an algebraic approach to the time optimal output regulator the time optimal output regulator is considered for a special class of linear time invariant discrete time systems it is shown that a simple state feedback law achieves time optimal output regulator response in one sampling period for a square system the state feedback law always assigns the invariant zeros as closed loop poles for a non square system time optimal regulator response is achieved even if the set of invariant zeros is empty if the set of invariant zeros is not empty the control law always assigns these zeros as closed loop poles the method of this paper for the discrete system described by the state and output equations x k 1 ax k bu k and z k cx k does not require that a be invertible and that the open loop system s a b c be state controllable furthermore the only requirement is the existence of a right inverse for the matrix cb which is sufficient for output controllability

a note on parameterization of the class of deadbeat controllers the problem of parameterizing the class of deadbeat controllers for a given discrete time system through the minimum number of parameters was solved by schlegel 1 this note shows how to utilize the above solution to study some problems in designing deadbeat controllers first an algorithm is developed to compute a controller which minimizes in an average sense a given objective function second a necessary and sufficient condition is given for the existence of an output deadbeat controller finally the problem of parameterizing the set of deadbeat controllers for those systems transformable to the phase variable block canonical form is reconsidered

a statistical decision rule with incomplete knowledge about classes abstract a statistical decision rule among m classes is presented when the a priori knowledge about classes is not complete either the number of classes is not the true one or it is not possible to obtain samples from all the possible classes the reject option proposed by chow is extended by defining an ambiguity reject option and a distance reject option these two types of reject can be defined in a parametric as well as in a non parametric way an example is given in r in order to illustrate this rule this method has been developed essentially to solve diagnostic problems

the integration of image segmentation maps using region and edge information we present an algorithm that integrates multiple region segmentation maps and edge maps it operates independently of image sources and specific region segmentation or edge detection techniques user specified weights and the arbitrary mixing of region edge maps are allowed the integration algorithm enables multiple edge detection region segmentation modules to work in parallel as front ends the solution procedure consists of three steps a maximum likelihood estimator provides initial solutions to the positions of edge pixels from various inputs an iterative procedure using only local information without edge tracing then minimizes the contour curvature finally regions are merged to guarantee that each region is large and compact the channel resolution width controls the spatial scope of the initial estimation and contour smoothing to facilitate multiscale processing experimental results are demonstrated using data from different types of sensors and processing techniques the results show an improvement over individual inputs and a strong resemblance to human generated segmentation

classifier design with incomplete knowledge abstract pattern classification is a well studied problem in which the identity of an unknown pattern is determined to be one of m classes spanning the pattern space a new criterion function the inck incomplete knowledge criterion function is proposed which approximates the error probability when the m classes do not span the entire pattern space this criterion is based on the probabilistic measures obtained from a modified version of dubuisson and masson s statistical decision rule with reject the error probability or conversely the probability of correct classification can be determined without having complete knowledge about the class distributions the attractiveness of this criterion is that it is highly correlated with the statistical decision rule with reject which can be used by the classifier thus the criterion provides a good indication of the classifier performance that can be expected with the reduced feature space a classifier design is presented which incorporates the new criterion function as well it is described how the rejection classes of the statistical decision rule with reject can be used in a multiresolution classifier design to determine the class identity of patterns which cannot be determined at a given resolution experimental evidence is provided which demonstrates the advantages of the inck criterion function used in conjunction with a multiresolution classifier design

use of the design freedom of time optimal control abstract a method for synthesizing a state feedback time optimal controller for linear n state r input discrete time systems is developed the nonuniqueness of the solution is organized in such a way as to select the controller with the minimum value of the frobenius norm of the feedback gain matrix k it is shown that among the rn design parameters in the parametric form of k only r n rp r need to be considered in the search technique where p r is the order of the smallest jordan block in the jordan form of the closed loop system

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

on controlling generalized state space descriptor systems linear time invariant control systems of the form edx dt ax bu are considered where e and a are not necessarily square matrices any vector x t0 that can be obtained as a solution of the system for some u t and some t t0 will be termed an admissible initial state and it will be assumed that the system has a unique solution for any input and for any admissible initial state an efficient numerical method for characterizing admissible inputs and establishing uniqueness of solutions has been developed by wilkinson 1978 the problem to be solved is this find an input u t that drives the system from an admissible initial state to a prescribed final state in a given time tf 0 if the basic assumption regarding uniqueness of solutions holds the problem of controlling the given generalized state space descriptor system can be reduced to a standard control problem involving an ordinary state space system of particularly simple form then if the ordinary system is completely controllable

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

global stabilization of the generalized korteweg de vries equation posed on a finite domain this paper is concerned with the internal stabilization of the generalized korteweg de vries equation on a bounded domain the global well posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval 1 4 the global exponential stability is obtained whatever the location where the damping is active confirming positively a conjecture of perla menzala vasconcellos and zuazua quart appl math 60 2002 pp 111 129

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

deadbeat algorithms for output controllers in discrete time multivariable systems abstract this paper studies the problem of designing output deadbeat controllers to force the state of discrete time multivariable systems to zero in a finite number of samples two algorithms are considered the first is based on the fact that the closed loop eigenstructure assignable by output feedback is constrained by the requirement that the left and right eigenvectors must be in certain subspaces in the second algorithm the output gain matrix is computed through the optimization of certain parameters of the controller while maintaining its structural constraints computer programs have been developed to realize the two algorithms and examples are given to illustrate the feasibility of the techniques

comments on design of optimal dead beat controllers it is shown that the system considered in the numerical example of the above paper belongs to a class of systems with n states and r inputs for which the set of all minimum time dead beat mtdb controllers is parameterized by an arbitrary matrix of order lambda 1 r n x n lambda r where is the greatest integer less than the ratio n r since the example treats the case of n 3 r 2 the mdtb controller is parameterized by a single scalar element

author s reply to comments on eigenstructure assignment in linear multivariable systems a parametric solution by m m fahmy and j o reilly the authors reply that klein is correct in his observation that the approaches to eigenstructure assignment in earlier articles by b c moore 1976 g klein and moore 1977 are equivalent to those of the authors they assert however that their philosophies are quite different these differences are then described

constrained clustering as an optimization method a deterministic annealing approach to clustering is derived on the basis of the principle of maximum entropy this approach is independent of the initial state and produces natural hierarchical clustering solutions by going through a sequence of phase transitions it is modified for a larger class of optimization problems by adding constraints to the free energy the concept of constrained clustering is explained and three examples are are given in which it is used to introduce deterministic annealing the previous clustering method is improved by adding cluster mass variables and a total mass constraint the traveling salesman problem is reformulated as constrained clustering yielding the elastic net en approach to the problem more insight is gained by identifying a second lagrange multiplier that is related to the tour length and can also be used to control the annealing process the open path constraint formulation is shown to relate to dimensionality reduction by self organization in unsupervised learning a similar annealing procedure is applicable in this case as well

output feedback stabilization of the korteweg de vries equation this paper presents an output feedback control law for the korteweg de vries equation the control design is based on the backstepping method and the introduction of an appropriate observer the local exponential stability of the closed loop system is proven some numerical simulations are shown to illustrate this theoretical result

