unfalsified probability estimation for a model set based on frequency domain data this paper deals with the problem of estimating the probability under which a model set is not falsified by a set of measured plant frequency response samples a definition of sample unfalsified probability has been proposed and an explicit formula has been derived computation issues are also discussed moreover an efficient algorithm has been developed for sample unfalsified probability calculation monte carlo simulations show that the defined sample unfalsified probability is appropriate in the evaluation of the quality of a model set compared with the deterministic approach simulation results suggest that the probabilistic approach is more suitable in model set validation

subgradient based neural networks for nonsmooth nonconvex optimization problems this paper presents a subgradient based neural network to solve a nonsmooth nonconvex optimization problem with a nonsmooth nonconvex objective function a class of affine equality constraints and a class of nonsmooth convex inequality constraints the proposed neural network is modeled with a differential inclusion under a suitable assumption on the constraint set and a proper assumption on the objective function it is proved that for a sufficiently large penalty parameter there exists a unique global solution to the neural network and the trajectory of the network can reach the feasible region in finite time and stay there thereafter it is proved that the trajectory of the neural network converges to the set which consists of the equilibrium points of the neural network and coincides with the set which consists of the critical points of the objective function in the feasible region a condition is given to ensure the convergence to the equilibrium point set in finite time moreover under suitable assumptions the coincidence between the solution to the differential inclusion and the ldquoslow solutionrdquo of it is also proved furthermore three typical examples are given to present the effectiveness of the theoretic results obtained in this paper and the good performance of the proposed neural network

dynamical system for computing the eigenvectors associated with the largest eigenvalue of a positive definite matrix a dynamical system for computing the largest eigenpair of a given positive matrix is introduced certain qualitative properties of the proposed system are analyzed in detail the authors results suggest that the weight bounding term in pca algorithms for extracting the first principal component could assume a class of forms

recurrent neural network for computing the drazin inverse this paper presents a recurrent neural network rnn for computing the drazin inverse of a real matrix in real time this recurrent neural network rnn is composed of n independent parts subnetworks where n is the order of the input matrix these subnetworks can operate concurrently so parallel and distributed processing can be achieved in this way the computational advantages over the existing sequential algorithms can be attained in real time applications the rnn defined in this paper is convenient for an implementation in an electronic circuit the number of neurons in the neural network is the same as the number of elements in the output matrix which represents the drazin inverse the difference between the proposed rnn and the existing ones for the drazin inverse computation lies in their network architecture and dynamics the conditions that ensure the stability of the defined rnn as well as its convergence toward the drazin inverse are considered in addition illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network

neural network approach to computing matrix inversion a neural network for matrix inversion is proposed we show both analytically and by simulations that this network is guaranteed to be stable and to provide results arbitrarily close to the accurate inversion of a matrix within an elapsed time of only a few characteristic time constants of the network the parameters such as the interconnection strengths of this network can be obtained from the known matrix without any computations

recurrent neural networks for computing pseudoinverses of rank deficient matrices three recurrent neural networks are presented for computing the pseudoinverses of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of moore penrose inversion under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a pseudoinverse matrix and a lagrangian matrix with constant connections all three recurrent neural networks are also composed of a number of independent subnetworks corresponding to the rows or columns of a pseudoinverse the proposed recurrent neural networks are shown to be capable of computing the pseudoinverses of rank deficient matrices

