extended stochastic gradient identification algorithms for hammerstein wiener armax systems an extended stochastic gradient algorithm is developed to estimate the parameters of hammerstein wiener armax models the basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates the obtained parameter estimates of the identification model include the product terms of the parameters of the original systems two methods of separating the parameter estimates of the original parameters from the product terms are discussed the average method and the singular value decomposition method to improve the identification accuracy an extended stochastic gradient algorithm with a forgetting factor is presented the simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor

iterative algorithms for solving a class of complex conjugate and transpose matrix equations this paper is concerned with iterative solutions to a class of complex matrix equations which include some previously investigated matrix equations as special cases by applying the hierarchical identification principle an iterative algorithm is constructed to solve this class of matrix equations a sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools by using some properties of the real representation a convergence condition that is easier to compute is also given in terms of original coefficient matrices a numerical example is employed to illustrate the effectiveness of the proposed methods

parameter identification of multi input single output systems based on fir models and least squares principle by means of auxiliary models finite impulse response fir models this paper develops an identification algorithm for multi input single output stochastic systems the basic idea is to estimate the fir model parameters of each fictitious subsystem submodel with the fir model orders increasing and to use auxiliary models to predict estimate the outputs of the submodels and further to use the pade approximation method to produce the parameter estimates of submodels some simulation results are given

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

partially coupled stochastic gradient identification methods for non uniformly sampled systems this technical note addresses identification problems of non uniformly sampled systems for the input output representation of non uniform discrete time systems a partially coupled stochastic gradient c sg algorithm is proposed to estimate the model parameters with high computational efficiency compared with the standard stochastic gradient sg algorithm the analysis indicates that the partially c sg algorithm can give more accurate parameter estimates than the sg algorithm the parameter estimates obtained using the partially c sg algorithm converge to their true values as the data length approaches infinity

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

iterative solutions of the generalized sylvester matrix equations by using the hierarchical identification principle abstract in this paper by extending the well known jacobi and gauss seidel iterations for ax b we study iterative solutions of matrix equations axb f and generalized sylvester matrix equations axb cxd f including the sylvester equation ax xb f as a special case and present a gradient based and a least squares based iterative algorithms for the solution it is proved that the iterative solution always converges to the exact solution for any initial values the basic idea is to regard the unknown matrix x to be solved as the parameters of a system to be identified and to obtain the iterative solutions by applying the hierarchical identification principle finally we test the algorithms and show their effectiveness using a numerical example

a fatou theorem for the solution of the heat equation at the corner points of a cylinder in this paper the author proves existence and uniqueness of the initial dirichlet problem for the heat equation in a cylindrical domain d 0 where d is a bounded smooth domain in r n with zero lateral values a unique representation of the strong solution is given in terms of measures on d and on d we also show that the strong solution u x t of the heat equation in a cylinder converges a e x 0 d 0 as x t converges to points on d 0 along certain nontangential paths

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

the role of vector autoregressive modeling in predictor based subspace identification subspace identification for closed loop systems has been recently studied by several authors a class of new and consistent closed loop subspace algorithms is based on identification of a predictor model in a way similar as prediction error methods pem do experimental evidence suggests that these methods have a behavior which is very close to pem in certain examples the asymptotical statistical properties of one of these methods have been studied recently allowing to show i its relation with cca and ii that cramer rao lower bound is not reached in general very little however is known concerning their relative performance in this paper we shall discuss the link between these predictor based methods to this purpose we exploit the role which vector auto regressive with exogenous input models play in all these algorithms the results of this paper provide a unifying framework under which all these algorithms can be viewed also the link with varx modeling have important implications as to computational complexity is concerned leading to very computationally attractive implementations we also hope that this framework and in particular the relation with varx modeling followed by model reduction will turn out to be useful in future developments of subspace identification such as the quest for efficient procedures and the statistical analysis with finite data

parameter estimation of dual rate stochastic systems by using an output error method in this note a new gradient based recursive algorithm for estimating parameters of dual rate sampled data systems is presented the basic idea is by using an output error method to identify the single rate models and the unknown noise free outputs true outputs directly from dual rate input output data further convergence properties of the proposed algorithm in parameter and output estimation are analyzed and the result is illustrated and tested with an experimental water level system

