the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

identification of thermal conductivities by temperature gradient profiles one dimensional steady flow the comparison model method cmm is applied to the identification of spatially varying thermal conductivity in a one dimensional domain this method deals with the discretized steady state heat equation written at the nodes of a lattice a lattice which models a stack of plane parallel layers the required data are temperature gradient and heat source or sink values the unknowns of this inverse problem are not nodal values but internode thermal conductivities which appear in the node heat balance equation the conductivities e g the solutions to the inverse problem obtained by the cmm are a one parameter family in order to achieve uniqueness which coincides with identifiability in this case a suitable value of this parameter must be found to this end we consider 1 parameterization i e introducing equality constraints between the unknown coefficients 2 the use of two data sets at least in a subdomain and 3 self identifiability each of these items formally translates the available

stability and stabilization of two time scale switched systems in discrete time in this technical note stability and stabilization of two time scale switched linear systems in the singular perturbation form are addressed in discrete time we show that under an arbitrary switching rule stability of the slow and fast switched subsystems is not sufficient to assess stability of the original two time scale switched system even if the singular perturbation parameter tends to zero therefore we propose lmi based conditions that guarantee the asymptotic stability of the two time scale switched system using switched quadratic lyapunov functions these conditions express the fact that the coupling between fast and slow subsystems has to be taken into account in addition to stability properties of the two subsystems when the switching rule is arbitrary the presented conditions are extended to state feedback control design a numerical example illustrates the features of the proposed approach

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

limits of nonlinear discrete time control systems with fast subsystems we investigate the asymptotic properties of nonlinear discrete time control systems with fast subsystems in particular we use the averaging method in order to construct a limiting system for the slow subsystem we show continuous dependence of the slow trajectories on the perturbation parameter measuring the ratio of the different step sizes as a byproduct we get an exponential formula for the reachable set of nonlinear continuous time control systems with finite control range

singularly perturbed difference equations in optimal control problems a linear regular problem involving singularly perturbed difference equations is considered the basic features of singularly perturbed systems order reduction separation of time scales boundary layers etc are highlighted application to the numerical treatment of control problems involving stiff differential equations is discussed

aggregation of the policy iteration method for nearly completely decomposable markov chains a steady state optimal control problem is considered for nearly completely decomposable markov chains in order to apply the policy iteration method of r a howard dynamic programming and markov processes cambridge ma mit press 1960 a high dimensional ill conditioned system of algebraic equations must be solved in the value determination step although algorithms exist for aggregation of the steady state probability distribution problem they only provide methods for computing the cost not the dual variables using a singular perturbation approach an aggregation method for the value determination equation is developed the aggregation method is developed in three steps first a class of similarity transformations that transform the system into a singularly perturbed form is developed second an aggregation method to compute the steady state probability distribution is derived third this aggregation method is applied to the value determination step of howard s method 1960

chain codes and their linear reconstruction filters a differential chain code implementation of the basic eight directional and n ring chain code for the encoding of line drawings is considered several distortion and rate criteria are considered and they are evaluated for the special case of encoding infinite straight lines these results indicate that the differential code outperforms ring codes and the ring delta code using a linear decoding filter for reconstructing a smoothed approximation to the original line is also considered optimal reconstruction filters for infinite straight lines at various angles are derived an angle invariant reconstruction filter that minimizes the expected square distortion taken over all angles is derived the overall performance using this filter is close to that of the optimum filter furthermore the impulse response of the angle invariant filter is approximately rectangular which can lead to simple hardware implementations

modelling and linear model following control of singularly perturbed discrete systems a new method for order reduction of singularly perturbed discrete systems is derived the discrete system is reduced to its dominant and parasitic parts this method can exactly exhibit the responses of the original system for control law design the linear model following control lmfc method is applied the order of the model is chosen the same as that of the dominant part of the plant i e we apply to the plant with and without parasitics the same lmfc law the conditions for reduced order lmfc systems are derived and some simulation results are illustrated

