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

vandermonde like determinants and n fold darboux backlund transformations we define vandermonde like determinants and analyze their structure the resulting scheme is well suited to achieve a remarkable compactness and transparency in n soliton formulas or more generally in formulas for n fold darboux or backlund transformations

solving soliton equations with self consistent sources by method of variation of parameters abstract starting from the solutions of soliton equations and corresponding eigenfunctions obtained by darboux transformation we present a new method to solve soliton equations with self consistent sources sescs based on method of variation of parameters the kdv equation with self consistent sources kdvscs is used as a model to illustrate this new method in addition we apply this method to construct some new solutions of the derivative nonlinear schrodinger equation with self consistent sources dnlsscs such as phase solution dark soliton solution bright soliton solution and breather type solution

transient periodic behaviour related to a saddle node bifurcation the authors investigate transient periodic orbits of dissipative invertible maps of r2 such orbits exist just before in parameter space a saddle node pair is formed they obtain numerically and analytically simple scaling laws for the duration of the transient and for the region of initial conditions which evolve into transient periodic orbits an estimate of this region is then obtained by the construction after extension of the map to c2 of the stable manifolds of the two complex saddles in c2 that bifurcate ino the real saddle node pair

integrity measures quantifying the erosion of smooth and fractal basins of attraction abstract the phase portraits of a dissipative dynamical system are characterized by the existence of one or more stable attractors which typically include point equilibria periodic oscillations harmonic and subharmonic quasi periodic solutions and chaotic attractors each attractor is embedded in its own domain or basin of attraction bounded by a separatrix associated with an unstable saddle solution under the variation of a control parameter as the attractors move and bifurcate the basins also undergo corresponding changes and metamorphoses these changes in size and shape are usually continuous but can be discontinuous as when an attractor vanishes along with its basin at a saddle node bifurcation associated with the homoclinic tangling of the invariant manifolds of the saddle solution basin boundaries can also change in nature from smooth to fractal in this paper the escape of a driven oscillator from a cubic potential well as an archetypal example is used to explore the engineering significance of the basin erosions that occur under increased forcing various measures of engineering integrity of the constrained attractor are introduced a global measure assesses the overall basin area a local measure assesses the distance from the attractor to the basin boundary and a velocity measure is related to the size of impulse that could be sustained without failure since engineering systems may be subjected to pulse loads of finite duration attention is given to both the absolute and transient basin boudaries the significant erosion of these at homoclinic tangencies is particularly highlighted in the present study the fractal basins having a severely reduced integrity under all three criteria

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

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

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

asymptotic properties of black box identification of transfer functions the problem of estimating the transfer function of a linear stochastic system is considered the transfer function is parametrized as a black box and no given order is chosen a priori this means that the model orders may increase to infinity when the number of observed data tends to infinity the consistency and convergence properties of the resulting transfer function estimates are investigated asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase it is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise to signal ratio at that frequency mulliplied by the model order to number of data points ratio

the hierarchy of multi soliton solutions of the derivative nonlinear schrodinger equation we provide a relatively simple approach to backlund transformations for the derivative nonlinear schrodinger equation by iteration it leads to compact n soliton formulae both with asymptotically vanishing and non vanishing amplitudes the phenomenology of these solutions is discussed and illustrated in some detail

backlund transformations for high order constrained flows of the akns hierarchy canonicity and spectrality property a new infinite number of one and two point backlund transformations bts with explicit expressions are constructed for the high order constrained flows of the akns hierarchy it is shown that these bts are canonical transformations including the backlund parameter and a spectrality property holds with respect to and the conjugated variable for which the point belongs to the spectral curve in addition the formulae of m times repeated darboux transformations for the high order constrained flows of the akns hierarchy are presented

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

vandermonde like determinants representations of darboux transformations and explicit solutions for the modified kadomtsev petviashvili equation abstract recently the 2 1 dimensional modified kadomtsev petviashvili mkp equation was decomposed into two known 1 1 dimensional soliton equations by dai and geng h h dai x g geng j math phys 41 2000 7501 in the present paper a systematic and simple method is proposed for constructing three kinds of explicit n fold darboux transformations and their vandermonde like determinants representations of the two known 1 1 dimensional soliton equations based on their lax pairs as an application of the darboux transformations three explicit multi soliton solutions of the two 1 1 dimensional soliton equations are obtained in particular six new explicit soliton solutions of the 2 1 dimensional mkp equation are presented by using the decomposition the explicit formulas of all the soliton solutions are also expressed by vandermonde like determinants which are remarkably compact and transparent

application of the darboux transformation to inverse problems with variable spectral parameters it is shown that darboux transformations can be used to find explicit solutions of deformed equations which have recently been found through the inverse method with a variable spectral parameter the author constructs in particular the soliton solution of the deformed maxwell bloch equations and analyses its asymptotic behaviour

darboux polynomial matrices the classical massive thirring model as a study case one way of constructing explicit expressions of solutions of integrable systems of partial differential equations goes via the darboux method this requires the construction of darboux matrices here we introduce a novel algorithm to obtain such matrices in polynomial form our method is illustrated by applying it to the classical massive thirring model and by combining it with the dihedral group of symmetries possessed by this model

multi solitonic solutions for the variable coefficient variant boussinesq model of the nonlinear water waves abstract for the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water we consider a variable coefficient variant boussinesq vcvb model with symbolic computation we construct the connection between the vcvb model and a variable coefficient ablowitz kaup newell segur vcakns system under certain constraints using the n fold darboux transformation of the vcakns system we present two sets of multi solitonic solutions for the vcvb model which are expressed in terms of the vandermonde like and double wronskian determinants respectively dynamics of those solutions are analyzed and graphically discussed such as the parallel solitonic waves shape changing collision head on collision fusion fission behavior and elastic fusion coupled interaction