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

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

nonnegative solutions of the initial dirichlet problem for generalized porous medium equations in cylinders in this paper we study nonnegative solutions u of a class of nonlinear evolutions au at a u whose best known example is the porous medium equation u u m 1 see 9 for a recent survey on these equations we study our solutions u subject to dirichlet boundary conditions in d x 0 t where d is a bounded smooth domain in rn i e uiadx 0 t 0 the corresponding theory for d rn was studied by the authors in 3 we find that there is one special solution x t the friendly giant which tends to infinity as t 1 0 and that all other solutions u x t are in one to one correspondence with suitable pairs of measures u on d and a ou ad we also show that any solution on d x 0 t extends to a solution in d x 0 oo and that the friendly giant f x t governs the asymptotic behavior as t t oo the nonlinearity is assumed to be continuous increasing with p 0 0 and also verifies the growth conditions

the boundary behavior of heat kernels of dirichlet laplacians we prove the following complete and qualitatively sharp description of heat kernels g of dirichlet laplacians on bounded c1 1 domains d there exist positive constants c1 c2 and t 0 depending on d such that for x dist x d x y t 1c1tn 2e c2 x y 2 t g x t y 0 x y t 11c1tn 2e x y 2 c2t for all x y d and 0 t are known bounds when d is unbounded are also given

overlapping block balanced canonical forms and parametrizations the stable siso case the balanced canonical form and parametrization of ober for the case of siso stable systems are extended to block balanced canonical forms and related input normal forms and parametrizations they form an overlapping atlas of parametrizations of the manifold of stable siso systems of given order this extends the usefulness of these parametrizations e g in gradient algorithms for system identification as an implication of our construction it follows that each of the subsets of the parametrization of r ober internat j control 46 1987 pp 643 670 corresponding to a choice for the structural indices is in fact an imbedded submanifold of the manifold of stable siso systems of fixed order

an efficient hierarchical identification method for general dual rate sampled data systems for the lifted input output representation of general dual rate sampled data systems this paper presents a decomposition based recursive least squares d ls identification algorithm using the hierarchical identification principle compared with the recursive least squares rls algorithm the proposed d ls algorithm does not require computing the covariance matrices with large sizes and matrix inverses in each recursion step and thus has a higher computational efficiency than the rls algorithm the performance analysis of the d ls algorithm indicates that the parameter estimates can converge to their true values a simulation example is given to confirm the convergence results

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

system identification using balanced parametrizations some general issues in the black box identification of multivariable systems are first discussed it is then suggested that balanced parametrizations can be used to give identifiable forms a particular advantage is that balanced parametrizations are known for several useful classes of linear dynamic models including stable minimal models minimum phase models positive real models and normalized coprime factor models before optimizing the parameters of balanced parametrizations an initial model must be found we use realization based methods and so called subspace methods for this purpose these methods are very effective at finding accurate initial models without preliminary estimation of various structural indexes the paper ends with two simulation examples which compare the use of balanced parametrizations with more traditional ones and three real examples based on practical problems a distillation column an industrial dryer and the irrational spectrum or sea waves

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

a proportional differential control method for a time delay system using the taylor expansion approximation abstract in this paper a proportional differential control algorithm is studied according to the system performance indices we uses the first order taylor expansion to approximate the time delay present an algorithm to determine the controller parameters so that the desired dynamic performance can be achieved the numerical examples are provided to show the advantages of the proposed algorithm for small time delay

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

hierarchical least squares identification methods for multivariable systems for multivariable discrete time systems described by transfer matrices we develop a hierarchical least squares iterative hlsi algorithm and a hierarchical least squares hls algorithm based on a hierarchical identification principle we show that the parameter estimation error given by the hlsi algorithm converges to zero for the deterministic cases and that the parameter estimates by the hls algorithm consistently converge to the true parameters for the stochastic cases the algorithms proposed have significant computational advantage over existing identification algorithms finally we test the proposed algorithms on an example and show their effectiveness

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

initial blow up of solutions of semilinear parabolic inequalities abstract we study classical nonnegative solutions u x t of the semilinear parabolic inequalities 0 u t u u p in 0 1 where p is a positive constant and is a bounded domain in r n n 1 we show that a necessary and sufficient condition on p for such solutions u to satisfy a pointwise a priori bound on compact subsets k of as t 0 is p 1 2 n and in this case the bound on u is max x k u x t o t n 2 as t 0 if in addition is smooth u satisfies the boundary condition u 0 on 0 1 and p 1 2 n then we obtain a bound for u on the entire set as t 0

simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise abstractin the present paper the identification and estimation problem of a single input single output siso fractional order state space system will be addressed a siso state space model is considered in which parameters and also state variables should be estimated the canonical fractional order state space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification the identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state space system recursively another subject that will be addressed in this paper is a novel fractional order kalman filter suitable for the systems with coloured measurement noise the promising performance of the proposed methods is verified using two stable fractional order systems

