Orthonormal Basis Function

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 171 Experts worldwide ranked by ideXlab platform

R.j.g.b. Campello - One of the best experts on this subject based on the ideXlab platform.

  • An Introduction To Models Based On Laguerre, Kautz And Other Related Orthonormal Functions - Part Ii: Non-linear Models
    International Journal of Modelling Identification and Control, 2012
    Co-Authors: Gustavo H. C. Oliveira, R.j.g.b. Campello, Jeremias Barbosa Machado, Alex Da Rosa, W.c. Amaral
    Abstract:

    This paper provides an overview of system identification using Orthonormal Basis Function models, such as those based on Laguerre, Kautz, and generalised Orthonormal Basis Functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the Orthonormal Basis Functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies.

  • An introduction to models based on Laguerre, Kautz and other related Orthonormal Functions - part I: linear and uncertain models
    International Journal of Modelling Identification and Control, 2011
    Co-Authors: Gustavo H. C. Oliveira, R.j.g.b. Campello, Jeremias Barbosa Machado, Alex Da Rosa, W.c. Amaral
    Abstract:

    This paper provides an overview of system identification using Orthonormal Basis Function models, such as those based on Laguerre, Kautz, and generalised Orthonormal Basis Functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identification. The second part approaches the issues related with non-linear models. The discussions comprise a broad bibliographical survey of the subjects involving linear models within the Orthonormal Basis Functions framework. Theoretical and practical issues regarding the identification of these models are presented and illustrated by means of a case study involving a polymerisation process.

  • GA Optimization of Generalized OBF TS Fuzzy Models with Global and Local Estimation Approaches
    2006 IEEE International Conference on Fuzzy Systems, 2006
    Co-Authors: Anderson V. Medeiros, Wagner C. Amaral, R.j.g.b. Campello
    Abstract:

    OBF (Orthonormal Basis Function) fuzzy models have shown to be a 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. A more general architecture, called generalized OBF Takagi-Sugeno fuzzy model, was introduced in previous work and provided the mathematical interpretation that was missing to the former OBF fuzzy models. In spite of its clear mathematical meaning, however, the identification of this new generalized model is not a trivial task. This paper discusses the use of a genetic algorithm (GA) especially designed for this task, where a fitness Function based on the Akaike information criterion plays a key role by considering both model accuracy and parsimony aspects. The hybridization of the GA with classical estimation algorithms is also investigated. Specifically, two different hybridization approaches (with global and local least squares) are evaluated in the modeling of a real nonlinear magnetic levitation system.

  • GA Optimization of OBF TS Fuzzy Models with Linear and Non Linear Local Models
    2006 Ninth Brazilian Symposium on Neural Networks (SBRN'06), 2006
    Co-Authors: Anderson V. Medeiros, Wagner C. Amaral, R.j.g.b. Campello
    Abstract:

    OBF (Orthonormal Basis Function) Fuzzy models have shown to be a 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. Although encouraging application results have been obtained, no automatic procedure had yet been developed to optimize the design parameters of these models. This paper elaborates on the use of a genetic algorithm (GA) especially designed for this task, in which a fitness Function based on the Akaike information criterion plays a key role by considering both model accuracy and parsimony aspects. The use of linear (actually affine) and nonlinear local models is also investigated. The proposed methodology is evaluated in the modeling of a real nonlinear magnetic levitation system.

  • Control of a bioprocess using Orthonormal Basis Function fuzzy models
    2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), 2004
    Co-Authors: R.j.g.b. Campello, L.a.c. Meleiro, W.c. Amaral
    Abstract:

    Fuzzy models within the framework of Orthonormal Basis Functions (OBF fuzzy models) were introduced in previous works and have shown to be a very promising approach to the areas of non-linear system identification and control since they exhibit several advantages over those dynamic model architectures usually adopted in the literature. In the present paper these models are reviewed and used as a Basis for a predictive control scheme which is applied to the control of a process for ethyl alcohol (ethanol) production.

W.c. Amaral - One of the best experts on this subject based on the ideXlab platform.