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

simultaneous deadbeat tracking controller synthesis abstract a direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented this novel approach is based on polynomial algebra and the principle of system realizability without solving linear polynomial diophantine equations the proposed procedure consists of solving a set of linear equations depending on system dynamics and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals since all solutions are described in a parametric form some performance criteria can be easily incorporated as well examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm

construction and parameterization of a class of minimum time deadbeat controllers abstract a method for constructing and parametrizing a class of minimum time deadbeat controllers mtdc for a discrete time system is presented the number of construction steps is equal to the controllability index of the controllable part of the system the method reduces the considered problem to that of solving at most r linear equations at each step where r is the input dimension the minimum number of free parameters that characterizes the constructed class of mtdc is specified and arranged in a new compact linear parametric form of mtdc contrary to many existing methods the presented method does not require the system to be controllable

the design of deadbeat controllers by state transition graph two kinds of deadbeat control problems are considered one is the state deadbeat control problem and the other is the pointwise minimum time deadbeat control problem a simple graph called the state transition graph of a matrix is introduced and simple algorithms based on it giving deadbeat controllers are presented the set of pointwise minimum time deadbeat controllers is characterized the set of output feedback deadbeat controller is also considered

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

multiresolution feature extraction and selection for texture segmentation an approach is described for unsupervised segmentation of textured images local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination local statistics texture energy measures are estimated at the output of an equivalent filter bank by means of a nonlinear transformation absolute value followed by an iterative gaussian smoothing algorithm this procedure generates a multiresolution sequence of feature planes with a half octave scale progression a feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions this approach provides a good approximation of r a fisher s 1950 multiple linear discriminants and has the advantage of requiring no a priori knowledge this feature reduction methods appears to be an improvement on the commonly used karhunen loeve transform and allows efficient texture segmentation based on simple thresholding

output dead beat control for a class of planar polynomial systems output dead beat control for a class of nonlinear discrete time systems which are described by a single input output i o polynomial difference equation is considered the class of systems considered is restricted to systems with a two dimensional state space description it is assumed that the highest degree with which the present input appears in the equation is odd necessary and sufficient conditions for the existence of output dead beat control and for the stability of the zero output constrained dynamics are presented we also design a minimum time output dead beat control algorithm feedback controller which yields stable zero dynamics whenever this is feasible a number of interesting phenomena are discussed and illustrated with examples

a unified view of class selection with probabilistic classifiers the possibility of selecting a subset of classes instead of one unique class for assignation is of great interest in many decision making systems selecting a subset of classes instead of singleton allows to reduce the error rate and to propose a reduced set to another classifier or an expert this second step provides additional information and therefore increases the quality of the result in this paper a unified view of the problem of class selection with probabilistic classifiers is presented the proposed framework based on the evaluation of the probabilistic equivalence allows to retrieve class selective frameworks that have been proposed in the literature we also describe an approach in which the decision rules are compared by the help of a normalized area under the error selection curve it allows to get a relative independence of the performance of a classifier without reject option and thus a reliable class selection decision rule evaluation the power of this generic proposition is demonstrated by evaluating and comparing it to several state of the art methods on nine real world datasets and four different probabilistic classifiers a unified framework of class selection by the use of probabilistic equivalence is presented a learning procedure for adapting the probabilistic equivalence is proposed a normalized performance measure for class selection is described experiments on real world datasets using different classifiers show the statistical significance of the proposition

robust stabilization of uncertain systems by periodic feedback an uncertain control system described by a family parametrized by an unknown parameter that takes values in a known constraint set is considered the robust stabilization problem is defined as finding a dynamic output controller that globally stabilizes the uncertain system that is no matter what the parameter value chosen by nature the closed loop system is globally asymptotically stable it is shown that in the class of dynamic periodic controllers the solution to this problem exists under reasonable assumptions given for a general family of abstract non linear models those assumptions in the case of a family of linear finite dimensional models are equivalent to suitable stabilizability and detectability assumptions for this case insensitivity of the design with respect to small errors in the data is proved

regulation of time invariant discrete time descriptor systems time invariant discrete time descriptor systems of the form exk 1 axk buk where e and a are n n matrices and e may be singular are considered the problem is to find a feedback law uk kxk that drives the descriptor from x 0 to the origin in less than n time steps

output feedback stabilization of the linearized korteweg de vries equation with right endpoint controllers abstract in this paper we prove the output feedback stabilization for the linearized korteweg de vries kdv equation posed on a finite domain in the case the full state of the system cannot be measured we assume that there is a sensor at the left end point of the domain capable of measuring the first and second order boundary traces of the solution this allows us to design a suitable observer system whose states can be used for constructing boundary feedbacks acting at the right endpoint so that both the observer and the original plant become exponentially stable stabilization of the original system is proved in the l 2 sense while the convergence of the observer system to the original plant is also proved in higher order sobolev norms the standard backstepping approach used to construct a left endpoint controller fails and presents mathematical challenges when building right endpoint controllers due to the overdetermined nature of the related kernel models in order to deal with this difficulty we use the method of ozsari and batal 2019 which is based on using modified target systems involving extra trace terms in addition we show that the number of controllers and boundary measurements can be reduced to one with the cost of a slightly lower exponential rate of decay we provide numerical simulations illustrating the efficacy of our controllers

finite settling time stabilisation for multivariable discrete time systems a polynomial equation approach the multivariable case of finite settling time stabilisation fsts of linear discrete time systems is considered in this paper an algebraic approach is adopted which leads to the solution of a polynomial matrix diophantine equation this gives rise to the parametrisation of all fsts controllers in a kucera youla bonjiorno sense and the fsts problem is further reduced to a linear algebra problem over the real numbers subsequently the family of all causal fsts controllers is parametrised and necessary and sufficient conditions for strong fsts stable controllers are derived the minimal mcmillan degree solution and minimal complexity controllers are examined and new bounds are given the analysis provides the means for the parametrisation of families of fsts controllers with certain complexity finally the problems of tracking disturbance rejection and partially assigned dynamics in fst sense are considered and conditions for their solvability are given

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

the korteweg de vries kawahara equation in a bounded domain and some numerical results abstract we are concerned with the initial boundary problem associated to the korteweg de vries kawahara perturbed by a dispersive term which appears in several fluids dynamics problems we obtain local smoothing effects that are uniform with respect to the size of the interval we also propose a simple finite different scheme for the problem and prove its unconditional stability finally we give some numerical examples

game theoretic integration for image segmentation robust segmentation of structures from an image is essential for a variety of image analysis problems however the conventional methods of region based segmentation and gradient based boundary finding are often frustrated by poor image quality here we propose a method to integrate the two approaches using game theory in an effort to form a unified approach that is robust to noise and poor initialization this combines the perceptual notions of complete boundary information using edge data and shape priors with gray level homogeneity using two computational modules the novelty of the method is that this is a bidirectional framework whereby both computational modules improve their results through mutual information sharing a number of experiments were performed both on synthetic datasets and datasets of real images to evaluate the new approach and it is shown that the integrated method typically performs better than conventional gradient based boundary finding

coupled system of korteweg de vries equations type in domains with moving boundaries we consider the initial boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for the coupled system of equations of korteweg de vries kdv type modelling strong interactions between internal solitary waves finite domains of wave propagation changing in time arise naturally in certain practical situations when the equations are used as a model for waves and a numerical scheme is needed we prove a global existence and uniqueness for strong solutions for the coupled system of equations of kdv type as well as the exponential decay of small solutions in asymptotically cylindrical domains finally we present a numerical scheme based on semi implicit finite differences and we give some examples to show the numerical effect of the moving boundaries for this kind of systems

mac magnetostatic active contour model we propose an active contour model using an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries the major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations weak edges and broken boundaries the proposed method is shown to achieve significant improvements when compared against six well known and state of the art shape recovery methods including the geodesic snake the generalized version of gradient vector flow gvf snake the combined geodesic and gvf snake and the charged particle model

