| 1. |
- