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

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

technical communique analysis of an output error identification algorithm an output error based algorithm proposed by landau and recently analysed by dugard and landau is shown to have a certain robustness property specifically it is proved that the parameters of the system transfer function can be estimated consistently with that algorithm even if the noise is not correctly modelled this fact was noticed empirically by dugard and landau but a theoretical analysis was not provided

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

on iterative solutions of general coupled matrix equations in this paper we study coupled matrix equations which are encountered in many systems and control applications first we extend the well known jacobi and gauss seidel iterations and present a large family of iterative methods which are then applied to develop iterative solutions to coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle next we generalize the sylvester equations to general coupled matrix equations and propose a gradient based iterative algorithm for the solutions using a block matrix inner product the star star product we prove that the iterative algorithm always converges to the unique solutions for any initial values one advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods finally we test the algorithms and show their effectiveness using numerical examples

modeling and parameter identification of systems with multisegment piecewise linear characteristics this paper deals with the modeling and parameter identification of nonlinear systems having multi segment piecewise linear characteristics the decomposition of the corresponding mapping provides a new form of multi segment nonlinearity representation leading to an output equation where all the parameters to be estimated are separated hence an iterative method with internal variable estimation can be applied for parameter identification using input output data records the only required a priori knowledge of the nonlinear characteristic represents the limits for the domain partition the proposed model of given static nonlinearity is also incorporated into the hammerstein model examples of parameter identification for static and dynamic systems with multi segment piecewise linear characteristics are presented

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

multiple solutions for coercive p laplacian equations we obtain multiple nonzero solutions for coercive p laplacian equations in order to obtain the third nonzero solution we use the second deformation lemma to construct the desired mountain pass path

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

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

recursive identification method for miso wiener hammerstein model a simple technique for recursive identification of the wiener hammerstein model with extension to the multi input single output miso case is presented we use a new transformation of the input output difference equation where parameters to be estimated are those of each subsystem of the initial and unique realization after that a weighted extended least squares method is employed to estimate recursively and separately parameters of the linear subsystems and the static nonlinear element the convergence analysis of the proposed procedure is also studied finally a numerical example is provided to show the efficiency of the algorithm

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

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

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

brief parameter identification of a class of hammerstein plants we consider parameter identification of plants that can be described by a piecewise affine nonlinear element in series with linear dynamics the identification scheme is based on a suitable plant parametrization obtained by an orthogonal expansion of the nonlinearity then a persistently exciting pe input sequence is generated to ensure the convergence of the estimated model to the true one

brief a random least trimmed squares identification algorithm the least trimmed squares lts estimator is a well known robust estimator in terms of protecting the estimate from the outliers its high computational complexity is however a problem in practice in this paper we propose a random lts algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval moreover if the number of data points goes to infinite the algorithm becomes a deterministic one that converges to the true lts in some probability sense

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

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

parameter bounds for discrete time hammerstein models with bounded output errors in this note we present a two stage procedure for deriving parameters bounds in hammerstein models when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are tightly bounded then for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are used for bounding the parameters of the linear dynamic block

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

gradient based iterative algorithms for solving a class of matrix equations in this note we apply a hierarchical identification principle to study solving the sylvester and lyapunov matrix equations in our approach we regard the unknown matrix to be solved as system parameters to be identified and present a gradient iterative algorithm for solving the equations by minimizing certain criterion functions we prove that the iterative solution consistently converges to the true solution for any initial value and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factor or step size appropriately furthermore the iterative method is extended to solve general linear matrix equations 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

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

compensation of the rls algorithm for output nonlinearities it is shown how the recursive least squares rls algorithm can be modified to compensate for a priori known errors of linearity in the output measurement a novel signal model is used for this purpose only the nonlinear effects are modeled by an output error model and much of the output measurements are used directly in the regression vector the main benefit with this approach is that the advantages of the rls like quick initial convergence for infinite impulse response models can be retained for small linearity errors at the same time the output nonlinearity is allowed to be noninvertible this can be important to treat for example small deadzones and also to avoid the amplification of additive measurement disturbances such amplification can result from inversion of the output nonlinearity simulations illustrate the performance of the algorithm

iterative algorithm for parameter identification of hammerstein systems with two segment nonlinearities this paper deals with parameter identification of hammerstein systems having two segment polynomial nonlinearities the application of a simple decomposition technique and using switching sequences provide a special form of a hammerstein model that is linear in parameters this model is used in an iterative algorithm enabling simultaneous estimation of all of the model parameters to demonstrate the feasibility of the identification method more illustrative examples are included

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