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

minimizing the condition number of a gram matrix the condition number of a gram matrix defined by a polynomial basis and a set of points is often used to measure the sensitivity of the least squares polynomial approximation given a polynomial basis we consider the problem of finding a set of points and or weights which minimizes the condition number of the gram matrix the objective function f in the minimization problem is nonconvex and nonsmooth we present an expression of the clarke generalized gradient of f and show that f is clarke regular and strongly semismooth moreover we develop a globally convergent smoothing method to solve the minimization problem by using the exponential smoothing function to illustrate applications of minimizing the condition number we report numerical results for the gram matrix defined by the weighted vandermonde like matrix for least squares approximation on an interval and for the gram matrix defined by an orthonormal set of real spherical harmonics for least squares approximation on the sphere

a one layer recurrent neural network for pseudoconvex optimization subject to linear equality constraints in this paper a one layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints the global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex the finite time state convergence to the feasible region defined by the equality constraints is also proved in addition global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network

recurrent neural network approach based on the integral representation of the drazin inverse in this letter we present the dynamical equation and corresponding artificial recurrent neural network for computing the drazin inverse for arbitrary square real matrix without any restriction on its eigenvalues conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the drazin inverse are considered several illustrative examples present the results of computer simulations

an algorithm for robust pole assignment via polynomial approach a computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented the analysis is based on transfer functions of characteristic polynomials and the problem is formulated as one of semi infinite programming an example of an application is given to illustrate this approach

brief paper probabilistic bounds for l 1 uncertainty model validation this paper is concerned with a mixed deterministic probabilistic model validation problem which amounts to determining the probability for a given model to reproduce given experimental data we consider an additive uncertain model in which the modelling uncertainty is characterized in time domain by the 1 induced system norm the data available for validation are input output time series and are assumed to have been corrupted by a random noise for a given uncertainty norm bound our objective is to compute the probability for an uncertainty to exist so that it may satisfy the prescribed bound and match the input output measurements while the exact computation of this probability poses a formidable task we derive its upper and lower bounds this is carried out with respect to noise sequences with gaussian distribution and more generally when only such statistical information as the expectation and covariance of the noise are known

complex neural network models for time varying drazin inverse two complex zhang neural network znn models for computing the drazin inverse of arbitrary time varying complex square matrix are presented the design of these neural networks is based on corresponding matrix valued error functions arising from the limit representations of the drazin inverse two types of activation functions appropriate for handling complex matrices are exploited to develop each of these networks theoretical results of convergence analysis are presented to show the desirable properties of the proposed complex valued znn models numerical results further demonstrate the effectiveness of the proposed models

recurrent neural networks for computing weighted moore penrose inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 three recurrent neural networks are presented for computing the weighted moore penrose inverse of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted moore penrose inverse under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a weighted moore penrose inverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a weighted moore penrose inverse and a lagrangian matrix with constant connections

model validation a connection between robust control and identification the gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data the model validation problem addressed is given experimental data and a model with both additive noise and norm bounded perturbations is it possible that the model could produce the observed input output data this problem is studied for the standard h sub infinity mu framework models a necessary condition for such a model to describe an experimental datum is obtained for a large class of models in the robust control framework this condition is computable as the solution of a quadratic optimization problem

a one layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints this paper presents a one layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints the proposed neural network is designed based on two projection operators linear equality constraints and bound constraints the objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex pseudoconvex on a set defined by the constraints compared with existing recurrent neural networks for nonsmooth optimization the proposed model does not have any design parameter which is more convenient for design and implementation it is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

a recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints this paper presents a continuous time recurrent neural network model for nonlinear optimization with any continuously differentiable objective function and bound constraints quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network the proposed recurrent neural network has the following characteristics 1 it is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network if the objective function to be minimized is convex then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network 2 the recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region 3 the recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region 4 for minimizing any strictly convex quadratic objective function subject to bound constraints the recurrent neural network is globally exponentially stable for almost any positive network parameters simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints

quality evaluation for a coprime factor perturbed model set based on frequency domain data quality assessment is investigated under a probabilistic framework for a prescribed model set the results on unfalsified probability estimation are extended from additive modeling errors to normalized coprime factor perturbations an analytic formula has been derived for the sample unfalsified probability it is shown that with increasing the data length the sample unfalsified probability converges in probability to a number which is independent of experimental data numerical simulations show that the proposed sample unfalsified probability is appropriate in the evaluation of the quality of a model set

automatic 1 d inversion of magnetotelluric data finding the simplest possible model that fits the data we demonstrate that automatic layered inversion of plane wave electromagnetic data can be carried out by modifying standard least squares inversion schemes the modifications include a logarithmic reparameterization of the unknown model parameters whereby all layer parameters are forced to remain within given bounds however the most important modification to help the optimization process find the best model and to avoid local minima is to split the data into several subbands starting from the highest frequencies by this stripping procedure the shallower part of the model becomes well estimated first as more data are introduced more layers may be required to improve the data fit the new inversion procedure has been applied to many sets of theoretical data representing increasingly complicated layering that is often found in near surface studies the main result of these simulations is that there is a very strong coupling between the resolution power of plane wave data and their random errors part

frequency estimation by principal component ar spectral estimation method without eigendecomposition an eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse it is shown using a computer simulation that compared to the forward backward method the proposed method enhances the threshold in snr by about 6 8 db further improvement is obtained by a simple subset selection method and a second eigenvalue filtering iteration

pole assignment via the schur form abstract we propose an algorithm for the state feedback pole assignment problem the algorithm is the first of its kind making direct use of the schur form and minimizing the departure from normality of the closed loop poles for a given first schur vector x 1 the robust pole assignment problem can then be solved via choosing x 1 optimally several numerical examples were presented to illustrate the feasibility of the algorithm

real time computation of the eigenvectors of a class of positive definite matrices this paper proposes an analog circuit approach to computing in real time the eigenvectors corresponding to all the eigenvalues of a class of positive definite matrices we show analytically and by simulations that the proposed circuit can provide the desired eigenvectors with arbitrarily small error during an elapsed time of only a few characteristic time constants of the circuit

pole assignment via sylvester s equation it is shown that the pole assignment problem can be reduced to solving the linear matrix equations ax xa bg fx g successively for x and then f for almost any choice of g the result is a new pole assignment procedure and proof of the pole assignment theorem that should play an important role in both theoretical and practical applications

optimizing condition numbers in this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite n times n matrices we show that the condition number is a clarke regular strongly pseudoconvex function we prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program this asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

probabilistic estimates for mixed model validation problems with cal h _ infty type uncertainties a mixed deterministic probabilistic model validation problem is investigated in this technical note which consists in an additive uncertain model with model uncertainty characterized by the h norm the data available for validation are time domain experimental data corrupted by a random noise sequence our aim is to compute the probability for such an uncertain model to be validated by the data and our main results are bounds on this probability that are computable based on the distribution of chi square random variables when the noise is a gaussian variable and solvable as an lmi problem when only statistical information such as the expectation and covariance of the noise are known

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

robustness in partial pole placement the robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined the projection procedure gives a reduced order pole assignment problem it is shown that the sensitivities of the assigned poles in the complete closed loop system are bounded in terms of the sensitivities of the assigned reduced order poles and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open loop poles if the assigned poles are well separated from the unaltered poles these bounds are expected to be tight the projection procedure is described in 3 and techniques for finding robust or insensitive solutions to the reduced order problem are given in 1 2

validation of linear fractional uncertain models solutions via matrix inequalities a time domain approach is provided in this paper to tackle the problem of model validation pertaining to uncertain models described by linear fractional transforms both unstructured and structured dynamic uncertainties are considered it is shown that in the first case the problem can be solved by finding a feasible solution to a convex optimization problem while in the second case it amounts to solving a biaffine matrix inequality problem to which only a convex optimization based necessary condition is given

model invalidation in spl lscr sub 1 using frequency domain data in this note we study the problem of invalidating uncertain models with an additive uncertainty the problem is to check the existence of an uncertainty and a measurement noise which fit to the given model structure and the uncertainty noise description as well as the experimental data used for invalidation we consider a mixed setting in which the uncertainty is characterized in time domain by the spl lscr sub 1 induced system norm while the available data are frequency response samples of the system we show that this problem which by formulation poses an infinite dimensional primal optimization problem can be solved in a dual finite dimensional space with finitely many constraints