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

feature selection in the pattern classification problem of digital chest radiograph segmentation in pattern classification problems the choice of variables to include in the feature vector is a difficult one the authors have investigated the use of stepwise discriminant analysis as a feature selection step in the problem of segmenting digital chest radiographs in this problem locally calculated features are used to classify pixels into one of several anatomic classes the feature selection step was used to choose a subset of features which gave performance equivalent to the entire set of candidate features while utilizing less computational resources the impact of using the reduced selected feature set on classifier performance is evaluated for two classifiers a linear discriminator and a neural network the results from the reduced selected feature set were compared to that of the full feature set as well as a randomly selected reduced feature set the results of the different feature sets were also compared after applying an additional postprocessing step which used a rule based spatial information heuristic to improve the classification results this work shows that in the authors pattern classification problem using a feature selection step reduced the number of features used reduced the processing time requirements and gave results comparable to the full set of features

fifo stable control systems abstract motivated by the dead beat and shortest correlation control strategies the paper introduces the notion of finite input finite output fifo stability for linear discrete time control systems a simple parametrization of all controllers that fifo stabilize a given plant is obtained the best controller is then chosen for various applications including h 2 optimization disturbance rejection and transfer function shaping

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

image segmentation by unifying region and boundary information a two stage method of image segmentation based on gray level cooccurrence matrices is described an analysis of the distributions within a cooccurrence matrix defines an initial pixel classification into both region and interior or boundary designations local consistency of pixel classification is then implemented by minimizing the entropy of local information where region information is expressed via conditional probabilities estimated from the cooccurrence matrices and boundary information via conditional probabilities which are determined a priori the method robustly segments an image into homogeneous areas and generates an edge map the technique extends easily to general edge operators an example is given for the canny operator applications to synthetic and forward looking infrared flir images are given

a direct computation of state deadbeat feedback gains a method for computing a feedback gain that achieves state deadbeat control is given from systems given in the staircase form this method derives the deadbeat gain in a numerically reliable way it is shown that the gain turns out to be lq optimal for some weightings

parameterization of the class of deadbeat controllers via the theory of decoupling a novel approach is presented for parameterizing the class of minimum time deadbeat controllers mtdc through the minimum number of parameters the approach is based on the theory of decoupling and the properties of square decouplable systems the main result is a compact parametric form for the class of mtdc of a discrete time system contrary to many existing techniques no special assumption on the invertibility of the transition matrix is required

on the inverse of a general pentadiagonal matrix in this paper employing the general doolittle factorization an efficient algorithm is developed to find the inverse of a general pentadiagonal matrix which is suitable for implementation using computer algebra systems software such as matlab and maple examples are given to illustrate the efficiency of the algorithm

the effect of sampling period on the behaviour of systems incorporating state feedback an exposition of the effects of sampling on the controllability characteristics and the kronecker invariants of the plant and the input matrices of sampled data systems is presented in particular the effect of sampling period on the feedback matrix for time optimal control of sampled data systems is investigated in detail and it is shown that different classes of systems produce different response characteristics as the sampling period becomes large also simple expressions for a nt in terms of a t and b nt as a function of a t and b t are derived these expressions are computationally attractive and therefore facilitate the study of the effect of sampling period on system behaviour by applying these expressions the effects of sampling period on the feedback matrices for time optimal control of three classes of systems whose open loop plants are asymptotically stable marginally stable and unstable are illustrated by numerical examples

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

output regulator problem of time invariant discrete time descriptor systems linear time invariant discrete time systems of the form exk 1 axk buk yk cxt are considered where e and a are square matrices and e may be singular the investigations are restricted to systems for which there exist non singular matrices and such that e diag lr 0 and a equation pending where f 2 has full row rank such systems are termed regular by luenberger 1977 and can be decomposed into two equations of the respective forms k 1 1 k 2 k and 2uk 0 where k k and xk are related by the equation xk equation pending thus the descriptor system might be reduced to a state space system whose state vector is k a reasonable choice for c is c i 0 1where is some m x r matrix of full row rank which yields yk k the problem is this given an initial descriptor vector xo find without reducing the descriptor system to a state space system a sequence of control vectors u o u 1 un 1 hy that will yield yn 0 for some n a necessary and sufficie