context tree based image contour coding using a geometric prior efficient encoding of object contours in images can facilitate advanced image video compression techniques such as shape adaptive transform coding or motion prediction of arbitrarily shaped pixel blocks we study the problem of lossless and lossy compression of detected contours in images specifically we first convert a detected object contour into a sequence of directional symbols drawn from a small alphabet to encode the symbol sequence using arithmetic coding we compute an optimal variable length context tree vct mathcal t via a maximum a posterior map formulation to estimate symbols conditional probabilities map can avoid overfitting given a small training set mathcal x of past symbol sequences by identifying a vct mathcal t with high likelihood p mathcal x mathcal t of observing mathcal x given mathcal t using a geometric prior p mathcal t stating that image contours are more often straight than curvy for the lossy case we design fast dynamic programming dp algorithms that optimally trade off coding rate of an approximate contour hat text x given a vct mathcal t with two notions of distortion of hat text x with respect to the original contour x to reduce the size of the dp tables a total suffix tree is derived from a given vct mathcal t for compact table entry indexing reducing complexity experimental results show that for lossless contour coding our proposed algorithm outperforms state of the art context based schemes consistently for both small and large training datasets for lossy contour coding our algorithms outperform comparable schemes in the literature in rate distortion performance

an efficient rate distortion optimal shape coding approach utilizing a skeleton based decomposition in this paper we present a new shape coding approach which decouples the shape information into two independent signal data sets the skeleton and the boundary distance from the skeleton the major benefit of this approach is that it allows for a more flexible tradeoff between approximation error and bit budget curves of arbitrary order can be utilized for approximating both the skeleton and distance signals for a given bit budget for a video frame we solve the problem of choosing the number and location of the control points for all skeleton and distance signals of all boundaries within a frame so that the overall distortion is minimized an operational rate distortion ord optimal approach using lagrangian relaxation and a four dimensional direct acyclic graph dag shortest path algorithm is developed for solving the problem to reduce the computational complexity from o n sup 5 to o n sup 3 where n is the number of admissible control points for a skeleton a suboptimal greedy trellis search algorithm is proposed and compared with the optimal algorithm in addition an even more efficient algorithm with computational complexity o n sup 2 that finds an ord optimal solution using a relaxed distortion criterion is also proposed and compared with the optimal solution experimental results demonstrate that our proposed approaches outperform existing ord optimal approaches which do not follow the same decomposition of the source data

feedback control of two time scale block implemented discrete time systems the block processing technique is applied to a class of two time scale linear discrete time systems block state space structures for slow and fast subsystems have been obtained based upon these models blocked slow and fast controls are designed in addition an extra control is designed to exactly compensate for the effects of the parasitics

multirate and composite control of two time scale discrete time systems the design of stabilizing feedback control of singularly perturbed diserete time systems is decomposed into the design of slow and fast controllers which are combined to form the composite control composite control strategies are developed for the case of single rate measurements all variables are measured at the same rate as well as for the case of multirate measurements slow variables are measured at a rate slower than that of fast variables

a stochastic inverse solution for transient groundwater flow parameter identification and reliability analysis in this paper a stochastic approach is developed for solving the inverse problem of parameter identification for transient groundwater flow adjoint state equations are derived for the stochastic partial differential equation spde relating transient head and log hydraulic conductivity perturbations the derived equations can be used to calculate the covariance matrix of head observations and the cross covariance matrix between head observations and log hydraulic conductivity measurements for each observation time as well as the covariance and cross covariance matrices between different observation times the number of simulation runs required for obtaining these matrices is equal to the number of head observations the reliability of model prediction is evaluated through the variance estimate method using adjoint sensitivity analysis and the cokriging estimate the reliability evaluation of model prediction can be used as an aid in the optimization of experimental design for sampling strategies a numerical example is given to illustrate the stochastic inverse procedure for a general transient flow problem the example shows that using head observations of all observation times simultaneously produces much better results than using them sequentially commonly known as the quasi steady approach the example also shows that it is possible to obtain a reliable stochastic inverse solution for meeting a given prediction objective based on a limited number of observations

the topology of locales and its effects on position uncertainty the precision to which the position of a target in a digital image can be estimated may be analyzed by considering the possible digital representations of the target such an analysis leads to regions of indistinguishable target position referred to as locales by considering the density distribution and shape of these locales the available precision can be estimated previously such analyses have presumed an absence of noise in the digital image it is shown how the noise tolerance for position estimation is affected by the topological properties of locales such as locale connectivity adjacency and clustering