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

instrumental variable methods for identification of hammerstein systems abstract consistency conditions for instrumental variable methods applied to hammerstein models are derived and analysed it is necessary to have a model that is not over parametrized and an input that is strongly persistently exciting i e the inputs and their powers are jointly persistently exciting some specific choices of the instruments are proved to give consistency those instruments are formed as filtered inputs and powers of the input consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive real the vector of instruments is in general of larger dimension than the parameter vector it is shown then that a non singular linear transformation of the instruments gives a new and still consistent estimate some simulations using the iv variants proposed in this paper are also included

darboux transformation and soliton solutions for the 2 1 dimensional nonlinear schrodinger hierarchy with symbolic computation abstract in this paper the n fold darboux transformation is applied to the lax pair associated with the 2 1 dimensional nonlinear schrodinger hierarchy the general explicit formula for n soliton solution is derived in terms of vandermonde like determinant expression on the zero background two different families of soliton solutions multi line soliton and multi parabola soliton solutions are constructed by applying the darboux transformation successively based on the figures for several sample solutions the soliton interactions are discussed by virtue of the physical parameters amplitude velocity and direction of the interacting solitons

brief paper computational complexity analysis of set membership identification of hammerstein and wiener systems this paper analyzes the computational complexity of set membership identification of hammerstein and wiener systems its main results show that even in cases where a portion of the plant is known the problems are generically np hard both in the number of experimental data points and in the number of inputs wiener or outputs hammerstein of the nonlinearity these results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point out the need for developing computationally tractable relaxations

parameter bounds for armax models from records with bounded errors in variables the errors in variables problem is that of parameter estimation where all observed variables are corrupted by noise so far the computation of parameter bounds for dynamical models has been performed using equation error and output error approaches in this paper parameter bounds for autoregres sive moving average exogenous armax models are derived on the assumption that both input and output are affected by bounded noise parameter bounding by both the bounded equation error and the bounded errors in variables approach is outlined together with the approximation of the feasible parameter region by an orthotope outer bounding set and is tested on simulated data

a minimal k step delay controller for robust tracking of non minimum phase systems abstract this paper considers the problem of look ahead robust tracking for a non minimum phase system under a sensitivity constraint because of non minimum phase zeros the exact tracking of arbitrary reference input is impossible however with an introduction of some delay tracking is possible within any given tolerance 1 0 it is shown in the paper that the minimum delay required to satisfy the tracking performance is decoupled from a sensitivity disturbance rejection constraint moreover it is shown that calculation of the minimum delay reduces to a binary search problem

darboux transformations for w problems abstract a type of spectral problem called w problem is discussed it appeared in several physical applications explicit formulas for an n fold darboux transformation are derived as an example of application the n soliton formula for the landau lifshitz equation with easy axis anisotropy is written down

chaotic phenomena triggering the escape from a potential well this paper explores the manner in which a driven mechanical oscillator escapes from the cubic potential well typical of a metastable system close to a fold the aim is to show how the well known atoms of dissipative dynamics saddle node folds period doubling flips cascades to chaos boundary crises etc assemble to form molecules of overall response hierarchies of cusps incomplete feigenbaum trees etc particular attention is given to the basin of attraction and the loss of engineering integrity that is triggered by a homoclinic tangle the latter being accurately predicted by a melnikov analysis after escape chaotic transients are shown to conform to recent scaling laws analytical constraints on the mapping eigenvalues are used to demonstrate that sequences of flips and folds commonly predicted by harmonic balance analysis are in fact physically inadmissible

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

identification of wiener type nonlinear systems in a noisy environment wiener systems are widely encountered in engineering and science applications this paper proposes a straightforward approach to the identification of wiener systems in a noisy environment the obtained models are represented in terms of the frequency response for the linear subsystem and the inverse of the static nonlinearity a variety of input excitation signals including random binary and periodic can be used with the proposed method simulation studies using a ph neutralization continuous stirred tank reactor show that excellent results are obtained with relatively short data lengths

parameter identification of discontinuous hammerstein systems the paper deals with the parameter identification of hammerstein systems having discontinuous asymmetric nonlinearities two segment piecewise linear with preload and dead zone application of a simple decomposition technique provides a special form of hammerstein model with a minimum number of parameters the identification is carried out with only one record of measured input output data despite the dead zone to demonstrate the feasibility of the identification method some illustrative examples are included

dynamic bifurcations in non stationary systems transitions with an unpredictable outcome in nonlinear non stationary systems dynamic bifurcations result in a transition to a qualitatively new state in this paper we examine how the dynamics of transition of such systems may be assessed using the concept of transient basins of attraction we delineate the phenomenon of indeterminate dynamic bifurcations where it is shown that the response after the system passes through critical parameter values may be extremely sensitive to the choice of initial conditions or parameter states this new form of unpredictability in systems whose parameters vary with time is clearly an important concept to be assimilated in the theory of non stationary dynamics

controller design oriented model identification method for hammerstein system abstract the paper proposes a new polynomial identification method for the hammerstein system by combining the results of parameter estimation theory and functions approximation theory the method circumvents many disadvantages of the earlier methods it is suitable for producing the controller design oriented model of hammerstein system consistency and convergency analysis are given for the obtained parameter estimates of the system s linear dynamics and approximating polynomial of its nonlinear memoryless element respectively simulation study verifies the effectiveness of the method