explicit expression of the parameter bias in identification of laguerre models from step responses this paper delivers an analysis of the least square estimation of the laguerre coefficients of a linear discrete time system from step response data the original contribution consists in an explicit formula for the bias error on the estimated coefficients due to the under modelling of the system the formula jointly with some a priori information on the neglected dynamics can be used to construct bounds on this error the results presented in this paper are illustrated with a simulation example c 2003 elsevier b v all rights reserved

on approximation of stable linear dynamical systems using laguerre and kautz functions approximation of stable linear dynamical systems by means of so called laguerre and kautz functions which are the laplace transforms of a class of orthonormal exponentials is studied since the impulse response of a stable finite dimensional linear dynamical system can be represented by a sum of exponentials times polynomials it seems reasonable to use basis functions of the same type assuming that the transfer function of a system is bounded and analytic outside a given disc it is shown that laguerre basis functions are optimal in a mini max sense this result is extended to the two parameter kautz functions which can have complex poles while the poles of laguerre functions are restricted to the real axis by conformai mapping techniques the two parameter kautz approximation problem is recast as two laguerre approximation problems thus the well developed theory of laguerre functions can be applied to analyze kautz approximations unilateral shifts are used to further develop the connection between laguerre functions and kautz functions results on 2 and approximation using kautz models are given furthermore the weighted l2 kautz approximation problem is shown to be equivalent to solving a block toeplitz matrix equation

simultaneous estimation of parameters for different orders of discrete orthonormal function models the augmented ud identification audi method is used to simultaneously estimate parameters of all 1 to nth order discrete orthonormal function models in one computational step this method is tested on different types of orthonormal functions such as the laguerre kautz fir and markov laguerre models

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

adaptive gpc based on laguerre filters modelling abstract a state space model based on laguerre filters is proposed to design an adaptive generalized predictive controller gpc for stable plants a sufficient stability condition is derived to study the convergence and stability of the proposed controller in case of a plant model match robustness conditions are also given for the case of plant model mismatch the results are applicable to gpc schemes based on moving average models in the presence of plant model mismatch illustrative examples show the robustness of the controller and compare it with other gpc versions

optimal choice of time scaling factor for linear system approximations using laguerre models clowes 1965 illustrated how to select the optimal time scaling factor for approximations of rational transfer functions using a series expansion of laguerre functions the present paper extends this result to approximations for general l sub 2 stable linear systems as a direct application of this extended result we are able to obtain approximations for irrational transfer functions which minimize the frequency domain error in the l sub 2 sense also we give empirical solutions for the optimal time scaling factor for approximations of first order plus delay systems which can then be applied to a larger class of overdamped systems

system identification with generalized orthonormal basis functions a least squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function where the expansion is in terms of recently introduced generalized basis functions the basis functions are orthogonal in h2 and generalize the pulse laguerre and kautz bases one of their important properties is that when chosen properly they can substantially increase the speed of convergence of the series expansion this leads to accurate approximate models with only a few coefficients to be estimated explicit bounds are derived for the bias and variance errors that occur in parameter estimates as well as in the resulting transfer function estimates

time series clustering via community detection in networks in this paper we propose a technique for time series clustering using community detection in complex networks firstly we present a method to transform a set of time series into a network using different distance functions where each time series is represented by a vertex and the most similar ones are connected then we apply community detection algorithms to identify groups of strongly connected vertices called a community and consequently identify time series clusters still in this paper we make a comprehensive analysis on the influence of various combinations of time series distance functions network generation methods and community detection techniques on clustering results experimental study shows that the proposed network based approach achieves better results than various classic or up to date clustering techniques under consideration statistical tests confirm that the proposed method outperforms some classic clustering algorithms such as k medoids diana median linkage and centroid linkage in various data sets interestingly the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process at the same time other techniques fail to identify such patterns moreover the proposed method is robust enough to group time series presenting similar pattern but with time shifts and or amplitude variations in summary the main point of the proposed method is the transformation of time series from time space domain to topological domain therefore we hope that our approach contributes not only for time series clustering but also for general time series analysis tasks