cauchy data requirement of the inverse problem of the mean age equation a classical theoretical inverse problem in groundwater hydraulics is the calibration of a heterogeneous isotropic hydraulic conductivity field using known hydraulic head data at each point in the domain it has been long known that a necessary condition for the uniqueness of the solution to this theoretical inverse problem is the cauchy data i e the hydraulic conductivity values or equivalently flux along a line crossing all streamtubes in the entire domain this result has been cited in identifying the value of boundary flux data in practical inverse problems although in general such data are generally not available in this work we show that groundwater mean age data replace this cauchy data requirement

identification of aquifer transmissivities the comparison model method a method for solving the inverse problem in hydrogeology is presented this method is suitable for computing the interblock transmissivities harmonic mean or others referred to the sides of the network blocks of a nonhomogeneous anisotropic aquifer in steady state flow the interblock transmissivities computing procedure is based on the comparison between real gradients and the ones generated by a comparison model whose initial transmissivity value is arbitrarily chosen and constant through out the surveyed area alternative solutions of interblock transmissivities one for each constant initial transmissivity value utilized in the comparison model are obtained generally these solutions differ from each other but all of them present the characteristics of being able to reproduce with the precision of an arbitrarily small the real piezometrie heads respecting the geometry and the boundary conditions of the real aquifer the selection of the value or set of values of the initial transmissivity to put into the comparison model in order to obtain one solution of computed interblock transmissivities close to the real ones both as trends and as absolute values is rather critical the minimum head anomaly criterion and the bottleneck criterion enable one to select a value or a set of values of initial transmissivity these criteria exploit only the data needed for the solution of the inverse problem real piezometric heads geometry and boundary conditions and they lead to a suitable initial transmissivity that put into the comparison model allow one to obtain a good and meaningful solution of computed interblock transmissivities the comparison model method and the two aforementioned criteria have been applied to a numerical case study bearing good results the method has been tested in order to evaluate its effectiveness even in the case of noisy piezometric heads piezometric heads with random errors even in this case the method bore satisfactory and useful results finally a promising approach to the inverse problem solution when one has at his disposal at least four sets of data coming from as many hydraulic situations has been briefly described

optimized polygonal approximation by dominant point deletion an algorithm for polygonal approximation based on dominant point dp deletion is presented in this paper the algorithm selects an initial set of dps and starts eliminating them one by one depending upon the error associated with each dp the associated error value is based on global measure a local optimization of few neighboring points is performed after each deletion although the algorithm does not guarantee an optimal solution the combination of local and global optimization is expected to produce optimal results the algorithm is extensively tested on various shapes with varying number of dps and error threshold in general optimal results were observed for about 96 of the times a good comparative study is also presented in this paper

a robust filtering algorithm for subpixel reconstruction of chain coded line drawings a robust algorithm is presented for smoothing and achieving subpixel accuracy in the reconstruction of chain coded line drawings the algorithm does not remove sharp corners and does not need a priori knowledge of curvature statistics a fast on line implementation can be achieved using a table look up a simplified algorithm can be used for reconstructing digitized polygons

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

higher accuracy output feedback sliding mode control of sampled data systems the problem of output feedback sliding mode control for sampled data systems in the presence of external disturbances is considered the proposed output feedback control strategy helps obtain a quasi sliding mode with an o t 3 boundary layer where t is the sampling period this outperforms the o t 2 result induced by the one step delayed disturbance approximation method the proposed scheme is applicable to linear systems which are relative degree one and minimum phase an example is given to illustrate the efficacy of the new method

assessing the behaviour of polygonal approximation algorithms abstract in a recent paper we described a method for assessing the accuracy of polygonal approximation algorithms ieee trans pami 19 6 1997 659 here we develop several measures to assess the stability of such approximation algorithms under two classes of variations namely perturbations of the data and changes in the algorithms scale parameters in order to quantify the former a break point stability index is defined and tested for the latter two indices are introduced 1 a monotonicity index is applied to analyse the change in the approximation error or the number of line segments against increasing scale and 2 a consistency index quantifies the variation in results produced at the same scale by an algorithm but with different input parameter values finally the previously developed accuracy figure of merit is calculated and averaged over 21 test curves for different parameter values to obtain more reliable scores

the observer based controller design of discrete time singularly perturbed systems a class of linear shift invariant discrete time singularly perturbed systems with inaccessible states is considered a design technique is formulated by which the stabilizing controller can be formed through the controllers of the slow and fast subsystems sufficient conditions for stability of the closed loop system under this composite controller are given