reconstruction of continuous time systems from their non uniformly sampled discrete time systems a continuous time system cannot be recovered solely from its uniformly sampled discrete time model through the zero order hold discretization or step invariant transformation but our studies indicate that it can be recovered uniquely from its non uniformly sampled discrete time model in this paper we discuss some related issues of non uniformly sampled systems including model derivation controllability and observability computation of single rate models with different sampling periods reconstruction of continuous time systems and parameter identification of non uniformly sampled discrete time systems a numerical example is also given for illustration

combined parameter and output estimation of dual rate systems using an auxiliary model for a dual rate sampled data system an auxiliary model based identification algorithm for combined parameter and output estimation is proposed the basic idea is to use an auxiliary model to estimate the unknown noise free output true output of the system and directly to identify the parameters of the underlying fast single rate model from the dual rate input output data it is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance and that the output estimates uniformly converge to the true outputs an example is included

a covariance matching approach for identifying errors in variables systems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper a covariance matching approach is proposed to solve the identification problem it applies for general types of input signals the method utilizes a small set of covariances of the measured input output data this property applies also for some other methods such as the frisch scheme and the bias eliminating least squares method algorithmic details for the proposed method are provided user choices for example specification of which input output covariances to utilize are discussed in some detail the method is evaluated by using numerical examples and is shown to have competitive properties as compared to alternative methods

hierarchical gradient based identification of multivariable discrete time systems in this paper we use a hierarchical identification principle to study identification problems for multivariable discrete time systems we propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation the proposed algorithms can be applied to identification of systems involving non stationary signals and have significant computational advantage over existing identification algorithms finally we test the proposed algorithms by simulation and show their effectiveness

the global behavior of heat kernels in exterior domains abstract we establish the global boundary behavior of dirichlet heat kernels on some unbounded domains these combined with the interior estimate in the recent paper by grigoryan and saloff coste comm pure appl math 55 1 2002 93 provide a complete and qualitatively sharp description of heat kernels g of dirichlet laplacians on some unbounded c1 1 domains d m here m is certain complete noncompact manifold with nonnegative ricci curvature for example there exist positive constants c1 c2 depending on the unbounded domain d m such that for x dist x d x t 1 1 y t 1 1 c 1 e c 2 d x y 2 t b x t g x t y 0 x t 1 1 y t 1 1 e d x y 2 c 2 t c 1 b x t for all x y d and t 0 existence of these global bounds had been an unresolved problem even in the euclidean case

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

identification for multirate multi input systems using the multi innovation identification theory this paper considers identification problems of multirate multi input sampled data systems using the continuous time system discretization technique with zero order holds the mapping relationship state space model between available multirate input and output data is set up the multi innovation identification theory is applied to estimate the parameters of the obtained multirate models and to present a multi innovation stochastic gradient algorithm for the multirate systems from the multirate input output data furthermore the convergence properties of the proposed algorithm are analyzed an illustrative example is given

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

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

constructive algebra methods for the l 2 problem for stable linear systems abstract we investigate the feasibility of using computer algebra for solving l 2 system approximation problems the first order optimality conditions yield a set of polynomial equations which can in principle be solved using grobner basis methods a general solution along these lines would be tremendously useful although it does not appear to be feasible at present except for rather low mcmillan degrees we demonstrate that it can be feasible for specific examples in such cases global optima can be found reliably we show that the use of a schwarz like canonical form simplifies the structure of the problem

balanced canonical forms for system identification parameterizations of linear state space systems by balanced canonical forms are considered the structure in particular the topological properties of these parameterizations are investigated based on these results an algorithm for identification obtained by optimizing a likelihood type criterion function is proposed and analyzed in the algorithm both the estimation of real valued parameters and of integer parameters defining dynamic specification is incorporated the analysis of the algorithm emphasizes consistency results

balanced realizations of discrete time stable all pass systems and the tangential schur algorithm in this paper the connections are investigated between two different approaches towards the parametrization of multivariable stable all pass systems in discrete time the first approach involves the tangential schur algorithm which employs linear fractional transformations it stems from the theory of reproducing kernel hilbert spaces and enables the direct construction of overlapping local parametrizations using schur parameters and interpolation points the second approach proceeds in terms of state space realizations in the scalar case a balanced canonical form exists that can also be parametrized by schur parameters this canonical form can be constructed recursively using unitary matrix operations here this procedure is generalized to the multivariable case by establishing the connections with the first approach it gives rise to balanced realizations and overlapping canonical forms directly in terms of the parameters used in the tangential schur algorithm

