on mds codes via cauchy matrices a special form of cauchy matrix is used to obtain a tighter bound for the validity region of the maximum distance separable mds conjecture and a new compact characterization of generalized reed solomon codes the latter is further used to obtain constructions and some existence results for long 2k k double circulant mds codes

multi innovation least squares identification methods based on the auxiliary model for miso systems for multi input single output output error systems a difficulty in identification is that the information vector in the identification model obtained contains unknown inner intermediate variables thus the standard least squares methods cannot be applied directly in this paper we present a multi innovation least squares identification algorithm based on the auxiliary model its basic idea is to replace the unknown inner variables with their estimates computed by an auxiliary model convergence analysis indicates that the parameter estimation error converges to zero under persistent excitation the algorithm proposed has significant computational advantage over existing identification algorithms a simulation example is included

the cavity of the optimal shape under the shear stresses the problem of optimal shape of a single cavity in an infinite 2 d elastic domain is analyzed an elastic plane is subjected to a uniform load at infinity the cavity of the fixed area is said to be optimal if it provides the minimal energy change between the homogeneous plane and the plane with the cavity we show that for the case of shear loading the contour of the optimal cavity is not smooth but is shaped as a curved quadrilateral the shape is specified in terms of conformal mapping coefficients and explicit analytical representations for components of the dipole tensor associated with the cavity are employed we also find the exact values of angles at the corners of the optimal contour the applications include the problems of optimal design for dilute composites

parameter estimation with scarce measurements in this paper the problems of parameter estimation are addressed for systems with scarce measurements a gradient based algorithm is derived to estimate the parameters of the input output representation with scarce measurements and the convergence properties of the parameter estimation and unavailable output estimation are established using the kronecker lemma and the deterministic version of the martingale convergence theorem finally an example is provided to demonstrate the effectiveness of the proposed algorithm

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

on superregular matrices and mdp convolutional codes superregular matrices are a type of lower triangular toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile these matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure in this paper we discuss how superregular matrices may be used to construct codes having a maximum distance profile we also present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field this in turn gives an upper bound on the smallest field size over which an mdp n k convolutional code can exist

adaptive digital control of hammerstein nonlinear systems with limited output sampling this paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints in particular for a hammerstein nonlinear sampled data system in which the output sampling period is an integer multiple of the input updating period we derive by using a polynomial transformation technique a mathematical model which is suitable for parameter estimation with dual rate measurement data further we present an adaptive control scheme for such a dual rate nonlinear system the parameter estimation based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed loop system is stable and globally convergent the simulation results are included

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search abstract this paper considers identification problems of a class of nonlinear systems by introducing a switching function and the finite impulse response model we obtain the identification model of a preload nonlinear system and develop a stochastic gradient algorithm to the parameters of the system furthermore a stochastic gradient algorithm with a forgetting factor is given to improve the identification accuracy a simulation results indicate that the forgetting factor can improve the parameter estimation accuracy

computation of matrix exponentials of special matrices computing matrix exponentials or transition matrices are important in signal processing and control systems this paper studies the methods of computing the transition matrices related to linear dynamic systems discusses and gives the properties of the transition matrices and explores the transition matrices of some special matrices some examples are provided to illustrate the proposed methods

adaptive control with recursive identification for stochastic linear systems this paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable inverse stable linear stochastic system with unknown parameters whenever that system satisfies a certain positive real condition on its moving average noise dynamics 1 the adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the limit of the sample mean square variation of the output around a given demand level equals that of a minimum variance control strategy implemented with known parameters this optimal behavior is subject to an offset 2where 2is the variance of a dither signal added to the control action in order to produce a continually disturbed control for mu 2 0 it is shown that the input output process satisfies a persistent excitation property and hence subject to a simple identifiability condition the next property holds 2 the observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm aml which generates strongly consistent estimates of the system s parameters results are presented for the scalar and multivariable cases

the residual based interactive stochastic gradient algorithms for controlled moving average models this paper derives a residual based interactive stochastic gradient isg parameter estimation algorithm for controlled moving average cma models and studied the performance of the residual based isg algorithm under weaker conditions on statistical properties of the noise compared with the residual based extended stochastic gradient algorithm for identifying cma models the proposed isg algorithm can give highly accurate parameter estimates by the simulation example

performance analysis of the am sg parameter estimation for multivariable systems the auxiliary model based stochastic gradient am sg parameter estimation method is an important identification one this paper analyzes the performances of the am sg estimation algorithm for multiple input single output systems i e multivariable systems under the strong persistent excitation condition the analysis and simulation results indicate that the parameter estimation errors converge to zero