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

parallel reduced order controllers for stochastic linear singularly perturbed discrete systems an approach to the decomposition and approximation of linear quadratic gaussian control problems for singularly perturbed discrete systems at steady state is presented the global kalman filter is decomposed into separate reduced order local filters through the use of a decoupling transformation a near optimal control law is derived by approximating coefficients of the optimal control law the proposed method allows parallel processing of information and reduces offline and online computational requirements a real world example demonstrates the efficiency of the proposed method

stability bounds of singularly perturbed discrete systems the authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems by combining three conditions of the critical stability criterion with a bialternate product for discrete time systems the stability problems of two types of singularly perturbed discrete time systems can be solved via the derived scheme several examples are given to illustrate the proposed results

an optimal polygonal boundary encoding scheme in the rate distortion sense in this paper we present fast and efficient methods for the lossy encoding of object boundaries that are given as eight connect chain codes we approximate the boundary by a polygon and consider the problem of finding the polygon which leads to the smallest distortion for a given number of bits we also address the dual problem of finding the polygon which leads to the smallest bit rate for a given distortion we consider two different classes of distortion measures the first class is based on the maximum operator and the second class is based on the summation operator for the first class we derive a fast and optimal scheme that is based on a shortest path algorithm for a weighted directed acyclic graph for the second class we propose a solution approach that is based on the lagrange multiplier method which uses the above mentioned shortest path algorithm since the lagrange multiplier method can only find solutions on the convex hull of the operational rate distortion function we also propose a tree pruning based algorithm that can find all the optimal solutions finally we present results of the proposed schemes using objects from the miss america sequence

a rate and distortion analysis of chain codes for line drawings the performance of chain codes for line drawings in the framework of source coding with a fidelity criterion is investigated a formal characterization is given for a broad class of chain codes that includes the generalized chain codes of freeman and the convex quantizers of koplowitz measures of distortion fidelity and rate efficiency are introduced the distortion and rate are calculated for several types of chain codes applied to straight and slowly curving lines several statistical models for straight lines are introduced and the average performance of chain codes for these models is investigated

discrete time observers for singularly perturbed continuous time systems the use of discrete time observers for nonlinear singularly perturbed continuous time systems is explored the observer design approach is based on inversion of state to measurement maps the two time scale nature of the system is exploited by constructing separate reduced order observers for the approximate slow and fast subsystems using multirate measurements and computation the reduced order observers are compared to a full order observer designed for the same system the comparison shows that although the reduced order observers exhibit some approximation error they also result in reduced computational requirements if the inversion is performed on line reduced memory requirements if the inversion is implemented by look up table and reduced stiffness the trade off between accuracy and implementation requirements always favors the reduced order approach for systems with significant separation of time scales numerical examples are provided including a case study of an observer based control system for permanent magnet synchronous motors

analysis of the precision of generalized chain codes for the representation of planar curves this paper examines a set of line segment approximation codes for the representation of planar curves the so called generalized chain codes and shows that the average quantization error measure of code s precision is directly proportional to the grid size and is independent of the form of the code thus to achieve a desired level of precision for the representation of a line drawing only the size of the grid need be determined the form of the code can be chosen on the basis of other criteria such as compactness smoothness or relative ease of encoding and processing

optimal control of discrete time singularly perturbed systems in this paper we present a new algorithm for solving the optimal control of discrete time singularly perturbed systems the main idea of this algorithm is based on two steps first the hamiltonian difference equation is reduced to the backward recursive form rather than the forward recursive form second the bilinear transformation is applied to transform the derived non symmetric discrete time riccati equations into continuous time equations in order to improve the efficiency of this scheme two matrix permutations are introduced into this algorithm by taking into account the previous work of gajic and shen 1991 therefore substantial numerical advantages are gained namely computation and memory requirements the f 8 aircraft model is used to illustrate the efficiency of the proposed method