sizing and least change secant methods oren and luenberger introduced in 1974 a strategy for replacing hessian approximations by their scalar multiples and then performing quasi newton updates generally least change secant updates such as the bfgs or dfp updates oren and luenberger management sci 20 1974 pp 845 862 in this paper the function omega a left frac operatorname trace a n operatorname det a 1 n right is shown to be a measure of change with a direct connection to the oren luenberger strategy this measure is interesting because it is related to the ell 2 condition number but it takes all the eigenvalues of a into account rather than just the extremes if the class of possible updates is restricted to the broyden class i e scalar premultiples are not allowed then the optimal update depends on the dimension of the problem it may or may not be in the convex class but it becomes the bfgs update as the dimension increases this seems to be yet another explanation for why

magnetotelluric inversion for minimum structure structure can be measured in terms of a norm of the derivative of a model with respect to a function of depth f z where the model m z is either the conductivity or log an iterative linearized algorithm can find models that minimize norms of this form for chosen levels of chi squared misfit the models found may very well be global minima of these norms since they are not observed to depend on the starting model overfitting data causes extraneous structure some choices of the depth function result in systematic overfitting of high frequencies a blue fit and extraneous shallow structure others result in systematic overfitting of low frequencies a red fit and extraneous deep structure a robust statistic is used to test for whiteness the fit can be made acceptably white by varying the depth function f z which defines the norm an optimum norm produces an inversion which does not introduce false structure and which approaches the true structure in a reasonable way as data errors decrease

on computational complexity of invalidating structured uncertainty models abstract in this paper we study a class of uncertainty model validation invalidation problems for linear discrete time systems we consider models described by a linear fractional transformation lft of modeling uncertainties which are structured time invariant or time varying and are bounded in h or l 1 norms the experimental data available for use in invalidation are either input output time series observations or frequency response measurements we analyze the computational complexity associated with these problems while earlier work showed that for lft models with an unstructured uncertainty the invalidation problems can be reduced to one of solving linear matrix inequalities and hence may be tackled readily using well developed numerical methods in this paper we provide a simple proof to show that in the presence of structured uncertainties they are all np hard with respect to the number of uncertainty blocks suggesting that the problems are inherently intractable from a computational standpoint additionally we also demonstrate that the problems do become tractable when the lft model description is changed to an additive one leading to lmi based invalidation tests similar to those obtained elsewhere these results indicate that the main source of the computational difficulty lies in the lft description together with the structured nature of the uncertainties

optimal inequalities in probability theory a convex optimization approach we propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for p x in s for a set s defined by polynomial inequalities and a random vector x defined on omega subseteq cal r n that has a given collection of up to kth order moments in the univariate case we provide optimal bounds on p x in s when the first k moments of x are given as the solution of a semidefinite optimization problem in k 1 dimensions in the multivariate case if the sets s and omega are given by polynomial inequalities we obtain an improving sequence of bounds by solving semidefinite optimization problems of polynomial size in n for fixed k we characterize the complexity of the problem of deriving tight moment inequalities we show that it is np hard to find tight bounds for k geq 4 and omega cal r n and for k geq 2 and omega cal r n when the data in the problem is rational for k 1 and omega cal r n we show that we can find tight upper bounds by solving n convex optimization problems when the set s is convex and we provide a polynomial time algorithm when s and omega are unions of convex sets over which linear functions can be optimized efficiently for the case k 2 and omega cal r n we present an efficient algorithm for finding tight bounds when s is a union of convex sets over which convex quadratic functions can be optimized efficiently

frequency domain tests for validation of linear fractional uncertain models a frequency domain approach is adopted in this paper to tackle the problem of validating uncertainty models described by linear fractional transforms this problem amounts to verifying the consistency of certain given mathematical models to experimental information obtained from a physical plant using either input output frequency domain measurements or frequency samples of the plant linear fractional models with both unstructured and structured uncertainties are considered the problem is resolved in the former case and solved approximately in the latter both results lead to tests that are readily computable via convex optimization methods and can be implemented using standard algorithms in comparison to previously available algorithms based on time domain information the main advantage of these tests is that they have a considerably lower level of computational complexity it is shown that the validation problem reduces to one of nevanlinna pick boundary interpolation and it can be solved by computing independently a sequence of convex programs of a lower dimension each of which corresponds to only one frequency sample

measures for symmetric rank one updates measures of deviation of a symmetric positive definite matrix from the identity are derived they give rise to symmetric rank one sr1 type updates the measures are motivated by considering the volume of the symmetric difference of the two ellipsoids which arise from the current and updated quadratic models in quasi newton methods the measure defined by the problem maximize the determinant subject to a bound of 1 on the largest eigenvalue yields the sr1 update the measure a 1 a det a 1 n yields the optimally conditioned sized symmetric rank one updates the volume considerations also suggest a correction for the initial stepsize for these sized updates it is then shown that the optimal updates as well as the oren luenberger self scaling updates are all optimal updates for the measure the l2 condition number moreover all four sized updates result in the same largest and smallest scaled eigenvalue and corresponding eigenvector in fact the inversesized bfgs is the mean of the

two finite time convergent zhang neural network models for time varying complex matrix drazin inverse abstract this paper concerns the computation of the drazin inverse of a complex time varying matrix based on two zhang functions constructed from two limit representations of the drazin inverse we present two complex zhang neural network znn models with the li activation function for computing the drazin inverse of a complex time varying square matrix we prove that our znn models globally converge in finite time in addition upper bounds of the convergence time are derived analytically via the lyapunov theory our simulation results verify the theoretical analysis and demonstrate the superiority of our znn models over the gradient based gnn models

recurrent neural network for computing the w weighted drazin inverse abstract two gradient based recurrent neural networks rnns for computing the w weighted drazin inverse of a real rectangular matrix are proposed and considered usage of the first rnn is limited by a specific constraint on the spectrum of a certain matrix the second rnn is usable without restrictions the stability of the recurrent neural networks as well as their convergence are considered numerical examples are given to show the efficiency of the proposed neural networks

recurrent neural networks for solving linear matrix equations abstract recurrent neural networks for solving linear matrix equations are proposed the proposed recurrent neural networks consist of two bidirectionally connected layers and each layer consists of an array of neurons the proposed recurrent neural networks are shown to be asymptotically stable in the large and capable of computing inverse matrices and solving lyapunov matrix equations the operating characteristics of the proposed recurrent neural networks are demonstrated via several illustrative examples

approaches to robust pole assignment abstract robust pole assignment is a non linear optimization problem in many variables we describe numerical methods for determining robust or well conditioned so lutions to the problem of pole assignment by state feedback the solutions are chosen to minimize various objective functions based on the condition number of the eigenvector matrix careful choice of parametrization and objective function avoids singularities and artificial variable constraints explicit formulae for the gradient and hessian permit rigorous stopping criteria and rapid local convergence several computational examples are included

a recurrent neural network for solving nonlinear convex programs subject to linear constraints in this paper we propose a recurrent neural network for solving nonlinear convex programming problems with linear constraints the proposed neural network has a simpler structure and a lower complexity for implementation than the existing neural networks for solving such problems it is shown here that the proposed neural network is stable in the sense of lyapunov and globally convergent to an optimal solution within a finite time under the condition that the objective function is strictly convex compared with the existing convergence results the present results do not require lipschitz continuity condition on the objective function finally examples are provided to show the applicability of the proposed neural network

pole assignment with optimal spectral conditioning this paper presents a novel method for pole assignment with robustness measured in terms of the spectral condition number of the closed loop eigenvector matrix it is established that the spectral condition number can be minimized asymptotically via a sequence of unconstrained minimizations on some auxiliary objective functions moreover the sequence of minimizers converges to a minimizer of the spectral condition number a numerical algorithm with analytical formulas of the gradient of the auxiliary objective functions is provided the efficiency and effectiveness of the approach is demonstrated via an example

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

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

analog approach for the eigen decomposition of positive definite matrices abstract this paper proposes an analog approach for performing the eigen decomposition of positive definite matrices we show analytically and by simulations that the proposed circuit is guaranteed to converge to the desired eigenvectors and eigenvalues of positive definite matrices

robust pole assignment abstract this paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots and applies them to the problem of robust pole placement we formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed loop poles within desired intervals for plants with unknown but bounded parameter uncertainties the algorithms are computationally reasonable and provide a useful addition to currently existing control cad tools

brief a gradient flow approach to on line robust pole assignment for synthesizing output feedback control systems pole assignment is a basic design method for synthesis of feedback control systems in this paper a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems the proposed approach is shown to be capable of synthesizing linear output feedback control systems via on line robust pole assignment convergence of the gradient flow can be guaranteed moreover with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed loop control system based on the gradient flow is globally exponentially stable these desired properties make it possible to apply the proposed approach to slowly time varying linear control systems simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach

consistency of open loop experimental frequency response data with coprime factor plant models the model data consistency problem for coprime factorization considered is given some possibly noisy frequency response data obtained by running open loop experiments on a system show that these data are consistent with a given family of perturbed coprime factor models and a time domain spl lscr sub spl infin noise model in the noise free open loop case the model data consistency problem boils down to the existence of an interpolating function in spl rscr spl hscr sub spl infin that evaluates to a finite number of complex matrices at a finite number of points on the imaginary axis a theorem on boundary interpolation in spl rscr spl hscr sub spl infin is a building block that allows one to devise computationally simple necessary and sufficient tests to check if the perturbed coprime factorization is consistent with the data for standard coprime factorizations the test involves the computation of minimum norm solutions to underdetermined complex matrix equations the schmidt mirsky theorem is used in the case of special factorizations of flexible systems for spl lscr sub spl infin noise corrupting the frequency response measurements a complete solution to the open loop noisy siso problem using the structured singular value spl mu is given

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

neural network for computing pseudoinverses and outer inverses of complex valued matrices we propose two continuous time neural networks for computing generalized inverses of complex valued matrices with rank deficient cases the first of them is applicable in the pseudoinverse computation and the second one is applicable in construction of outer inverses the proposed continuous time neural networks have a low complexity of implementation and they are proved to be globally convergent without any condition compared with the existing algorithms for computing the pseudoinverse and outer inverses of matrices the global convergence of the proposed continuous time neural networks is analyzed in the complex domain effectiveness of the proposed continuous time neural networks is evaluated numerically via examples

robust exact pole placement via an lmi based algorithm this technical note deals with the robust exact pole placement problem pole placement algorithms that guarantee a small variation of the assigned poles against possible perturbations the solution to this problem is related to the solvability of a sylvester like equation thus the main issue is to compute a well conditioned solution to this equation also the best candidate solution must possess the minimal condition number to reduce sensitivity to perturbation this problem is cast as a global optimization under linear matrix inequality constraints for which a numerical convergent algorithm is provided and compared with the most attractive methods in the literature

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

on the robustness of multivariable linear feedback systems in state space representation a singular values based approach to specify the robustness of a multivariable linear feedback system in state space representation is investigated the robustness measure which is considered is the largest spectral norm of an additive uncertainty in the closed loop system matrix for which stability is guaranteed it is shown that under the constraint of prescribed pole placement a lower bound for the robustness measure is maximized when the frobenius norm of the closed loop system matrix is minimized

robust pole assignment in systems subject to structured perturbations the problem of robust pole assignment by feedback in a linear multivariable time invariant system which is subject to structured perturbations is investigated a measure of robustness or sensitivity of the poles to a given class of perturbations is derived and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure