closer to the neighborhood of the global minimum we apply the multigrid method to a subsampled low frequency version of the marmousi data set although issues of source estimation source bandwidth and noise are not treated results show that iterative inversion methods perform much better when employed with a decomposition by scale furthermore the method greatly reduces the computational burden of the inversion that will be of importance for 3 d extensions to the method

efficient calculation of the steepest descent direction for source independent seismic waveform inversion an amplitude approach in seismic waveform inversion if we have no information on source signature we need to invert seismic data and source signature either simultaneously or successively in order to avoid the iterative update of the source signature in waveform inversion based on classical local optimization techniques we propose two source independent objective functions using amplitude spectra of fourier transformed wavefields one is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes the other is achieved by cross multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes in the computation of the steepest descent direction we circumvent explicitly computing the jacobian by employing a matrix formalism of the wave equation in the frequency domain through numerical examples for the marmousi model we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature

on exponential stabilization for a class of neutral type systems with parameter uncertainties an integral sliding mode approach this paper is focused on integral sliding mode control ismc for a class of parameter uncertain neutral type systems with time varying delays ntstd an integral sliding surface functional is firstly constructed for the ntstd then a delay dependent robust stability criterion is established for all admissible uncertainties which can guarantee the sliding mode dynamic system to be robustly exponentially stable under a certain decay rate in addition by solving the generalized eigenvalue problem gevp presented in the subsequent work the global maximal value of the decay rate as well as the condition of exponential stability for the sliding mode system are derived furthermore a sliding mode control smc law is then synthesised to ensure the stability of the closed loop system and the proposed smc law can drive the state of controlled dynamic system into the predefined sliding surface in finite time finally a numerical example is provided to demonstrate the effectiveness of the obtained results

laplace fourier domain elastic full waveform inversion using time domain modeling to obtain subsurface information from onshore seismic exploration data using full waveform inversion fwi based on the acoustic wave equation elastic waves such as ground roll and mode converted waves should be suppressed through heavy preprocessing however such preprocessing deforms not only the elastic waves but also the acoustic waves moreover it is not easy to separate body waves from surface waves in seismic traces for these reasons we need to generate both types of waves in the modeling step to obtain seismic waves that are similar to real seismic waves therefore elastic fwi using the elastic wave equation is necessary to achieve a more accurate fwi in addition elastic fwi can provide better geologic information than acoustic fwi because it inverts the p wavevelocity s wave velocity and density laplace fourier domain elastic fwi is an effective method because it inverts these multiple parameters and can be applied to real seismic data that lack low frequency components however the conventional laplace fourier domain fwi requires a matrix solver with a huge memory cost to perform the modeling in the laplace fourierdomain and memory usage becomes more intensive in the elastic case in the present study we combined time domain wave propagation modeling and laplace fourier domain elastic fwi to invert multiple parameters with less memory cost by using time domain modeling which does not require a matrix solver we obtainedthe forwardand adjoint wavefields withless memory cost the residuals between the recorded and modeled data the virtual sources the hessian matrices and the gradient directions were calculated in the laplace fourier domain to validate the proposed algorithm we performed numerical tests with model 94 synthetic data and benjamin creek real seismic data

principal bifurcations and symmetries in the emergence of reaction diffusion advection patterns on finite domains pattern formation mechanisms of a reaction diffusion advection system with one diffusivity differential advection and robin boundary conditions of danckwerts type are being studied pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions which for the general case of far from instability onsets is conducted using spatial dynamics and numerical continuations the selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model accordingly we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves including solitary against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory hopf instability consequently the resulting pattern selection is qualitatively different from the symmetric finite wavenumber turing or hopf instabilities

nonlinear integral type sliding surface for both matched and unmatched uncertain systems this note presents a new nonlinear integral type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications first the plant with matched uncertainties is considered the resultant closed loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications second the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions numerical results demonstrate the validity of the proposed concept