fast polygonal approximation of digital curves using relaxed straightness properties several existing digital straight line segment dss recognition algorithms can be used to determine the digital straightness of a given one pixel thick digital curve because of the inherent geometric constraints of digital straightness these algorithms often produce a large number of segments to cover a given digital curve representing a real life object image thus a curve segment which is not exactly digitally straight but appears to be visually straight is fragmented into multiple dss when these algorithms are run in this paper a new concept of approximate straightness is introduced by relaxing certain conditions of dss and an algorithm is described to extract those segments from a digital curve the number of such segments required to cover the curve is found to be significantly fewer than that of the exact dss cover as a result the data set required for representing a curve also reduces to a large extent the extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance the proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact dss the overall time complexity becomes linear in the number of points present in the representative set experimental results on several digital curves demonstrate the speed elegance and efficacy of the proposed method

a perceptually motivated three component image model part ii applications to image compression for past i see ibid vol 4 no 4 p 405 1995 the use of the image model of part i is investigated in the context of image compression the model decomposes the image into a primary component that contains the strong edge information a smooth component that represents the background slow intensity variations and a texture component that contains the textures the primary component which is known to be perceptually important is encoded separately by encoding the intensity and geometric information of the strong edge brim contours two alternatives for coding the smooth and texture components are studied entropy coded adaptive dct and entropy coded subband coding it is shown via simulations that the proposed schemes which can be thought of as a hybrid of waveform coding and feature based coding techniques result in both subjective and objective performance improvements over several other image coding schemes and in particular over the jpeg continuous tone image compression standard these improvements are especially noticeable at low bit rates furthermore it is shown that a perceptual tuning based on the contrast sensitivity of the human visual system can be used in the dct based scheme which in conjunction with the three component model leads to additional subjective performance improvements

stabilization bound of discrete two time scale systems abstract in this paper the exact bound problem in various types of discrete two time scale tts system is considered a set of stability criteria based on the frequency domain representation is derived two interesting examples are used to demonstrate the proposed scheme

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

transmissivity of a heterogeneous formation the objective of this paper is to derive the transmissivity of an equivalent homogeneous medium having the same macroscopic flow behavior as the actual heterogeneous formation we apply generalized taylor ans moment analysis in order to determine the phenomenological coefficient of transmissivity for the case of saturated flow confined in a heterogeneous permeable formation with variable thickness the generalized taylor aris moment analysis yields a two step procedure for determining the constant two dimensional transmissivity tensor from the three dimensional spatially variable conductivity tensor solve a flow problem and then perform an integration for the special case that the conductivity is locally isotropic and the impermeable confining surfaces are parallel the equations governing transmissivity are discretized using a pseudospectral fourier galerkin scheme the resultant system of linear algebraic equations is solved efficiently using preconditioned conjugate gradients in order nt in nt operations where nt is the number of spatial discretization points the numerical method is used in several examples to compute the transmissivity of lognormally distributed hydraulic conductivity and the results are compared with the transmissivity found using the usual depth averaging approach and another method suggested in the literature the numerical results show that the averaging volume required to obtain an effective value of transmissivity is about 10 horizontal integral scales when the flow field has a significant three dimensional character the standard method of finding transmissivities by depth averaging can lead to significant errors in the prediction of global scale flows it is shown that depth averaging consistently overestimates transmissivities an example illustrates how in the case of tilted strata anisotropic transmissivities arise and how the degree of transmissivity anisotropy depends on the angle of the dip and the horizontal to vertical integral scale ratio