  • An Introduction To Models Based On Laguerre, Kautz And Other Related Orthonormal Functions - Part Ii: Non-linear Models
    International Journal of Modelling Identification and Control, 2012
    Co-Authors: Gustavo H. C. Oliveira, R.j.g.b. Campello, Jeremias Barbosa Machado, Alex Da Rosa, W.c. Amaral
    Abstract:

    This paper provides an overview of system identification using Orthonormal Basis Function models, such as those based on Laguerre, Kautz, and generalised Orthonormal Basis Functions. The paper is separated in two parts. The first part of the paper approached issues related with linear models and models with uncertain parameters. Now, the mathematical foundations as well as their advantages and limitations are discussed within the contexts of non-linear system identification. The discussions comprise a broad bibliographical survey of the subject and a comparative analysis involving some specific model realisations, namely, Volterra, fuzzy, and neural models within the Orthonormal Basis Functions framework. Theoretical and practical issues regarding the identification of these non-linear models are presented and illustrated by means of two case studies.

  • An introduction to models based on Laguerre, Kautz and other related Orthonormal Functions - part I: linear and uncertain models
    International Journal of Modelling Identification and Control, 2011
    Co-Authors: Gustavo H. C. Oliveira, R.j.g.b. Campello, Jeremias Barbosa Machado, Alex Da Rosa, W.c. Amaral
    Abstract:

    This paper provides an overview of system identification using Orthonormal Basis Function models, such as those based on Laguerre, Kautz, and generalised Orthonormal Basis Functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identification. The second part approaches the issues related with non-linear models. The discussions comprise a broad bibliographical survey of the subjects involving linear models within the Orthonormal Basis Functions framework. Theoretical and practical issues regarding the identification of these models are presented and illustrated by means of a case study involving a polymerisation process.

  • Control of a bioprocess using Orthonormal Basis Function fuzzy models
    2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), 2004
    Co-Authors: R.j.g.b. Campello, L.a.c. Meleiro, W.c. Amaral
    Abstract:

    Fuzzy models within the framework of Orthonormal Basis Functions (OBF fuzzy models) were introduced in previous works and have shown to be a very promising approach to the areas of non-linear system identification and control since they exhibit several advantages over those dynamic model architectures usually adopted in the literature. In the present paper these models are reviewed and used as a Basis for a predictive control scheme which is applied to the control of a process for ethyl alcohol (ethanol) production.

  • FUZZ-IEEE - Control of a bioprocess using Orthonormal Basis Function fuzzy models
    2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), 2004
    Co-Authors: R.j.g.b. Campello, Luiz Augusto Da Cruz Meleiro, W.c. Amaral
    Abstract:

    Fuzzy models within the framework of Orthonormal Basis Functions (OBF fuzzy models) were introduced in previous works and have shown to be a very promising approach to the areas of non-linear system identification and control since they exhibit several advantages over those dynamic model architectures usually adopted in the literature. In the present paper these models are reviewed and used as a Basis for a predictive control scheme which is applied to the control of a process for ethyl alcohol (ethanol) production.

  • FUZZ-IEEE - Takagi-Sugeno fuzzy models within Orthonormal Basis Function framework and their application to process control
    2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37, 2002
    Co-Authors: R.j.g.b. Campello, W.c. Amaral
    Abstract:

    Fuzzy models within Orthonormal Basis Function framework (OBF Fuzzy Models) have been introduced in previous works and shown to be a very promising approach to the areas of non-linear system identification and control since they exhibit several advantages over those dynamic model topologies usually adopted in the literature. In the present paper, it is demonstrated that the OBF Takagi-Sugeno fuzzy models previously introduced by the authors are particular realizations of a more general and interpretable formulation presented here, while being able to approximate to desired accuracy a wide class of non-linear dynamic systems. In addition, a predictive control scheme based on the linearization of these models is applied to the control of a polymerization reactor.

P.s.c. Heuberger - One of the best experts on this subject based on the ideXlab platform.

  • A general transform theory of rational Orthonormal Basis Function expansions
    Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000
    Co-Authors: T.j. De Hoog, P.s.c. Heuberger
    Abstract:

    A general transform theory is presented that underlies expansions of stable discrete-time transfer Functions in terms of rational Orthonormal bases. The types of bases considered are generated by cascade connections of stable all-pass Functions. If the all-pass sections in such a network are all equal, this gives rise to the Hambo Basis construction. In the paper a more general construction is studied in which the all-pass Functions are allowed to be different, in terms of choice and number of poles that are incorporated in the all-pass Functions. It is shown that many of the interesting properties of the so-called Hambo transform that underlies the Hambo Basis expansion carry over to the general case. Especially the expressions for the computation of the Hambo transform on the Basis of state-space expressions can be extended to the general Basis case. This insight can for instance be applied for the derivation of a recursive algorithm for the computation of the expansion coefficients, which are then obtained as the impulse response coefficients of a linear time-varying system.