average classification accuracy over collections of gaussian problems common covariance matrix case abstract the mean probability of correct classification p cr is calculated over a collection of equiprobable two class gaussian problems with a common covariance matrix for each problem the bayes minimum error classification rule in which the unbiased estimates of the mean vectors and covariance matrices are used in place of the true values is the classification rule considered the variation of p cr with the dimensionality n is investigated for three interesting cases with different complexities in the first case all the parameters of the class conditional densities are known for the second case the common covariance matrix is assumed known and only the mean vectors need to be estimated while all the parameters need to be estimated in the last case for these three cases the relationship between p cr and n is plotted for a specific collection of problems for the case of finite sample size peaking of p cr with n is encountered in most of the cases considered

on the general solution of the state deadbeat control problem in this note the state deadbeat control problem is considered it is shown that after appropriate change of basis of input and state spaces the general solution of the state deadbeat control problem can be expressed completely by the rows of the powers of system matrix this result yields a very simple procedure for the calculation of a state feedback deadbeat control gain it also provides the number of free parameters which could be used for further design purposes the results are illustrated by an example at the end of the note

stabilizability and dead beat controllers for two classes of wiener hammerstein models two classes of block oriented models of the wiener hammerstein type are considered we prove that a generic condition is sufficient for a null controllable discrete time system of this form to have a stabilizing minimum time dead beat controller when the condition is violated we show how to design a nonminimum time stabilizing dynamic dead beat controller the result is used to obtain stabilizability conditions for these systems

relaxation evaluation and applications probabilistic relaxation labeling processes are iterative parallel schemes that use contextual information to reduce local ambiguities the behavior of these processes can be described by examining the rates of change and entropies of the probability vectors at each iteration examples are given comparing three relaxation processes as applied to several basic image analysis tasks

uniform exponential long time decay for the space semi discretization of a locally damped wave equation via an artificial numerical viscosity we consider the finite difference space semi discretization of a locally damped wave equation the damping being supported in a suitable subset of the domain under consideration so that the energy of solutions of the damped wave equation decays exponentially to zero as time goes to infinity the decay rate of the semi discrete systems turns out to depend on the mesh size h of the discretization and tends to zero as h goes to zero we prove that adding a suitable vanishing numerical viscosity term leads to a uniform with respect to the mesh size exponential decay of the energy of solutions this numerical viscosity term damps out the high frequency numerical spurious oscillations while the convergence of the scheme towards the original damped wave equation is kept we discuss this problem in 1d and 2d in the interval and the square respectively our method of proof relies on discrete multiplier techniques

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

convergence of galerkin approximations for the korteweg de vries equation standard galerkin approximations using smooth splines on a uniform mesh to 1 periodic solutions of the korteweg de vries equation are analyzed optimal rate of convergence estimates are obtained for both semidiscrete and second order in time fully discrete schemes at each time level the resulting system of nonlinear equations can be solved by newton s method it is shown that if a proper extrapolation is used as a starting value then only one step of the newton iteration is required

existence of blow up solutions in the energy space for the critical generalized kdv equation from these conservation laws h appears as an energy space so that it is a natural space in which to study the solutions note that p 2 is a special case for equation 2 indeed from the integrability theory see lax 14 we have for suitable u0 u0 and its derivatives with fast decay at infinity an infinite number of conservation laws the general question is to understand the dynamics induced by such equations local existence in time of solutions of 2 in the energy space is now well understood see kato 10 ginibre and tsutsumi 8 for the h theory s 32 kenig ponce and vega 11 for the l theory in the case of equation 1 and sharp h theory for 2 and bourgain 3 and 4 for the periodic case

a semi implicit monotone difference scheme for an initial boundary value problem of a strongly degenerate parabolic equation modeling sedimentation consolidation processes we prove the convergence of a semi implicit monotone finite difference scheme approximating an initial boundary value problem for a spatially one dimensional quasilinear strongly degenerate parabolic equation which is supplied with two different inhomogeneous flux type boundary conditions this problem arises in the modeling of the sedimentation consolidation process we formulate the definition of entropy solution of the model in the sense of kruzkov and prove convergence of the scheme to the unique bv entropy solution of the problem up to satisfaction of one of the boundary conditions