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

bit allocation for dependent quantization with applications to multiresolution and mpeg video coders we address the problem of efficient bit allocation in a dependent coding environment while optimal bit allocation for independently coded signal blocks has been studied in the literature we extend these techniques to the more general temporally and spatially dependent coding scenarios of particular interest are the topical mpeg video coder and multiresolution coders our approach uses an operational rate distortion r d framework for arbitrary quantizer sets we show how a certain monotonicity property of the dependent r d curves can be exploited in formulating fast ways to obtain optimal and near optimal solutions we illustrate the application of this property in specifying intelligent pruning conditions to eliminate suboptimal operating points for the mpeg allocation problem for which we also point out fast nearly optimal heuristics additionally we formulate an efficient allocation strategy for multiresolution coders using the spatial pyramid coder as an example we then extend this analysis to a spatio temporal 3 d pyramidal coding scheme we tackle the compatibility problem of optimizing full resolution quality while simultaneously catering to subresolution bit rate or quality constraints we show how to obtain fast solutions that provide nearly optimal typically within 0 3 db full resolution quality while providing much better performance for the subresolution layer typically 2 3 db better than the full resolution optimal solution

theory of lattice based fine coarse vector quantization the performance of a lattice based fast vector quantization vq method which yields rate distortion performance to that of an optimal vq is analyzed the method which is a special case of fine coarse vector quantization fcvq uses the cascade of a fine lattice quantizer and a coarse optimal vq to encode a given source vector the second stage is implemented in the form of a lookup table which needs to be stored at the encoder the arithmetic complexity of this method is essentially that of lattice vq its distortion can be made arbitrarily close to that of an optimal vq provided sufficient storage for the table is available it is shown that the distortion of lattice based fcvq is larger than that of full search quantization by an amount that decreases as the square of the diameter of the lattice cells and it provides exact formulas for the asymptotic constant of proportionality in terms of the properties of the lattice coarse codebook and source density it is shown that the excess distortion asymptotically equals that of the fine quantizer simulation results indicate how small the lattice cells must be in order for the asymptotic formulas to be applicable

data reduction of large vector graphics fast algorithm for joint near optimal approximation of multiple polygonal curves is proposed it is based on iterative reduced search dynamic programming introduced earlier for the min eproblem of a single polygonal curve the proposed algorithm jointly optimizes the number of line segments allocated to the different individual curves and the approximation of the curves by the given number of segments trade off between time and optimality is controlled by the breadth of the search and by the numbers of iterations applied

optimal buffered compression and coding mode selection for mpeg 4 shape coding we propose an optimal buffered compression algorithm for shape coding as defined in the forthcoming mpeg 4 international standard the mpeg 4 shape coding scheme consists of two steps first distortion is introduced by down and up scaling then context based arithmetic encoding is applied since arithmetic coding is lossless the down up scaling step is considered as a virtual quantizer we first formulate the buffer constrained adaptive quantization problem for shape coding and then propose an algorithm for the optimal solution under buffer constraints previously the fact that a conversion ratio cr of 1 4 makes a coded image irritating to human observers for qcif size was reported for mpeg 4 shape coding therefore careful consideration for small size images such as qcif should be given to prevent coded images from being unacceptable to this end a low bit rate tuned algorithm is proposed in this paper as well experimental results are given using an mpeg 4 shape codec

singular perturbation analysis of cheap control problem for sampled data systems this paper studies the discrete time cheap control problem for sampled data systems using the theory of singular perturbations it is shown by using the two time scale property of singularly perturbed systems that the problem can be solved in terms of two reduced order subproblems for which computations can be done in parallel thus increasing the computational speed similarly to the continuous time case the singular perturbation approach enables the decomposition of the algebraic riccati equation into two reduced order pure slow and pure fast continuous time algebraic equations

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

singularly perturbed boundary value problems in discrete systems various types of singularly perturbed boundary value problems arising in discrete systems are formulated for the general type it is seen that the degenerate problem is of reduced order and hence shows its inability to accommodate all the given boundary conditions those left over boundary conditions are readmitted through appropriate corrections for the initial and final boundary layers a perturbation method is developed to obtain an approximate solution composed of an outer series initial boundary layer correction series and final boundary layer correction series an important feature of the method is that the corrections for the original boundary value problem are solved as an initial value problem and a final value problem facilitating a considerable reduction in computation an example is given to demonstrate the method

