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orthonormal basis functions for Memory Predistorter in Oversampled Systems

INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING 2015年第3期25卷 202-212页

作者： Yao, Saijie Huang, Hao Qian, Hua Feng, Weifeng Chinese Acad Sci Shanghai Inst Microsyst & Informat Technol Shanghai 200050 Peoples R China Chinese Acad Sci Key Lab Wireless Sensor Network & Commun Shanghai 200050 Peoples R China Shanghai Res Ctr Wireless Commun Shanghai 200335 Peoples R China Haoxin Microelect Technol Shanghai Co Ltd Shanghai 201203 Peoples R China

Volterra model or memory polynomial model are commonly used to describe the nonlinearity with memory effects for power amplifier (PA) modeling as well as digital predistorter designs. Different monomial terms of the Volterra model or memory polynomial model are highly correlated, which become a challenge during the fixed-point implementation of the coefficients estimation as the data matrix is ill-conditioned. Previous works derived orthogonal basis functions to eliminate the correlation among different monomial terms. Conversely, models of the PAs or the digital predistorters work in the oversampled domain to capture the adjacent band and/or out of band emissions. The correlation among data samples, which was neglected in previous works, can also be a major issue to the numerical instability in the coefficients estimation. In this article, we propose a set of new orthonormal basis functions to eliminate the correlation among different monomial terms as well as the correlation among data samples. As the proposed orthonormal basis functions can be predetermined and implemented with look up tables, the fixed-point implementation is feasible and online computational complexity is greatly reduced. Simulation and experimental results show that the proposed orthonormal basis functions outperform the conventional ones in terms of condition number reduction as well as spectral regrowth suppression. (c) 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:202-212, 2015.

关键词： nonlinearity power amplifiers digital predistorter oversampling orthonormal basis functions

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orthonormal basis functions for continuous-time systems and L_p convergence

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MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS 1999年第3期12卷 295-305页

作者： Akçay, H Ninness, B Univ Bremen Inst Dynam Syst D-28334 Bremen Germany Univ Newcastle Ctr Integrated Dynam & Control Newcastle NSW 2308 Australia Univ Newcastle Dept Elect & Comp Engn Newcastle NSW 2308 Australia

In this paper, model sets for linear-time-invariant continuous-time systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalize the well-known Laguerre and two-parameter Kautz cases. It is shown that the obtained model sets are everywhere dense in the Hardy space H-1(Pi) under the same condition as previously derived by the authors for the denseness in the (Pi is the open right half plane) Hardy spaces H-p(Pi), 1 < p < infinity. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in H-p(Pi), 1 less than or equal to p < infinity, and which have a prescribed asymptotic order, may be constructed. Finally, it is established that the Fourier series formed by orthonormal basis functions converge in all spaces H-p(Pi) and (D is the open unit disk) H-p(D), 1 < p < infinity. The results in this paper have application in system identification, model reduction, and control system synthesis.

关键词： orthonormal basis functions continuous-time fourier series L-p convergence

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orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

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INTERNATIONAL JOURNAL OF CONTROL 2014年第12期87卷 2644-2656页

作者： Velasquez, Ivan G. Yuz, Juan I. Salgado, Mario E. Univ Tecn Federico Santa Maria Dept Elect Engn Valparaiso Chile

This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.

关键词： control design constraints control effort H-2 optimal control Youla parameter orthonormal basis functions

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Asymptotically optimal orthonormal basis functions for LPV system identification

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AUTOMATICA 2009年第6期45卷 1359-1370页

作者： Toth, Roland Heuberger, Peter S. C. Van den Hof, Paul M. J. Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

A global model structure is developed for parametrization and identification of a general class of Linear Parameter-Varying (LPV) systems. By using a fixed orthonormal basis function (OBF) structure, a linearly parametrized model structure follows for which the coefficients are dependent on a scheduling signal. An optimal set of OBFs for this model structure is selected on the basis of local linear dynamic properties of the LPV system (system poles) that occur for different constant scheduling signals. The selected OBF set guarantees in an asymptotic sense the least worst-case modeling error for any local model of the LPV system. Through the fusion of the Kolmogorov n-width theory and Fuzzy c-Means clustering, an approach is developed to solve the OBF-selection problem for discrete-time LPV systems, based on the clustering of observed sample system poles. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Linear parameter-varying systems System identification orthonormal basis functions Pole clustering

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Wiener system identification with generalized orthonormal basis functions

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AUTOMATICA 2014年第12期50卷 3147-3154页

作者： Tiels, Koen Schoukens, Johan Vrije Univ Brussel Dept ELEC B-1050 Brussels Belgium

Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs are needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infinite impulse response dynamics and a polynomial nonlinearity. We propose to use a limited number of generalized OBFs (GOBFs). The pole locations, needed to construct the GOBFs, are estimated via the best linear approximation of the system. The coefficients of the multivariate polynomial are determined with a linear regression. This paper provides a convergence analysis for the proposed identification scheme. It is shown that the estimated output converges in probability to the exact output. Fast convergence rates, in the order O-p(N-F (-nrep/2)), can be achieved, with N-F the number of excited frequencies and n(rep) the number of repetitions of the GOBFs. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Dynamic systems Nonlinear systems orthonormal basis functions System identification Wiener systems

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System identification with generalized orthonormal basis functions: an application to flexible structures

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CONTROL ENGINEERING PRACTICE 2003年第3期11卷 245-259页

作者： Nalbantoglu, V Bokor, J Balas, G Gaspar, P Middle E Tech Univ Dept Aerosp Engn TR-06531 Ankara Turkey Hungarian Acad Sci Comp & Automat Res Inst H-1518 Budapest Hungary Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA

This paper presents an application of a multi-input/multi-output identification technique based on system-generated orthonormal basis functions to a flexible structure. A priori information about the poles of the system, part of which corresponds to the natural frequencies of the structure, is used to generate the orthonormal basis functions. A multivariable model is identified for the experimental flexible structure by using these orthonormal basis functions. It is shown that including a priori knowledge of the system dynamics via the use of orthonormal basis functions into the identification process has the advantage of reducing the number of parameters to be estimated. The multivariable model is used to design an H., controller for the experimental structure to suppress vibrations. The controller is implemented on the structure and very good agreement is obtained between the simulations and the experimental results. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： system identification orthonormal basis functions flexible structures matrix partial fraction expansion H-infinity control

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A state-space description for perfect-reconstruction wavelet FIR filter banks with special orthonormal basis functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年 290卷 290-297页

作者： Uzinski, Julio C. Paiva, Henrique M. Duarte, Marco A. Q. Galvao, Roberto K. H. Villarreal, Francisco Univ Estadual Paulista UNESP Dept Elect Engn FEIS Ilha Solteira SP Brazil Mectron Org Odebrecht Sao Jose Dos Campos SP Brazil Univ Estadual Mato Grosso Sul Dept Math UEMS Cassilandia MS Brazil Dept Elect Engn ITA Sao Jose Dos Campos SP Brazil Univ Estadual Paulista UNESP Dept Math FEIS Ilha Solteira SP Brazil

This paper presents a state space description for wavelet FIR filter banks with perfect reconstruction using special orthonormal basis functions. The FIR structure guarantees the BIBO stability, robustness and improves the filter divergence problem while orthonormal basis functions have characteristics that make them attractive in the modeling of dynamic systems. The state space description presented in this paper has all of those advantages and is minimal. (C) 2015 Published by Elsevier B.V.

关键词： State space description Wavelets FIR filter banks orthonormal basis functions

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Hierarchical fuzzy models within the framework of orthonormal basis functions and their application to bioprocess control

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CHEMICAL ENGINEERING SCIENCE 2003年第18期58卷 4259-4270页

作者： Campello, RJGB Von Zuben, FJ Amaral, WC Meleiro, LAC Maciel, R UNICAMP FEEC DCA BR-13083970 Campinas SP Brazil UNICAMP FEQ DPQ LOPCA BR-13081970 Campinas SP Brazil UNISANTOS Posgrad Informat Santos SP Brazil

Fuzzy models within the framework of orthonormal basis functions (OBF fuzzy models) have been introduced in previous works and shown to be a very promising approach to the areas of nonlinear system identification and control, since they exhibit several advantages over those dynamic model topologies usually adopted in the literature. As fuzzy models, however, they exhibit the dimensionality problem which is the main drawback to the application of neural networks and fuzzy systems to the modeling and control of large-scale systems. This problem has successfully been dealt with in the literature by means of hierarchical structures composed of submodels connected in cascade. In the present paper a hierarchical fuzzy model within the OBF framework is presented. A data-driven hybrid identification method based on genetic and gradient-based algorithms is described in details. A model-based predictive control scheme is also presented and applied to control of a complex industrial process for ethyl alcohol (ethanol) production. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： hierarchical fuzzy models orthonormal basis functions predictive control biotechnology

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Stationarity conditions for the L-2 error surface of the generalized orthonormal basis functions lattice filter

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SIGNAL PROCESSING 1997年第3期56卷 233-253页

作者： Silva, TOE Departamento de Electronica e Telecomunicações/ INESC-Aveiro Universidade de Aveiro 3810 Aveiro Portugal

Recently, a novel model to perform system identification, based on the so-called generalized orthonormal basis functions, appeared in the automatic control literature. This model generalizes the Laguerre and ''two-parameter'' Kautz models (which are IIR models with a restricted structure), and has some remarkable properties. Among them is the fact that under ideal conditions the correlation matrix of its internal signals has a block Toeplitz structure. In this paper we explore this property of the correlation matrix, with the result that a lattice version of the aforementioned model is uncovered. This lattice model is then used to determine under which conditions the model's mean-squared-error has a stationary point with respect to the position of its poles, assuming that there is no external feedback between the model's output and input. The results of this study generalize known similar results for Laguerre and ''two-parameter'' Kautz filters. As a by-product of this study the stationarity conditions for the error surface of ARMA(m,m-1) filters with respect to their pole positions, in an output error configuration and for an arbitrary input signal, are obtained. (C) 1997 Elsevier Science B.V.

关键词： system identification orthonormal basis functions IIR filters error surfaces lattice filters Laguerre models Kautz models

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Continuous-time stable and unstable system modelling with orthonormal basis functions

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2000年第6期10卷 513-531页

作者： Akçay, H Anadolu Univ Dept Elect & Elect Engn TR-26470 Eskisehir Turkey

In this paper, model sets for linear time-invariant continuous-time systems which are spanned by fixed-pole orthonormal bases are investigated. The obtained model sets are shown to be complete in the Lebesque spaces L-p (1 < p < infinity) and in C, the space of complex-valued functions that are continuous on the extended imaginary axis. The L-p norm error bounds for estimating systems in L-p by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1 < p < infinity. Some inequalities on the l(p) means of the Fourier coefficients are also derived. These results have application in estimation and model reduction of stable and unstable continuous-time linear time-invariant systems. A numerical example illustrates the use of the basis functions for the approximation of unstable infinite-dimensional dynamics. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： continuous time orthonormal basis functions completeness Fourier series

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