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

brief paper least squares based iterative identification for a class of multirate systems this paper studies modeling and identification problems for multi input multirate systems with colored noises the state space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained to solve the difficulty of identification models with unmeasurable noises terms the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates finally the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms

a parallel two scale method for eikonal equations numerous applications of eikonal equations prompted the development of many efficient numerical algorithms the heap cell method hcm is a recent serial two scale technique that has been shown to have advantages over other serial state of the art solvers for a wide range of problems a chacon and a vladimirsky siam j sci comput 34 2012 pp a547 a578 this paper presents a parallelization of hcm for a shared memory architecture the numerical experiments in r 3 show that the parallel hcm exhibits good algorithmic behavior and scales well resulting in a very fast and practical solver

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

hierarchical gradient parameter estimation algorithm for hammerstein nonlinear systems using the key term separation principle in this paper we use the hierarchical identification principle to decompose a hammerstein controlled autoregressive system into three subsystems apply the key term separation principle to express the system output as a linear combination of the system parameters and then derive a hierarchical gradient parameter estimation algorithm for identifying all subsystems finally a multi innovation stochastic gradient algorithm is presented to improve the estimation accuracy by making full of the identification innovation the simulation results show that the proposed algorithm is effective

data based stochastic model reduction for the kuramoto sivashinsky equation national science foundation dms 1217065 dms 1418775 dms 1419044 u s department of energy de ac02 05ch11231 national science foundation

isotropic isotopy and symplectic null sets capacity is an important numerical invariant of symplectic manifolds this paper studies when a subset of a symplectic manifold is null i e can be removed without affecting the ambient capacity after examples of open null sets and codimension 2 non null sets geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow it follows that sets of dimension 0 and 1 are null for isotropic sets of higher dimensions obstructions to the perturbation are found in homotopy groups of the orthogonal groups

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

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

brief paper making parametric hammerstein system identification a linear problem in this paper we study the identification of parametric hammerstein systems with fir linear parts by a proper normalization and a clever characterization it is shown that the average squared error cost function for identification can be expressed in terms of the inner product between the true but unknown parameter vector and its estimate further the cost function is concave in the inner product and linear in the inner product square therefore the identification of parametric hammerstein systems with fir linear parts is a globally convergent problem and has one and only one local and global minimum this implies that the identification of such systems is a linear problem in terms of the inner product square and any local search based identification algorithm converges globally

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

parameter estimation error bounds for hammerstein nonlinear finite impulsive response models abstract this paper presents a parameter estimation algorithm for a class of hammerstein nonlinear systems input nonlinear fir finite impulse response models and studies in detail the convergence properties of the proposed identification algorithm in the stochastic framework and derives the upper and lower bounds of the parameter estimation errors pee from the available input output data the analysis indicates that the mean square pee upper and lower bounds of the algorithm approach zero as the data length increases a simulation example is given

an ordered line integral method for computing the quasi potential in the case of variable anisotropic diffusion abstract nongradient stochastic differential equations sdes with position dependent and anisotropic diffusion are often used in biological modeling the quasi potential is a crucial function in the large deviation theory that allows one to estimate transition rates between attractors of the corresponding ordinary differential equation and find the maximum likelihood transition paths unfortunately the quasi potential can rarely be found analytically it is defined as the solution to a certain action minimization problem in this work the recently introduced ordered line integral method olim is extended for computing the quasi potential for 2d sdes with anisotropic and position dependent diffusion scaled by a small parameter on a regular rectangular mesh the presented solver employs the dynamical programming principle at each step a local action minimization problem is solved using straight line path segments and the midpoint quadrature rule the solver is tested on two examples where analytic formulas for the quasi potential are available the dependence of the computational error on the mesh size the update factor k a key parameter of olims as well as the degree and the orientation of anisotropy is established the effect of anisotropy on the quasi potential and the maximum likelihood paths is demonstrated on the maier stein model the proposed solver is applied to find the quasi potential and the maximum likelihood transition paths in a model of the genetic switch in lambda phage between the lysogenic state where the phage reproduces inside the infected cell without killing it and the lytic state where the phage destroys the infected cell

a nonparametric polynomial identification algorithm for the hammerstein system almost all existing hammerstein system nonparametric identification algorithms can recover the unknown system nonlinear element up to an additive constant and one functional value of the nonlinearity is usually assumed to be known to make the constant solvable to overcome this defect in this paper a new nonparametric polynomial identification algorithm for the hammerstein system is proposed which extends the idea in the author s previous work 1993 1994 on the hammerstein system identification to a more general and practical case where no functional value of the system nonlinearity is known a priori convergence and convergence rates in both uniform and global senses are established and simulation studies demonstrate the effectiveness and advantage of the new algorithm