a continuous time inverse operator for groundwater and contaminant transport modeling model identifiability general identifiability conditions are derived for the model coefficients of the spatially discretized continuous time diffusion equation these conditions in turn determine some sufficient and necessary conditions for the existence and uniqueness of the continuous time inverse operator described in a previous article the identifiability conditions are in terms of the initial conditions and the flux vector containing boundary condition information and the eigenspace of the spatially discretized system the derivation of these conditions gives some insight into the location of the solution of the inverse problem in terms of the direct operator under investigation in the space of the laplace transform and limited insight into the stability of the solution near that location

analysis for a class of singularly perturbed hybrid systems via averaging a class of singularly perturbed hybrid dynamical systems is analyzed the fast states are restricted to a compact set a priori the continuous time boundary layer dynamics produce solutions that are assumed to generate a well defined average vector field for the slow dynamics this average the projection of the jump map in the direction of the slow states and flow and jump sets from the original dynamics define the reduced or average hybrid dynamical system assumptions about the average system lead to conclusions about the original higher dimensional system for example forward pre completeness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains in addition global asymptotic stability for the average system implies semiglobal practical asymptotic stability for the original system we give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems we also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuous time plants implemented by fast but continuous actuators

a multirate digital control via a discrete time observer for non linear singularly perturbed continuous time systems based on euler s methodology we present a new discretization scheme of two time scale non linear continuous time systems this scheme of the discretization consists in using two periods slow and fast which are determined with respect to slow and fast variables rate respectively and allows us to define and then implement a multirate digital control for such systems to cope with this multirate measurements on line to this end two reduced order observers are constructed for the slow and fast subsystems by referring to the knowledge of the left inversion of the state to measurements map problem

tree searched chain coding for subpixel reconstruction of planar curves coding schemes for the quantization of line drawings that outperform basic chain codes are investigated first subpixel accuracy reconstruction is obtained by a simple linear filtering of the chain code points which achieves a factor of three to four reduction in average reconstruction distortion for smooth curves second the basic chain encoding schemes are generalized to a multipath tree searched encoding scheme a variation of the m l algorithm is used to maintain m contending chain code paths in storage and choose the best path from these over a wide variety of source curves tree searched chain coding results in nearly an order of magnitude reduction in average reconstruction distortion over smoother chain codes the performance improvement for curves is obtained with only a slight increase in bit rate over basic chain codes

digital multirate control for a class of non linear singularly perturbed systems this paper deals with the digital control of a particular class of non linear singularly perturbed nlsp systems three distinct multi rate composite control strategies are discussed in the first case it is assumed that measurements of the slow and fast variables are scheduled at the same fast sampling period ndelta then multi rate measurements are considered and two different strategies are presented the paper ends with an academic example and simulations

infinite time regulators for singularly perturbed difference equations linear quadratic regulators for singularly perturbed difference equations are considered asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied the composite feedback control strategy of continuous time singularly perturbed systems is extended to the new problem

chain coding with a hexagonal lattice this paper investigates the performance of chain code quantization of general curves using a hexagonal lattice structure as a means of improving efficiency over the standard square lattice performance is first computed theoretically assuming a generalization of grid intersect quantization and the curve to be quantized is assumed to be a straight line an algorithm is then developed to perform chain coding using the hex lattice computer simulations were performed to evaluate hexagonal chain coding for a variety of curves including circles of various curva ture straight lines and a stochastic curve model we find that the straight line theory is substantiated for curves whose radius of curvature is roughly twice the lattice constant for a given peak error in quanti zation hexagonal coding reduces the bit rate about 15 percent relative to the square lattice codes and exhibits qualitative improvements in fidelity as well

an inverse problem for the steady state diffusion equation we consider the problem of identifying a spatially varying diffusion coefficient using an observed solution to the forward problem under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient we develop some continuous dependence results for this problem and also propose a particularly advantageous set of test conditions for observing the forward solution

digital representation schemes for 3d curves digital representation of three dimensional 3 d curves is considered two dimensional representation schemes are first reviewed then methods applicable to curves in three and higher dimensional spaces are described desirable properties of curve representation schemes are identified and used as a basis for qualitative and quantitative comparison of the various methods that have been suggested conclusions concerning the selection of a digital 3 d curve representation scheme for shape analysis and coding are drawn it is shown that grid intersect quantization is a poor choice for curve representation in 3 d space and that cube quantization that leads to 6 connected chain codes meets all the identified requirements and should be preferred