technical communique a note on the optimal expansion of volterra models using laguerre functions this work tackles the problem of expanding volterra models using laguerre functions a strict global optimal solution is derived when each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases each of which parameterized by an individual laguerre pole intended for representing the dominant dynamic of the kernel along a particular dimension it is proved that the solution derived minimizes the upper bound of the squared norm of the error resulting from the practical truncation of the laguerre series expansion into a finite number of functions this is an extension of the results in campello favier and amaral 2004 optimal expansions of discrete time volterra models using laguerre functions automatica 40 815 822 where an optimal solution was obtained for the usual yet particular case in which a single laguerre pole is used for expanding a given kernel along all its dimensions it is also proved that the particular and extended solutions are equivalent to each other when the volterra kernels are symmetric

superlinear schrodinger operators abstract we find nontrivial and ground state solutions for the nonlinear schrodinger equation under conditions weaker than those previously assumed

ground state solutions for some indefinite variational problems abstract we consider the nonlinear stationary schrodinger equation u v x u f x u in r n here f is a superlinear subcritical nonlinearity and we mainly study the case where both v and f are periodic in x and 0 belongs to a spectral gap of v inspired by previous work of li et al 2006 11 and pankov 2005 13 we develop an approach to find ground state solutions i e nontrivial solutions with least possible energy the approach is based on a direct and simple reduction of the indefinite variational problem to a definite one and gives rise to a new minimax characterization of the corresponding critical value our method works for merely continuous nonlinearities f which are allowed to have weaker asymptotic growth than usually assumed for odd f we obtain infinitely many geometrically distinct solutions the approach also yields new existence and multiplicity results for the dirichlet problem for the same type of equations in a bounded domain

improved method for optimum choice of free parameter in orthogonal approximations we report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions this method requires limited knowledge of the signal to be approximated and has a low computational cost

approximation of stable systems by laguerre filters laguerre methods are used to develop concrete techniques and results for approximating stable infinite dimensional systems both hankel norm and l approximation by laguerre filters are studied the infimum of the hankel norm approximation error when the system is approximated by laguerre filters of given maximum order is given by the norm of a certain shifted hankel operator and the best laguerre filter to approximate the system is obtained essentially from the associated eigenproblem for the shifted hankel operator hankel optimal laguerre filters are here called cf laguerre filters as there is a certain connection to the caratheodory fejer interpolation problem and typically provide near best solutions to related l approximation problems a time domain compressed laguerre shift method for solving certain nehari problems for delay systems is used to determine analytically the achievable hankel error norms and thus also to obtain bounds for the achievable l error norm for delay systems a result on a laguerre filter approximation problem in the hilbert schmidt norm is given as well

on pid controller tuning using orthonormal series identification abstract the step response of a closed loop system is identified by means of a laguerre expansion this offers certain advantages over arma models namely lack of bias in the estimates structural flexibility and the ability to precompute the regressors the laguerre coefficients of the retuned system are calculated in terms of the tuning constants and a quadratic performance index is optimized results from simulations and from industrial trials are given

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

online identification of the arx model expansion on laguerre orthonormal bases with filters on model input and output this article proposes a new representation of the arx models on independent and orthonormal laguerre bases by filtering the process input and output using laguerre orthonormal functions the resulting model entitled arx laguerre model ensures the parameter number reduction with a recursive and easy representation however this reduction is still subject to an optimal choice of the laguerre poles defining both laguerre bases therefore we propose an analytical solution to optimise the laguerre poles which depend on fourier coefficients defining the arx laguerre model and that are identified using the regularised square error the identification procedures of the laguerre poles and fourier coefficients are combined and carried out on a sliding window to provide an online identification algorithm of the arx laguerre model the proposed algorithm is tested on numerical simulation and validated on a benchmark system manufactured by feedback known as process trainer pt326