  • Identification of a fluidized catalytic cracking unit: an Orthonormal Basis Function approach
    Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998
    Co-Authors: E.t. Van Donkelaar, P.s.c. Heuberger
    Abstract:

    Multivariable system identification of a model IV fluidized catalytic cracking unit is performed using a linear time invariant model parametrization based on Orthonormal Basis Functions. This model structure is a linear regression structure which results in a simple convex optimization problem for least squares prediction error identification. Unknown initial conditions are estimated simultaneously with the system dynamics to account for the slow drift of the measured output from the given initial condition to a stationary working point. The model accuracy for low frequencies is improved by a steady-state constraint on the estimated model and incorporation of prior knowledge of the large time constants in the model structure. The model accuracy is furthermore improved by an iteration over identification of a high order model and model reduction. First a high order model is estimated using an Orthonormal Basis. This model is reduced and used to generate a new Orthonormal Basis which is used in the following iteration step for high order estimation. With the approach followed accurate models over a large frequency range are estimated with only a limited amount of data.

J. Bokor - One of the best experts on this subject based on the ideXlab platform.

  • Robust control synthesis to achieve a required loop shape-a generalized Orthonormal Basis Function approach
    Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
    Co-Authors: P. Gaspar, Z. Szabo, J. Bokor
    Abstract:

    In the paper a new control design method is developed to obtain a robust controller that realize the required loop shape. First, a transfer Function, namely a fictitious controller, is identified between the model and the required loop transfer Function. Then a robust controller is designed taking into consideration the approximation error of the designed loop transfer Function. The designed controller achieves the loop transfer Function and meets the robust stability and nominal performance requirements. In the paper the steps of the robust control synthesis are discussed, moreover a simulation example is shown to demonstrate the method in a numerical example.

  • L/sup p/ norm convergence of rational Orthonormal Basis Function expansions
    Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1999
    Co-Authors: Z. Szabo, J. Bokor
    Abstract:

    In this paper model sets for discrete-time LTI systems that are spanned by generalized Orthonormal Basis Functions are investigated. It is established that the partial sums of Fourier series of generalized Orthonormal Basis expansions converge in all the spaces L/sup p/ and H/sup p/, 1

J. Bokor - One of the best experts on this subject based on the ideXlab platform.

  • minimal partial realization from generalized Orthonormal Basis Function expansions
    Automatica, 2002
    Co-Authors: T.j. De Hoog, P.s.c. Heuberger, Z. Szabo, J. Bokor
    Abstract:

    A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its first N expansion coefficients in terms of generalized Orthonormal Basis match a given sequence. The Basis considered, also known as the Hambo Basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing general dynamic information to be incorporated in the Basis. For the solution of the problem use is made of the properties of the Hambo operator transform theory that underlies the Basis Function expansion. As corollary results compact expressions are found by which the Hambo transform and its inverse can be computed efficiently. The resulting realization algorithms can be applied in an approximative sense, for instance, for computing a low-order model from a large Basis Function expansion that is obtained in an identification experiment.

  • Minimal partial realization from Orthonormal Basis Function expansions
    Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2001
    Co-Authors: P.s.c. Heuberger, T.j. De Hoog, Z. Szabo, J. Bokor
    Abstract:

    Given an expansion of a dynamical system in terms of a generalized Orthonormal (Hambo) Basis, the problem of realizing a state-space model of minimal McMillan degree such that its first N expansion coefficients match the given ones is addressed and solved. For the solution use is made of the properties of the Hambo operator transform theory. The resulting realization algorithms can be applied in an exact and approximative sense and can also be applied to solve a related interpolation problem.

  • l sup p norm convergence of rational Orthonormal Basis Function expansions
    Conference on Decision and Control, 1999
    Co-Authors: Z. Szabo, J. Bokor
    Abstract:

    In this paper model sets for discrete-time LTI systems that are spanned by generalized Orthonormal Basis Functions are investigated. It is established that the partial sums of Fourier series of generalized Orthonormal Basis expansions converge in all the spaces L/sup p/ and H/sup p/, 1trigonometric interpolation L/sup p/ norm convergence is proved for the discrete rational operators, too.

Orthonormal Basis Function - 15 days free trial to Access Experts & Abstracts