generalized interframe vertex based shape encoding scheme for video sequences the efficiency of shape coding is an important problem concerning content based image manipulations and object based coding of the video sequences in order to encode the shape information of an object the boundary is approximated by a polygon which can be encoded with the smallest number of bits for maximum allowable distortion the conventional boundary coding schemes however does not successfully remove the temporal redundancy of the video sequences this paper proposes a new boundary encoding scheme by which the temporal redundancy between two successive frames is efficiently removed resulting in lower bit rate than the conventional algorithms the interframe vertex selection problem is solved by finding the path with the minimum cost in the directed acyclic graph dag and its fast version using a simplified graph is introduced to reduce the computational load the vertices were selected from both the current frame to be encoded and the previous frame already encoded and thus the temporal redundancy was effectively removed

a continuous time inverse operator for groundwater and contaminant transport modeling deterministic case the value of time dependent data in the calibration of numerical models of groundwater flow has been recently highlighted in the literature in this paper the background for a new development in the inverse problem is placed and a new operator for inversion of the spatially discretized diffusion equation is introduced the motivation for the development of an inverse problem solution procedure which uses information in transient data is illustrated with a focused review of recent literature such an approach which implicitly incorporates the continuous time dependency of the flow model is then presented this approach is based upon the new concept of inverting the model after the for example finite element spatial discretization but before the typically finite difference temporal discretization of the model not afterward as has been done in the past the laplace transform is used to replace discretization in time of the system of ordinary differential equations to discretization in the laplace variable of the algebraic system in laplace space the existence of the deterministic solution in the laplace transform space does not require knowledge of the eigenvalues of the diffusion matrix but only the specification of the laplace variables near zero a simple numerical example from the literature is used to generate a set of three simplified test cases upon which the proposed method is tested the implications of the theoretical investigation and the results of the numerical experiments are discussed with a view toward prospects of practical implementation

stability constraints of active magnetic bearing control systems direct lyapunov stability method is employed to analyse the closed loop stability of an electromagnetically suspended rotor system in which non linearity and singular perturbation nature are embedded five explicit sets of stability constraints are proposed so that the state feedback loop is not over designed under impact of modeling inaccuracy due to neglected higher order terms stability conditions for equilibrium point slow mode manifold and boundary layer are studied in addition the singular perturbation order reduction technique is used to simplify the feedback loop and reduce the order of a state feedback controller the stability margin can be numerically evaluated as long as the upper bound of the singular perturbation parameter is available the proposed state feedback controller is verified by intensive computer simulations such that superior performance in terms of stiffness rise time and overshoot is illustrated in comparison to output feedback law and deadbeat control the reported st

brief paper design of observer based controllers for a class of discrete systems design of observers and observer based controllers for linear discrete control systems with fast and slow modes are considered in this paper the time separation is expressed in terms of an inequality relating norms of system submatrices it is shown that reconstruction of fast and slow states can be accomplished by a full order observer the gains of which are computed using a two stage procedure then provided that the fast subsystem is asymptotically stable it is shown that a low order observer based controller can be designed with independent gain matrices to stabilize the original discrete system the theoretical analysis is illustrated by a ninth order boiler system model

delta codes for line drawings a new class of chain codes for line drawings named delta codes is introduced two specific types of fixed angle delta codes and ring delta codes are described the area of error distortion and rate are calculated for two types of delta codes applied to straight and slowly curving lines and it is shown that the delta outperforms other chain codes with the same set of link types for rapidly curving lines however the delta codes introduce curvature overload distortion analogous to the slope overload distortion of traditional delta modulation for waveforms

study of the discrete singularly perturbed linear quadratic control problem by a bilinear transformation this paper presents a new approach in the study of the linear quadratic control problem of singularly perturbed discrete systems by applying a bilinear transformation the algebraic discrete riccati equation is converted into a continuous one which can be solved by using the reduced order recursive method already documented in the control literature this method produces the reduced order near optimal solution up to an arbitrary order of accuracy and reduces the size of required computations the method is very suitable for parallel programming a real world example an f 8 aircraft demonstrates the efficiency of the proposed method