uniform stabilization of numerical schemes for the critical generalized korteweg de vries equation with damping this work is devoted to the analysis of a fully implicit numerical scheme for the critical generalized korteweg de vries equation gkdv with p 4 in a bounded domain with a localized damping term the damping is supported in a subset of the domain so that the solutions of the continuous model issuing from small data are globally defined and exponentially decreasing in the energy space based in this asymptotic behavior of the solution we introduce a finite difference scheme which despite being one of the first order has the good property to converge in l 4 strong combining this strong convergence with discrete multipliers and a contradiction argument we show that the smallness of the initial condition leads to the uniform with respect to the mesh size exponential decay of the energy associated to the scheme numerical experiments are provided to illustrate the performance of the method and to confirm the theoretical results

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

effects of sample size in classifier design the effect of finite sample size on parameter estimates and their subsequent use in a family of functions are discussed general and parameter specific expressions for the expected bias and variance of the functions are derived these expressions are then applied to the bhattacharyya distance and the analysis of the linear and quadratic classifiers providing insight into the relationship between the number of features and the number of training samples because of the functional form of the expressions an empirical approach is presented to enable asymptotic performance to be accurately estimated using a very small number of samples results were experimentally verified using artificial data in controlled cases and using real high dimensional data

regular article finite difference schemes for u t x α δg δu that inherit energy conservation or dissipation property we propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations such as the korteweg de vries kdv equation and the cahn hilliard equation the most important feature of our procedure is a rigorous discretization of variational derivatives using summation by parts which implies that the inherited properties are satisfied exactly since the inherited properties are kept even if the time mesh size changes in the time evolution process we can use some appropriate time mesh adaptive methods to obtain numerical solutions through the derived schemes because of these properties the derived schemes are expected to be numerically stable and yield solutions converging to pde solutions and sufficiently flexible to treat the inheritance of the energy conservation and dissipation properties are verified numerically for the kdv equation and the cahn hilliard equation

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

scale invariant image recognition based on higher order autocorrelation features we propose a framework and a complete implementation of a translation and scale invariant image recognition system for natural indoor scenes the system employs higher order autocorrelation features of scale space data which permit linear classification an optimal linear classification method is presented which is able to cope with a large number of classes represented by many as well as very few samples in the course of the analysis of our system we examine which numerical methods for feature transformation and classification show sufficient stability to fulfill these demands the implementation has been extensively tested we present the results of our own application and several classification benchmarks

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

an initial boundary value problem that approximate the quarter plane problem for the korteweg de vries equation in this paper we continue the study of the initial boundary value prob lem for the korteweg de vries equation that has been initiated in 9 we obtain global smoothing eects that are uniform with respect to the size of the interval this allows us to show that the solution of the boundary value problem converges as the size of the interval converges to infinity towards the solution of the quarter plane problem we also propose a simple finite dierents scheme for the problem on 0 1 and prove its stability

bscan image segmentation by thresholding using cooccurrence matrix analysis abstract in this paper we present innovative research for the processing of an uktrasonic image obtained in non destructive testing ndt we also present an algorithm for automatic thresholding segmentation the image analysis is based on the calculation of cooccurrence matrices the method we used is the spatial grey level dependence method sgldm it shows the distribution of the intensities of pairs of pixels separated by a vector d we show that it is necessary to build optimized matrices in order to improve the existing techniques while adapting to the specifics of the ultrasonic image obtained in ndt we solve for the vector d through an automatic analysis of the matrix behaviour for several vectors based on the characterization curves the developed method allows us to present an efficient thresholding algorithm that is tested on real images

state deadbeat control of nonlinear systems construction via sets a geometric generalization of the discrete time linear deadbeat control problem is studied the proposed method to generate a deadbeat tracker for a given nonlinear system is constructive and makes use of sets that can be computed iteratively for demonstration derivations of the deadbeat feedback law and tracker dynamics are provided for an example system based on the method a simple algorithm that computes the deadbeat gain for a linear system with scalar input is given