a hybrid genetic algorithm for estimating the optimal time scale of linear systems approximations using laguerre models we deal with the problem of finding the optimal time scale of the truncated laguerre series using numerical search techniques we develop a hybrid genetic algorithm ga to search the nonlinear multimodal squared error function that results from least squares approximations of the impulse response of causal linear time invariant stable systems the hybrid ga incorporates a newton raphson nr local optimizer for fast convergence to the global minimum point the proposed method competes favorably with the pure ga in solution accuracy the number of function evaluations being the same and with an established gradient directed optimization algorithm in number of function evaluations the solution accuracy being the same

deterministic adaptive control based on laguerre series representation the behaviour of adaptive controllers in the presence of unmodelled dynamics and the need for reduced a priori information have led us to abandon the usual arma transfer function representation for a representation by an orthonormal series the appeal of our new approach is that it eliminates the need for assumptions about the plant order and the time delay the plant is modelled by an orthonormal laguerre network put in state space form a simple predictive control law is proposed an explicit deterministic adaptive controller is then designed simulations show that it is easy to use able to handle non minimum phase plants and more robust than the conventional model based approach although we chose laguerre functions other orthonormal functions may be used we have already tested some with success

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

an optimal expansion of volterra models using independent kautz bases for each kernel dimension a new solution for the problem of selecting poles of the two parameter kautz functions in volterra models is proposed in general a large number of parameters are required to represent the volterra kernels although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions such as the kautz basis this representation has a wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non linear static mapping represented by the volterra series the resulting wiener volterra model can be truncated into fewer terms if the kautz functions are properly designed the underlying problem is how to select the arbitrary complex poles that fully parametrize these functions this problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion the present paper goes even further in that each multidimensional kernel is decomposed into a set of independent kautz bases each of which is parametrized by an individual pair of conjugate kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension an analytical solution for one of the kautz parameters valid for volterra models of any order is derived a simulated example is presented to illustrate these theoretical results the same approach is then used to model a real non linear magnetic levitation system with oscillatory behaviour

brief paper choice of free parameters in expansions of discrete time volterra models using kautz functions this work tackles the problem of modeling nonlinear systems using volterra models based on kautz functions the drawback of requiring a large number of parameters in the representation of these models can be circumvented by describing every kernel using an orthonormal basis of functions such as the kautz basis the resulting model so called wiener volterra model can be truncated into a few terms if the kautz functions are properly designed the underlying problem is how to select the free design complex poles that fully parameterize these functions a solution to this problem has been provided in the literature for linear systems which can be represented by first order volterra models a generalization of such strategy focusing on volterra models of any order is presented in this paper this problem is solved by minimizing an upper bound for the error resulting from the truncation of the kernel expansion into a finite number of functions the aim is to minimize the number of two parameter kautz functions associated with a given series truncation error thus reducing the complexity of the resulting finite dimensional representation the main result is the derivation of an analytical solution for a sub optimal expansion of the volterra kernels using a set of kautz functions

a decomposition based multi objective optimization for simultaneous balance computation and transformation in signed networks many social systems have a set of opposite interactions such as friend enemy cooperation competition and support opposition in these signed systems there exist functional imbalances from the system level view because of the existence of unbalanced interactions however it is difficult to compute the unbalance degree and transform unbalanced factors to balanced ones in real signed systems earlier studies tackled these two issues separately and gave a unique solution and thus cannot be well applied to real applications with constraints in this paper we devise a decomposition based and network specific multi objective optimization algorithm to solve the balance computation and transformation of signed networks simultaneously the devised algorithm aims at finding a set of optimal balance transformation solutions and each of which is the trade off between the twin objectives i e the minimization of inter cluster positive links and the minimization of intra cluster negative links of these solutions the one with the fewest unbalanced links corresponds to the solution to the balance computation and each trade off solution corresponds to an optimal balance transformation way under a certain transformation cost extensive experiments on four social networks demonstrate the effectiveness of the devised algorithm on both the computation and the transformation of structural balance they also show that the devised algorithm can provide multiple optimal solutions at the same transformation cost

pertinent choice of parameters for discrete kautz approximation kautz functions have received much attention in the recent mathematical modeling and identification literature these functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior we consider here the choice of the free parameters in discrete two parameter kautz approximation using a key relationship between kautz and laguerre expansions we derive an upper bound for the quadratic truncation error minimization of this upper bound yields pertinent parameters whose computation then requires reduced knowledge of the function to be modeled