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

correspondence comments on identification of hammerstein nonlinear armax systems this note points out some errors in the proof of the main result of ding and chen 2005 identification of hammerstein nonlinear armax systems automatica 41 9 1479 1489 and mentions the well known results that have solved the problem discussed in theorem 1 of the above paper by ding and chen

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

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

decoupling the linear and nonlinear parts in hammerstein model identification the main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in hammerstein model identification therefore identification of the linear part for a hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent

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

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

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

finite model order accuracy in hammerstein model estimation hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems a static input nonlinearity followed by a linear dynamical part is an adequate way to model many real life systems this paper investigates the asymptotic in terms of sample size variance of hammerstein model estimates the work extends earlier results by ninness and gibson 2002 in the following ways not only frequency function estimation but estimation of general quantities is considered the expressions are not restricted to be valid asymptotically in the model order in addition the results cover model structures having noise models and allow for data generated under feedback the increase in variance due to the estimation of the input nonlinearity is characterized in particular under open loop operation white additive noise and the assumption of a separable process it is shown that the variance increase is exactly a term that was observed in ninness and gibson 2002 to result in good agreement with simulations this term vanishes in the formal asymptotic in model order analysis in ninness and gibson 2002

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics many physical systems are described by nonlinear differential equations that are too complicated to solve in full a natural way to proceed is to divide the variables into those that are of direct interest and those that are not formulate solvable approximate equations for the variables of greater interest and use data and statistical methods to account for the impact of the other variables in the present paper we consider time dependent problems and introduce a fully discrete solution method which simplifies both the analysis of the data and the numerical algorithms the resulting time series are identified by a narmax nonlinear autoregression moving average with exogenous input representation familiar from engineering practice the connections with the mori zwanzig formalism of statistical physics are discussed as well as an application to the lorenz 96 system

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

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

optimal control with budget constraints and resets we consider both discrete and continuous control problems constrained by a fixed budget of some resource which may be renewed upon entering a preferred subset of the state space in the discrete case we consider deterministic shortest path problems on graphs with a full budget reset in all preferred nodes in the continuous case we derive augmented pdes of optimal control which are then solved numerically on the extended state space with a full instantaneous budget reset on the preferred subset we introduce an iterative algorithm for solving these problems efficiently the method s performance is demonstrated on a range of computational examples including optimal path planning with constraints on prolonged visibility by a static enemy observer

a general multirate approach for direct closed loop identification to the nyquist frequency and beyond without injecting any external persistently exciting signals a general multirate approach is proposed for direct closed loop identification first an extended least squares algorithm is designed to identify the mixed rate model after polynomial transformation next the identified mixed rate model is used to compute the fast rate model from which system dynamics to the nyquist frequency and beyond can be obtained identifiability is mathematically proven if the plant output sampling rate is non integer multiples of the controller sampling rate the effectiveness of the proposed approach is evaluated by both the simulation and experimental results in a hard disk drive

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

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

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

convergence analysis of estimation algorithms for dual rate stochastic systems identification is to estimate the unknown parameters of systems by using the measured input output data u t y t most existing identification approaches assume that the input output u t y t is available at each sampling instant t this paper focuses on a class of dual rate sampled data systems in which all inputs u t are available but only scarce outputs y qt are available q 1 being an integer we derive a mathematical model for such dual rate systems by using a polynomial transformation technique and present new algorithms for parameter identification and intersample output estimation using directly the dual rate input output data u t y qt and study in detail convergence properties of the algorithms in the stochastic framework by using the stochastic process theory and stochastic martingale theory we show that 1 the parameter estimation error consistently converges to zero under the persistent excitation condition 2 the intersample output estimation error is uniformly bounded finally we illustrate and test the proposed algorithms with example systems including an experimental water level system

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

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

a finite data window least squares algorithm with a forgetting factor for dynamical modeling in this paper we extend the forgetting factor least squares and finite data window least squares identification algorithms develop a finite data window least squares algorithm with a forgetting factor for dynamical system modeling derive its recursive version and also give its simplified form we illustrate the advantages of the proposed algorithm with simulation examples