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

parametrization of minimum time output deadbeat controllers for all classes of invertible systems this paper considers the problem of parametrizing through the minimum number of parameters the minimum time output deadbeat controller mtodc for a given linear multivariable output controllable system s a b c e having n states m inputs p outputs and a transfer function matrix h z of full rank r the main result is a new compact linear parametric form for a class of mtodc that zeros the outputs of the system s in the minimum number of control iterations 1 where 1 i 1 2 r assumed to be decreasingly ordered are equal lo the negatives of the right factorization indices at infinity of h z the developed parametric class is a linear function in effective free parameters the principal benefits of this explicit parametrization of mtodcs lie in the ability to accommodate directly various different design criteria

some further results of three stage ml classification applied to remotely sensed images abstract recently a three stage maximum likelihood tsml classifier n b venkateswarlu and p s v s k raju pattern recognition24 1113 1116 1991 has been proposed to reduce the computational requirements of the ml classification rule some modifications are proposed here further to improve this fast algorithm the winograd method is proposed for use with range calculations and is also used with lower triangular and unitary canonical form approaches w eppler ieee trans geoscience electronics14 1 26 33 1976 in calculating quadratic forms new types of range are derived by expanding the discriminant function which are then used with a tsml algorithm to identify their usefulness in eliminating groups at stages i and ii the use of pre calculated values is proposed to obviate some multiplications while calculating the ranges further threshold logic a h feiveson ieee trans pattern analysis mach intell 5 1 48 54 1983 is used with an old and a modified tsml classifier and its effectiveness observed in further reducing computation time performance of the old and the modified tsml algorithms is studied in detail by varying the dimensionality and number of samples for the purpose of experiment 6 channel thematic mapper tm and randomly generated 12 dimensional data sets are used a maximum speed up factor of 4 8 is observed with these data sets these experiments are also repeated with modified maximum likelihood and mahalanobis distance classifiers to inspect cpu time requirements

a family of measures for best top n class selective decision rules when classes strongly overlap in the feature space or when some classes are not known in advance the performance of a classifier heavily decreases to overcome this problem the reject option has been introduced it simply consists in withdrawing the decision and let another classifier or an expert take the decision whenever exclusively classifying is not reliable enough the classification problem is then a matter of class selection from none to all classes in this paper we propose a family of measures suitable to define such decision rules it is based on a new family of operators that are able to detect blocks of similar values within a set of numbers in the unit interval the soft labels of an incoming pattern to be classified using a single threshold experiments on synthetic and real datasets available in the public domain show the efficiency of our approach

active contouring based on gradient vector interaction and constrained level set diffusion this paper presents an extension of our recently introduced mac model to deal with the initialization dependency problem that commonly appears in edge based approaches its dynamic force field unique bidirectionality and constrained diffusion based level set evolution provide great freedom in contour initialization and show significant improvements in initialization independency compared to other edge based techniques it can handle more sophisticated topological changes than splitting and merging it provides new potentials for edge based active contour methods particularly when detecting and localizing objects with unknown location geometry and topology

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

explicit parameterization of state deadbeat controllers a general state deadbeat control problem not restricted to the controllability indexes is posed and solved a result for the explicit parameterization of deadbeat controllers is obtained with the parameterization only the genuine independent free parameters appear in the deadbeat controllers

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed

closed loop expressions of minimum energy control for single input linear digital systems closed loop expressions for the minimum energy control of a single input linear digital system are described they are obtained by two different methods the optimal inputs are given by state feedback with the bounded variable gains the gains are independent of the initial state of the system