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

on a periodic schrodinger equation involving periodic and nonperiodic nonlinearities in r2 abstract we study the existence of solutions for the nonlinear schrodinger equation u v x u f x u in r 2 where the potential v is 1 periodic 0 lies in a spectral gap from the spectrum of the schrodinger operator s v and the nonlinearity f x t has exponential growth in the sense of trudinger moser the main feature here is that f x t is allowed to be both periodic and nonperiodic in the x variable our proofs rely on a linking theorem and the lions concentration compactness principle

optimal free parameters in orthonormal approximations we consider orthonormal expansions where the basis functions are governed by some free parameters if the basis functions adhere to a certain differential or difference equation then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error this expression is a function of the free parameters and some simple signal measurements restrictions on the differential or difference equation that make this possible are given minimization of either the upper bound or the enforced convergence criterion as a function of the free parameters yields the same optimal parameters which are of a simple form this method is applied to several continuous time and discrete time orthonormal expansions that are all related to classical orthogonal polynomials

new conditions on nonlinearity for a periodic schrodinger equation having zero as spectrum abstract we consider the semilinear schrodinger equation u v x u f x u for x r n u x 0 as x where f is a superlinear and subcritical nonlinearity we mainly study the case when both v and f are periodic in x and 0 is a boundary point of a spectral gap of v we extend a linking theorem of kryszewski and szulkin 15 and establish a new variational setting which is more suitable to the above case we obtain two theorems on the existence of ground state solutions with mild assumptions on f

an optimum time scale for discrete laguerre network any discrete time stable transfer function can be expressed by a discrete time laguerre series with a chosen time scale an optimum time scale such that an index is minimized is derived this index ensures that the coefficients of higher order laguerre functions go toward zero quickly the solution derived requires the knowledge of the impulse response of the discrete plant cases of first order plants second order underdamped plants and plants with multiunit delay are also discussed

online optimization of the time scale in adaptive laguerre based filters a new online method to optimize the free parameter in adaptive laguerre based filters is presented it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error the proposed technique presents a fast convergence and a good robustness

a multiobjective evolutionary programming framework for graph based data mining subgraph mining is the process of identifying concepts describing interesting and repetitive subgraphs within graph based data the exponential number of possible subgraphs makes the problem very challenging existing methods apply a single objective subgraph search with the view that interesting subgraphs are those capable of not merely compressing the data but also enhancing the interpretation of the data considerably usually the methods operate by posing simple constraints or user defined thresholds such as returning all subgraphs whose frequency is above a specified threshold such search approach may often return either a large number of solutions in the case of a weakly defined objective or very few in the case of a very strictly defined objective in this paper we propose a framework based on multiobjective evolutionary programming to mine subgraphs by jointly maximizing two objectives support and size of the extracted subgraphs the proposed methodology is able to discover a nondominated set of interesting subgraphs subject to tradeoff between the two objectives which otherwise would not be achieved by the single objective search besides it can use different specific multiobjective evolutionary programming methods experimental results obtained by three of the latter methods on synthetically generated as well as real life graph based datasets validate the utility of the proposed methodology when benchmarked against classical single objective methods and their previous nonevolutionary multiobjective extensions

optimum choice of free parameter in orthonormal approximations this correspondence investigates the choice of a free parameter usually related to time scale that minimizes the error energy when approximating a given signal with some widely used orthonormal basis functions the proposed solution is the best that can be achieved with the limited required knowledge of the signal it is appealing for experimental data for which no exact mathematical expression is available

parametric least squares approximation using gamma bases we study the problem of linear approximation of a signal using the parametric gamma bases in l sup 2 space these bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space thereby yielding an extra degree of freedom in the approximation gamma bases have a simple analog implementation that is a cascade of identical lowpass filters we derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights using statistical signal processing tools we further develop a numerical method for estimating the optimum time scale