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

stability and instability of limit points for stochastic approximation algorithms it is shown that the limit points of a stochastic approximation sa algorithm consist of a connected set conditions are given to guarantee the uniqueness of the limit point for a given initial value examples are provided wherein x sub n of sa algorithm converges to a limit x independent of initial values but x is unstable for the differential equation x spl dot f x with a nonnegative lyapunov function finally sufficient conditions are given for stability of x spl dot f x at x if x sub n tends to x for any initial values

column distances of convolutional codes over mathbb z _ p r maximum distance profile codes over finite non binary fields have been introduced and thoroughly studied in the last decade these codes have the property that their column distances are maximal among all codes of the same rate and degree in this paper we aim at studying this fundamental concept in the context of convolutional codes over a finite ring we extensively use the concept of p encoder to establish the theoretical framework and derive several bounds on the column distances in particular a method for constructing not necessarily free maximum distance profile convolutional codes over mathbb z p r is presented

hierarchical estimation algorithms for multivariable systems using measurement information abstract with the development of industry information technology many modelling methods have been focusing on the estimation problems of multivariable systems especially for the multivariable systems with output error autoregressive noises from input output measurement information since such a system includes both a parameter vector and a parameter matrix the conventional methods cannot be applied to parameter estimation and modelling in order to solve this difficulty a hierarchical least squares based iterative identification algorithm and a hierarchical generalized least squares identification algorithm are proposed the basic idea is to decompose the system into two fictitious subsystems to estimate the parameters of each subsystem and to coordinate the associated items between the two subsystems the simulation results indicate that the proposed algorithm is effective

superregular matrices and applications to convolutional codes abstract the main results of this paper are twofold the first one is a matrix theoretical result we say that a matrix is superregular if all of its minors that are not trivially zero are nonzero given a a b a b superregular matrix over a field we show that if all of its rows are nonzero then any linear combination of its columns with nonzero coefficients has at least a b 1 nonzero entries secondly we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code namely the rate and the forney indices these results answer some open questions on distances and constructions of convolutional codes posted in the literature 6 9

almost sure rate of convergence of the parameter estimates in stochastic approximation algorithm this paper presents novel results on the almost sure convergence of the parameter estimates in stochastic approximation algorithm it is proved that this rate has the same order as the best one established for the least squares algorithm although we consider the case of self tuning controllers the presented results can easily be extended to some other adaptive processes

observable state space realizations for multivariable systems this paper derives two canonical state space forms i e the observer canonical form and the observability canonical form from multiple input multiple output systems described by difference equations the state space model is expressed by the first order difference equation and is equivalent to the input output representation more specifically by setting the different state variables the difference equations or the input output representations can be transformed into two observable canonical forms and the canonical state space model can be also transformed into the difference equations finally two examples are given

stochastic approximation in nonparametric identification of hammerstein systems derived from the idea of stochastic approximation recursive algorithms to identify a hammerstein system are presented two of them recover the characteristic of the nonlinear memoryless subsystem while the third one estimates the impulse response of the linear dynamic part the a priori information about both subsystems is nonparametric consistency in quadratic mean is shown and the convergence rate is examined results of numerical simulation are also presented

hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems according to the hierarchical identification principle a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems i e multivariable oema like models which is different from multivariable carma like models as there exist unmeasurable noise free outputs and unknown noise terms in the information vector matrix of the corresponding identification model this paper is by means of the auxiliary model identification idea to replace the unmeasurable variables in the information vector matrix with the estimated residuals and the outputs of the auxiliary model a numerical example is provided

global convergence conditions in maximum likelihood estimation maximum likelihood estimation has been widely applied in system identification because of consistency its asymptotic efficiency and sufficiency however gradient based optimisation of the likelihood function might end up in local convergence in this article we derive various new non local minimum conditions in both open and closed loop system when the noise distribution is a gaussian process here we consider different model structures in particular ararmax bj and oe models

cavities vis a vis rigid inclusions elastic moduli of materials with polygonal inclusions in this paper we explore the correspondence between rigid inclusions and cavities dundurs 1989 j appl mech 56 786 790 as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities in the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions by employing the dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities finally we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions

convolutional codes with maximum distance profile abstract maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible minimum distance from each other relative to any other convolutional code of the same rate and degree in this paper we use methods from systems theory to characterize maximum distance profile codes algebraically the main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree

hierarchical least squares based iterative estimation algorithm for multivariable box jenkins like systems using the auxiliary model abstract this paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable box jenkins like systems by combining the hierarchical identification principle and the auxiliary model identification idea the key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle as there exist the unmeasurable noise free outputs and noise terms in the information vector the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals a numerical example is given to show the performance of the proposed algorithm

maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique this paper considers the identification problems of hammerstein finite impulse response moving average fir ma systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique in order to improve the convergence rate a maximum likelihood multi innovation stochastic gradient algorithm is presented the simulation results show that the proposed algorithms can effectively estimate the parameters of the hammerstein fir ma systems