fast line searches for the robust solution of linear systems in the hybrid l1 l2 and huber norms linear systems of equations arise in traveltime tomography deconvolution and many other geophysical applications nonlinear problems are often solved by successive linearization leading to a sequence of linear systems overdetermined linear systems are solved by minimizing some measure of the size of the misfit or residual the most commonly used measure is the l2 norm squared leading to least squares problems the advantage of least squares problems for linear systems is that they can be solved by methods for example qr factorization that retain the linear behavior of the problem the disadvantage of least squares solutions is that the solution is sensitive to outliers more robust norms approximating the l1 norm can be used to reduce the sensitivity to outliers unfortunately these more robustnorms lead to nonlinear minimization problems even for linear systems and many efficient algorithms for nonlinear minimiza tion problems require line searches one iterative method for solving linear

brief variable structure output feedback control design for a class of uncertain dynamic systems in this paper we consider the problem of designing a variable structure output feedback control vsofc law for a class of uncertain systems with mismatched uncertainty in the state matrix we derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities lmis and we give vsofc strategies we also give a simple design procedure and parameterizations of the linear switching surfaces together with solvability conditions for the given constrained lmis finally we give a design example in order to show the effectiveness of our method

pattern selection in a general model of convection diffusion and catalytic reaction abstract we study the process of pattern selection in a large class of heterogeneous models of catalytic reactor by analyzing the behavior of a simple condensed model which obeys reflection and inversion symmetries and which captures the main features of a detailed model the three variable model incorporates a very fast and long ranged variable which may describe the fluid phase in a mixed plug flow or an axial dispersion reactor or the pore phase in a catalytic particle and two variables a medium ranged activator and a localized inhibitor that describe the solid phase patterns are classified according to their symmetry properties patterns may emerge already with simple bistable kinetics in a plug flow reactor i e a single integrodifferential equation pattern selection is determined by the phase planes spanned by the reactor by the ratio of front residence time to the period of oscillations and by the ratio of convection to fluid phase diffusions terms patterns include stationary or oscillatory fronts or pulses antiphase oscillations which appear at the transition from homogeneous solution unidirectional pulses that are the dominant patterns when mixing is weak and stationary or oscillatory waves that emerge with strong fluid mixing the simple form of the model allows us to suggest a general classification of emerging patterns and to identify the corresponding conditions in term of realistic models of reactors

growth of domains under global constraints abstract we develop growth rates for domains in bistable systems far from equilibrium the governing equation is a bistable reaction diffusion equation including a nonlocal inhibiting term the latter one will be responsible for the existence of stable localized domains the growth of the size of different domains shows quite surprising similarities with coalescence phenomena of droplets in van der waals gases eventually we discuss the possibility of breathing of the domains induced by a time delayed nonlocal interaction

a rectangular grid lattice spring model for modeling elastic waves in poisson s solidsrectangular lsm to model elastic waves lattice spring model lsm combined with the velocity verlet algorithm is a newly developed scheme for modeling elastic waves propagation in solid media unlike conventional wave equations lsm is established on the basis of micro mechanics of the subsurface media which enjoys better dynamic characteristics of elastic systems we present a rectangular grid lsm scheme for elastic waves simulation in poisson solids and the direction dependent elastic constants are deduced to keep the isotropy of the discrete grid the stability condition and numerical dispersion properties of lsm are discussed and compared with other numerical methods two and three dimensional numerical simulations are carried out using the rectangular grid lsm as well as the second and fourth order accuracy staggered finite difference method fdm wavefields obtained by lsm are fairly similar with those by analytical solution ana and fdm which demonstrates the correctness of the proposed scheme and its capability of modeling elast

patterns of temperature pulses on electrically heated catalytic ribbons abstract a rich and intricate variety of spatiotemporal temperature patterns is predicted to exist on the surface of a thin catalytic ribbon the average temperature of which is kept by electrical heating at a preset value when the catalytic surface undergoes slow activation deactivation the control of the average temperature introduces an integral constraint that generates patters that are not observed in its absence this one dimensional system exhibits in addition to a chaotic behavior four basic motions unidirectional pulses back and forth pulses antiphase oscillation and a source point from which two pulses emanate and move in opposite directions other motions we observed are combinations and transitions among these four several of the motions have already been observed experimentally at some transitions spatial structures appear to change discontinuosly and without hysteresis suggesting global bifurcations

analysis and design of integral sliding manifolds for systems with unmatched perturbations the robustness properties of integral sliding mode controllers are studied this note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal it is also shown that when the minimum is attained the resulting perturbation is not amplified this selection is particularly useful if integral sliding mode control is to be combined with other methods to further robustify against unmatched perturbations h sub spl infin is taken as a special case simulations support the general analysis and show the effectiveness of this particular combination

which data residual norm for robust elastic frequency domain full waveform inversion elastic full waveform inversion is an ill posed data fitting procedure that is sensitive to noise inaccuracies of the starting model definitionofmultiparameterclasses andinaccuratemodeling of wavefield amplitudes we have investigated the performance of different minimization functionals as the least squares norm 2 the least absolute values norm 1 and combinations of both the huber and so called hybrid criteria with reference to twonoisyoffshorevalhallmodelandonshoreoverthrustmodel synthetic data sets the four minimization functionals were implemented in 2d elastic frequency domain full waveform inversion fwi where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies for the offshore and onshore case studies the 1 norm provided the most reliable models for p and s wave velocities vp and vs even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data the 2 norm can provide reliable results in the presence of uniform white noise for vp and vs if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency the 1 norm and the huber and hybrid criteria unlike the 2 norm allowforsuccessfulimagingofthevsmodelfromnoisydataina soft seabed environment where the p to s waves have a small footprint in the data however the huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial and error investigations for reliable estimation the 1 norm provides a robust alternativetothe2 normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency domainfwi

multicomponent joint migration velocity analysis in the angle domain for pp waves and ps waves employing the vector processing of multicomponent seismic data elastic kirchhoff migration is used to conduct a multicomponent joint migration velocity analysis mva of pp and ps waves in the angle domain in vector wavefield imaging the elastic imaging condition has been extended to nonzero time and space shifts we apply the extended imaging condition to elastic kirchhoff migration to extract angle domain common image gathers adcigs of pp and ps waves this method which is derived from 3d wave propagation theory directly operates on the vector wavefields and automatically resolves the problem of ps wave polarity reversal in the migration sections based on the kinematic characteristics of pp and ps waves in the incident angle domain the velocity updating functions for p and s waves are derived by combining the adcigs flatness criterion and the pp and ps wave image depth consistency principle the accuracy of p and s wave velocities can be assessed the method was tested on a 2d thin inter

seismic waveform inversion in the frequency domain part 1 theory and verification in a physical scale model seismic waveforms contain much information that is ignored under standard processing schemes seismic waveform inversion seeks to use the full information content of the recorded wavefield in this paper i present apply and evaluate a frequency space domain approach to waveform inversion the method is a local descent algorithm that proceeds from a starting model to refine the model in order to reduce the waveform misfit between observed and model data the model data are computed using a full wave equation viscoacoustic frequency domain finite difference method ray asymptotics are avoided and higher order effects such as diffractions and multiple scattering are accounted for automatically the theory of frequency domain waveform wavefield inversion can be expressed compactly using a matrix formalism that uses finite difference finite element frequency domain modeling equations expressions for fast local descent inversion using back propagation techniques then follow naturally implementation of

an lmi based switching surface design method for a class of mismatched uncertain systems in this note we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix in terms of linear matrix inequalities we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties we also give an explicit formula of such linear switching surfaces together with a design example

hybrid l 1 l 2 minimization with applications to tomography least squares or l2 solutions of seismic inversion and tomography problems tend to be very sensitive to data points with large errors the lp minimization for 1 p 2 gives more robust solutions but usually with higher computational cost iteratively reweighted least squares irls gives efficient approximate solutions to these lp problems we apply irls to a hybrid l2 l2 minimization problem that behaves like an l2 fit for small residuals and like an l1 fit for large residuals the smooth transition from l2 to l1 behavior is controlled by a parameter that we choose using an estimate of the standard deviation of the data error for linear problems of full rank the hybrid objective function has a unique minimum and irls can be proven to converge to it we obtain a robust efficient method for nonlinear problems a version of the gauss newton algorithm can be applied synthetic crosswell tomography examples and a field data vsp tomography example demonstrate the improvement of the hybrid method over le