on the generalized reflexive and anti reflexive solutions to a system of matrix equations let p and q be two generalized reflection matrices i e p ph p2 i and q qh q2 i an n n matrix a is said to be generalized reflexive generalized anti reflexive with respect to the matrix pair p q if a paq a paq it is obvious that any n m matrix is also a generalized reflexive with respect to the matrix pair in im by extending the conjugate gradient least square cgls approach the present paper treats two iterative algorithms to solve the system of matrix equations f1 x a1 f2 x a2 fm x am including the sylvester and lyapunov matrix equations as special cases over the generalized reflexive and anti reflexive matrices where f1 f2 fm are the linear operators from cn n onto cri si and ai cri si for i 1 2 m when this system is consistent over the generalized reflexive generalized anti reflexive matrix it is proved that the first second iterative algorithm converges to a generalized reflexive generalized anti reflexive solution for any initial generalized reflexive generalized anti reflexive matrix also the first second iterative algorithm can obtain the the least frobenius norm generalized reflexive generalized anti reflexive solution for special initial generalized reflexive generalized anti reflexive matrix furthermore the optimal approximation generalized reflexive generalized anti reflexive solution to a given generalized reflexive generalized anti reflexive matrix can be derived by finding the least frobenius norm generalized reflexive generalized anti reflexive solution of a new system of matrix equations finally we test the proposed iterative algorithms and show their effectiveness using numerical examples

parameter estimation methods for nonlinear systems this paper discusses parameter estimation problems of nonlinear system modeling two model transformation based estimation methods are proposed the basic idea is to transform a complex nonlinear optimization problem into a linear or simple nonlinear optimization problem which is easy to solve then according to the gradient search principle and the newton method a gradient based iterative algorithm and a newton iterative algorithm are derived to determine the parameters of the nonlinear systems finally a numerical example is provided

overlapping block balanced canonical forms for various classes of linear systems abstract through the use of balanced realizations it has been possible to derive parametrizations and canonical forms for various classes of minimal linear systems of given dimension a possible problem of these parametrizations is that they are not overlapping this could be a drawback for the application of balanced parametrizations in such areas as system identification model reduction and optimization it is the topic of this paper to derive overlapping parametrizations which are closely related to the existing balanced parametrizations we first introduce input normal canonical forms which are defined through a novel way of choosing nice selections of columns of the reachability matrix these canonical forms provide overlapping parametrizations in the sense that they form a real analytic atlas of the manifold of systems which are considered then we introduce so called block balanced input normal forms which use the previously constructed input normal forms as building blocks the classes of systems for which such parametrizations are given are the stable minimal systems positive real minimal systems bounded real minimal systems and the class of all minimal systems of given mcmillan degree the results include both the single input single output and the multivariable case in the single input single output case however the issue of choosing nice selections of columns does not occur therefore in this case the derivation and presentation of the results is considerably simplified

hierarchical least squares identification for linear siso systems with dual rate sampled data this technical note studies identification problems for dual rate sampled data linear systems with noises a hierarchical least squares hls identification algorithm is presented to estimate the parameters of the dual rate armax models the basic idea is to decompose the identification model of a dual rate system into several sub identification models with smaller dimensions and fewer parameters the proposed algorithm is more computationally efficient than the recursive least squares rls algorithm since the rls algorithm requires computing the covariance matrix of large sizes while the hls algorithm deals with the covariance matrix of small sizes compared with our previous work a detailed study of the hls algorithm is conducted in this technical note the performance analysis and simulation results confirm that the estimation accuracy of the proposed algorithm are close to that of the rls algorithm but the proposed algorithm retains much less computational burden

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

the residual based extended least squares identification method for dual rate systems in this paper we focus on a class of dual rate sampled data systems in which all the inputs u t are available at each instant while only scarce outputs y qt can be measured q being an integer more than unity to estimate the parameters of such dual rate systems we derive a mathematical model by using the polynomial transformation technique and apply the extended least squares algorithm to identify the dual rate systems directly from the available input output data u t y qt then we study the convergence properties of the algorithm in details finally we give an example to test and illustrate the algorithm involved

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

on the adi method for sylvester equations this paper is concerned with the numerical solution of large scale sylvester equations ax xb c lyapunov equations as a special case in particular included with c having very small rank for stable lyapunov equations penzl 2000 22 and li and white 2002 20 demonstrated that the so called cholesky factor adi method with decent shift parameters can be very effective in this paper we present a generalization of the cholesky factor adi method for sylvester equations an easily implementable extension of penz s shift strategy for the lyapunov equation is presented for the current case it is demonstrated that galerkin projection via adi subspaces often produces much more accurate solutions than adi solutions