a new class of superregular matrices and mdp convolutional codes abstract this paper deals with the problem of constructing superregular matrices that lead to mdp convolutional codes these matrices are a type of lower block triangular toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular we present a new class of matrices that are superregular over a sufficiently large finite field f such construction works for any given choice of characteristic of the field f and code parameters n k such that n k we also discuss the size of f needed so that the proposed matrices are superregular

on generator matrices of mds codes corresp it is shown that the family of q ary generalized reed solomon codes is identical to the family of q ary linear codes generated by matrices of the form i a where i is the identity matrix and a is a generalized cauchy matrix using cauchy matrices a construction is shown of maximal triangular arrays over gf q which are constant along diagonals in a hankel matrix fashion and with the property that every square subarray is a nonsingular matrix by taking rectangular subarrays of the described triangles it is possible to construct generator matrices i a of maximum distance separable codes where a is a hankel matrix the parameters of the codes are n k d for 1 leq n leq q 1 1 leq k leq n and d n k 1

convolutional codes with maximum column sum rank for network streaming the column hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels we introduce a metric known as the column sum rank that parallels the column hamming distance when streaming over a network with link failures we prove the rank analogues of several known column hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory our construction involves finding a class of super regular matrices that preserve this property after multiplication with non singular block diagonal matrices in the ground field

multi innovation stochastic gradient algorithm for multiple input single output systems using the auxiliary model in order to reduce computational burden and improve the convergence rate of identification algorithms an auxiliary model based multi innovation stochastic gradient am misg algorithm is derived for the multiple input single output systems by means of the auxiliary model identification idea and multi innovation identification theory the basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm and then to derive the am misg algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length the simulation example shows that the proposed algorithms work quite well

data filtering based recursive least squares algorithm for hammerstein systems using the key term separation principle this paper concerns parameter identification of hammerstein output error moving average systems with a two segment piecewise nonlinearity by combining the key term separation principle and the data filtering technique we transfer the hammerstein model into two regression identification models and present a data filtering based recursive least squares method to estimate the parameters of these two identification models the proposed algorithm achieves a higher computational efficiency than the standard approach by using covariance matrices of smaller dimensions from the two identification models instead of one identification model in the standard approach

recursive identification of time varying systems self tuning and matrix rls algorithms abstract in this paper a new parallel adaptive self tuning recursive least squares rls algorithm for time varying system identification is first developed regularization of the estimation covariance matrix is included to mitigate the effect of non persisting excitation the desirable forgetting factor can be self tuning estimated in both non regularization and regularization cases we then propose a new matrix forgetting factor rls algorithm as an extension of the conventional rls algorithm and derive the optimal matrix forgetting factor under some reasonable assumptions simulations are given which demonstrate that the performance of the proposed self tuning and matrix rls algorithms compare favorably with two improved rls algorithms recently proposed in the literature

auxiliary model based rels and mi els algorithm for hammerstein oema systems this paper considers the identification problem for hammerstein output error moving average oema systems an auxiliary model based recursive extended least squares rels algorithm and an auxiliary model based multi innovation extended least squares mi els algorithm are presented using the multi innovation identification theory the basic idea is to express the system output as a linear combination of the parameters by using the key term separation principle and auxiliary model method the proposed algorithms can give highly accurate parameter estimates the simulation results show the effectiveness of the proposed algorithms

two stage least squares based iterative identification algorithm for controlled autoregressive moving average carma systems a two stage least squares based iterative two stage lsi identification algorithm is derived for controlled autoregressive moving average carma systems the basic idea is to decompose a carma system into two subsystems and to identify each subsystem respectively because the dimensions of the involved covariance matrices in each subsystem become small the proposed algorithm has a high computational efficiency the simulation results indicate that the proposed algorithm is effective

strongly mds convolutional codes maximum distance separable mds convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree in this paper a class of mds convolutional codes is introduced whose column distances reach the generalized singleton bound at the earliest possible instant such codes are called strongly mds convolutional codes they also have a maximum or near maximum distance profile the extended row distances of these codes will also be discussed briefly

genetic algorithm perspective to identify energy optimizing inclusions in an elastic plate abstract analytical methods in optimization of elastic structures are often problematic due to the high order of the governing equations it is therefore useful to try various numerical schemes in parallel to better understand the optimized object behavior the paper describes the theoretical grounds and technical features that had to be introduced for effective implementation of a regular genetic algorithm ga to the shape optimization problems in planar elasticity these features concern the fitness calculation and imposing specific geometric constraints as a way to drastically reduce the computational efforts finally we demonstrate a successful ga application for numerical shape optimization of a hole or rigid inclusion in a plate arbitrarily loaded at infinity not only the known results have been reliably reproduced for the energy minimizing holes but this approach has allowed us to extend the findings for the worst energy maximizing inclusions as well