dynamics of reaction diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection a one component bistable reaction diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two component activator inhibitor reaction diffusion model with differential advection the effects of asymmetric nonlocal couplings in such a bistable reaction diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling we carry out a linear stability analysis of the spatially homogeneous steady states of the model and numerical simulations of the model to show how the asymmetric nonlocal coupling controls and alters the steady states and the front dynamics in the system in a second step a third fast reaction diffusion equation is included which induces the formation of more complex patterns a linear stability analysis predicts traveling waves for asymmetric nonlocal coupling in contrast to a stationary turing patterns for a system with symmetric nonlocal coupling these findings are verified by direct numerical integration of the full equations with nonlocal coupling

a strategy for nonlinear elastic inversion of seismic reflection data the problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory in its roughest formulation the inverse problem consists of obtaining the earth model for which the predicted data best fit the observed data if an adequate forward model is used this best model will give the best images of the earth s interior three parameters are needed for describing a perfectly elastic isotropic earth the density x and the lame parameters x and x or the density x and the p wave and s wave velocities x and x the choice of parameters is not neutral in the sense that although theoretically equivalent if they are not adequately chosen the numerical algorithms in the inversion can be inefficient in the long spatial wavelengths of the model adequate parameters are the p wave and s wave velocities while in the short spatial wavelengths p wave impedance s wave impedance and density are adequate the problem of inversion o

h sub 2 guaranteed cost switching surface design for sliding modes with nonmatching disturbances this paper presents an extension of utkin and yang s method 1978 for sliding surface design via the minimization of a quadratic performance criterion the method proposed takes into account nonmatching disturbance signals and nonmatching system model uncertainties an upper bound for the h sub 2 norm of the disturbance to output transfer function is minimized leading to a guaranteed cost h sub 2 controller

crosshole seismic inversion with normalized full waveform amplitude data we investigate a simple scheme for full waveform amplitude spectrum inversion of crosshole seismic data with an unknown source wavelet the method is based on our 2d 2 5d finite element method of acoustic wave modeling the normalized amplitude data defined as the spectral ratio of the original trace amplitude to the average amplitude for the entire common shot gather are used for full waveform inversion in the frequency domain in essence the normalization of amplitudes removes the source wavelet and is easily carried out in the time domain or frequency domain from crosshole seismic surveying two synthetic models simulating respectively a dipping fracture model and a complicated sedimentary structure are examined with the inversion scheme the numerical results show that clear images of the targets can be obtained by using the single and multiple frequency data for comparison two other amplitude inversion schemes in which the source signatures are known and estimated with an iterative procedure were carried out for the same models the results show that the iteratively source estimated procedure also produces satisfactory images of the velocity structure and yields an approximate amplitude of the source wavelet with the multifrequency data three such schemes yield very competitive results

waveform inversion using a back propagation algorithm and a huber function norm waveforminversionfacesdifficultieswhenappliedtoreal seismic data including the existence of many kinds of noise the 1 norm is more robust to noise with outliers than the least squares method nevertheless the least squares method is preferred as an objective function in many algorithms because the gradient of the 1 norm has a singularity when the residual becomes zero we propose a complex valued huber function for frequency domain waveform inversion that combines the 2 norm for small residuals with the 1 norm for large residuals we also derive a discretized formula for the gradient of the huber function through numericaltestsonsimplesyntheticmodelsandmarmousidata we find the huber function is more robust to outliers and coherent noise we apply our waveform inversion algorithm to field data taken from the continental shelf under the east sea in korea in this setting we obtain a velocity model whose syntheticshotprofilesaresimilartotherealseismicdata

h controller design for affine fuzzy systems based on piecewise lyapunov functions in finite frequency domain this paper studies the problem of state feedback controller design for a class of nonlinear systems described by continuous time affine fuzzy models based on a piecewise continuous lyapunov function combined with s procedure and some matrix decoupling techniques a novel control law is derived in the formulation of linear matrix inequalities lmis in finite frequency domain first a so called finite frequency h performance index is defined which extends the standard h performance then a sufficient condition is derived such that the fuzzy closed loop system satisfies a finite frequency h performance by introducing the s procedure and adding slack variables piecewise controllers are designed to deal with disturbances in the low middle and high frequency domain respectively the proposed piecewise controller design method can get a better disturbance attenuation performance when the frequency ranges of disturbances are known beforehand finally two examples are given to illustrate the effectiveness and superiority of the new results

lmi based sliding surface design for integral sliding mode control of mismatched uncertain systems we propose a linear matrix inequality lmi based sliding surface design method for integral sliding mode control of mismatched uncertain systems the uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix we give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics we also give an lmi characterization of the sliding surface together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time additionally we give an lmi condition of sliding surfaces guaranteeing the alpha stability constraint finally we give a simulation result to show the effectiveness of our method

h sliding mode control for uncertain neutral type stochastic systems with markovian jumping parameters this paper is devoted to the investigation of h sliding mode control smc for uncertain neutral stochastic systems with markovian jumping parameters and time varying delays a sliding surface functional is firstly constructed then the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval the sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities lmis finally an example is provided to illustrate the efficiency of the proposed method

brief paper invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control a new sliding mode control design algorithm for a linear and a class of nonlinear quasi lipschitz disturbed system is presented it is based on the appropriate selection of the sliding surface via invariant ellipsoid method the designed control guarantees minimization of unmatched disturbances effects to system motions in a sliding mode the obtained theoretical results are approved by numerical simulations

nonlinear and nonlocal dynamics of spatially extended systems stationary states bifurcations and stability abstract spatially extended systems with nonlocal dynamics e g ferromagnetic resonance or current instability of the type t u f 1 l 0 l u dx u 2 x u 4 x u with u r n will be studied near the soft mode instability wave number kc 0 of a stationary and uniform state an amplitude equation is derived within the framework of a multiple scale perturbation theory a particular example of this class of nonlocal dynamics is also treated numerically as the main result we find that in contrast to the well known supercritical bifurcation into a stable periodic state the uniform state can bifurcate supercritically into a stationary state of an amplitude modulated fast oscillation in space

brief designing robust sliding hyperplanes for parametric uncertain systems a riccati approach in this paper we propose a method to design robust sliding hyperplanes in the presence of mismatched parametric uncertainty based on quadratic stability the robust sliding hyperplane is constructed from a riccati inequality associated with quadratic stabilizability the proposed method enables us to deal with structured uncertainty and optimize the sliding motion by applying the guaranteed cost control idea

an efficient multiscale method for time domain waveform tomography this efficient multiscale method for time domain waveform tomography incorporates filters that are more efficient than hamming window filters a strategy for choosing optimal frequency bands is proposed to achieve computational efficiency in the time domain a staggered grid explicit finite difference method with fourth order accuracy in space and second order accuracy in time is used for forward modeling and the adjoint calculation the adjoint method is utilized in inverting for an efficient computation of the gradient directions in the multiscale approach multifrequency data and multiple grid sizes are used to overcome somewhat the severe local minima problem of waveform tomography the method is applied successfully to 1d and 2d heterogeneous models it can accurately recover low and high wavenumber components of the velocity models the inversion result for the 2d model demonstrates that the multiscale method is computationally efficient and converges faster than a conventional single scale method

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

technical communique on the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties recently choi 1998 automatica 34 8 1015 1020 has considered the problem of designing a variable structure control vsc law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition he has given a sufficient condition for the existence of linear sliding surfaces in terms of lmis in this note we show that the lmi existence condition given in the above paper is a necessary and sufficient one and we give lmi existence conditions of a sliding surface guaranteeing general lmi regional pole placement constraints while in the above paper pole placement only in a vertical half plane and a disk has been considered finally we give simulation results for controlling an inverted pendulum mounted on a cart