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

on identification of the controlled plants described by the hammerstein system a new polynomial identification method for the hammerstein system is proposed the method employs the results of nonparametric statistics and best approximation theory obtaining a polynomial form estimate of the nonlinearity in the system except continuity no conditions are imposed on the nonlinearity the uniform as well as global convergence of the method is established the rates of convergence in both cases are derived under mild conditions on the smoothness of the nonlinearity the method is especially suitable for identifying the controlled plants with the description of hammerstein systems

fast two scale methods for eikonal equations fast marching and fast sweeping are the two most commonly used methods for solving the eikonal equation each of these methods performs best on a different set of problems fast sweeping for example will outperform fast marching on problems where the characteristics are largely straight lines fast marching on the other hand is usually more efficient than fast sweeping on problems where characteristics frequently change their directions and on domains with complicated geometry in this paper we explore the possibility of combining the best features of both approaches by using marching on a coarser scale and sweeping on a finer scale we present three new hybrid methods based on this idea and illustrate their properties in several numerical examples with continuous and piecewise constant speed functions in r 2

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

gradient based and least squares based iterative algorithms for matrix equations axb cxtd f abstract this paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation axb cx t d f the basic idea is to decompose the matrix equation system under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving ax b and axb f the analysis shows that when the matrix equation has a unique solution under the sense of least squares the iterative solution converges to the exact solution for any initial values a numerical example verifies the proposed theorems

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

parametric identification of hammerstein systems with consistency results using stochastic inputs the extended least squares algorithm is applied to identify the hammerstein system where the nonlinear static function f is expressed as a linear combination of basic functions with unknown coefficients strong consistency of the estimates is established and their convergent rates are obtained as well

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

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

extended least squares and their applications to adaptive control and prediction in linear systems herein strong consistency of recursive extended least squares is established under considerably weaker assumptions than previously assumed in the literature the argument used to establish consistency also leads to certain basic properties of adaptive predictors based on these recursive estimators making use of these properties of the adaptive predictors simple modifications of the astrom wittenmark self tuning regulator are proposed and shown to be asymptotically optimal

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

can local single pass methods solve any stationary hamilton jacobi bellman equation the use of local single pass methods like e g the fast marching method has become popular in the solution of some hamilton jacobi equations the prototype of these equations is the eikonal equation for which the methods can be applied saving cpu time and possibly memory allocation then some questions naturally arise can local single pass methods solve any hamilton jacobi equation if not where should the limit be set this paper tries to answer these questions in order to give a complete picture we present an overview of some fast methods available in the literature and briefly analyze their main features we also introduce some numerical tools and provide several numerical tests which are intended to exhibit the limitations of the methods we show that the construction of a local single pass method for general hamilton jacobi equations is very hard if not impossible nevertheless some special classes of problems can actually be solved making local single pass methods very useful from a p

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

recursive identification for multi input multi output hammerstein wiener system abstractin this paper an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi input multi output hammerstein wiener system with process noise in the proposed identification method the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible then the auxiliary variable is constructed the parameters of the regression equations are identified and the system parameter matrices can be obtained by matrix composition of the parameter product matrix a theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance the effectiveness of the proposed method is validated through the experiments

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

label setting methods for multimode stochastic shortest path problems on graphs stochastic shortest path ssp problems arise in a variety of discrete stochastic control contexts an optimal solution to such a problem is typically computed using the value function which can be found by solving the corresponding dynamic programming equations in the deterministic case these equations can be often solved by highly efficient label setting methods such as dijkstra s and dial s algorithms in this paper we define and study a class of multimode stochastic shortest path mssp problems and develop sufficient conditions for the applicability of label setting methods we illustrate our approach in a number of discrete stochastic control examples we also discuss the relationship of ssps with discretizations of static hamilton jacobi equations and provide an alternative derivation for several fast noniterative numerical methods for these partial differential equations pdes

convergence of hls estimation algorithms for multivariable arx like systems a hierarchical least squares hls algorithm is derived in details for identifying mimo arx like systems based on the hierarchical identification principle it is shown that the parameter estimation errors by the hls algorithm consistently converge to zero for bounded noise variances by using the stochastic martingale theory a numerical example is given

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

identification scheme for hammerstein output error models with bounded noise this technical note presents a method for the identification of hammerstein output error hoe models corrupted by bounded noise the method is based on an iterative scheme using two optimal bounding ellipsoid obe type algorithms the proposed approach allows the joint estimation of the linear part and of the nonlinear part with a low computational burden a numerical example is given so as to show the efficiency of the method