the existence of strongly mds convolutional codes it is known that maximum distance separable and maximum distance profile convolutional codes exist over large enough finite fields of any characteristic for all parameters n k delta it has been conjectured that the same is true for convolutional codes that are strongly maximum distance separable using methods from linear systems theory we resolve this conjecture by showing that over a large enough finite field of any characteristic codes which are simultaneously maximum distance profile and strongly maximum distance separable exist for all parameters n k delta

constructions of mds convolutional codes maximum distance separable mds convolutional codes are characterized through the property that the free distance attains the generalized singleton bound the existence of mds convolutional codes was established by two of the authors by using methods from algebraic geometry this correspondence provides an elementary construction of mds convolutional codes for each rate k n and each degree spl delta the construction is based on a well known connection between quasi cyclic codes and convolutional codes

generalized column distances the notion of generalized hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography in this paper we extend this concept to the context of convolutional codes in particular we focus on column distances and introduce the novel notion of generalized column distances gcd we first show that the hierarchy of gcd is strictly increasing we then provide characterizations of such distances in terms of the truncated parity check matrix of the code that will allow us to determine their values finally the case in which the parity check matrix is in systematic form is treated

strong consistency of parameter estimates in direct self tuning control algorithms based on stochastic approximation in this paper convergence of the regulator parameter estimates generated by direct self tuning control algorithms of stochastic approximation type is considered the process is supposed to be represented by an armax model with an arbitrary delay while a dither signal converging to zero in the mean square sense is superimposed on a deterministic reference the strong consistency of the regulator parameter estimates is proved under assumptions concerning the estimator complexity and the properties of the optimal regulator transfer function for a broad class of dither signals the impact of a priori information on the dimension of the estimator and the consistency of the parameter estimates is indicated it is demonstrated that the classical persistence of excitation condition is not satisfied for the analyzed algorithms

self tuning control based on multi innovation stochastic gradient parameter estimation abstract this paper uses the multi innovation stochastic gradient misg algorithm to estimate the parameters of discrete time systems and presents an misg based self tuning control scheme furthermore we prove that the parameter estimation error converges to zero under persistent excitation and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control and ensure that the closed loop systems are stable and globally convergent the simulation example is included

superregular lower triangular toeplitz matrices for low delay wireless streaming a matrix is termed superregular if all of its possible submatrices are non singular superregular lower triangular toeplitz matrices are useful for mds convolutional codes and sequential network codes in this paper we present the explicit matrix constructions for superregular lower triangular toeplitz matrices in mathrm gf 2 p k times k k leq 5 for k 5 we provide a greedy algorithm which over sufficiently large fields is guaranteed to find a superregular lower triangular toeplitz matrix we introduce product preserving joint superregularity and extend our explicit matrix constructions to these cases we provide methods for deriving the exact symbol loss probability and delay for any deterministic block code we derive the exact symbol loss probability and delay for codes using a superregular lower triangular matrix and for codes using two product preserving jointly superregular lower triangular matrices we then compare these results with those obtained from both simulations and our practical implementation and for each case we also compare with random based codes furthermore our experiments show a gain in coding throughput above 40 for superregular lower triangular toeplitz matrices over random matrices

quasi gradient based inversion free iterative algorithm for solving a class of the nonlinear matrix equations abstract inspired by the gradient based and inversion free iterations a new quasi gradient based inversion free iterative algorithm is proposed for solving the nonlinear matrix equation x a t x n a i the convergence proof of the suggested algorithm is given several matrix norm inequalities are established to depict the convergence properties of this algorithm three numerical examples are given to illustrate the effectiveness of the suggested algorithms

convolutional goppa codes in this correspondence we define convolutional goppa codes over algebraic curves and construct their corresponding dual codes examples over the projective line and over elliptic curves are described obtaining in particular some maximum distance separable mds convolutional codes

convergence of stochastic gradient estimation algorithm for multivariable arx like systems this paper studies the convergence of the stochastic gradient identification algorithm of multi input multi output arx like systems i e multivariable arx like systems by using the stochastic martingale theory this arx like model contains a characteristic polynomial and differs from the conventional multivariable arx system the results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions the simulation results validate the proposed convergence theorem

least squares linear estimation of signals from observations with markovian delays abstract the least squares linear estimation of signals from randomly delayed measurements is addressed when the delay is modeled by a homogeneous markov chain to estimate the signal recursive filtering and fixed point smoothing algorithms are derived using an innovation approach assuming that the covariance functions of the processes involved in the observation equation are known recursive formulas for filtering and fixed point smoothing error covariance matrices are obtained to measure the goodness of the proposed estimators

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed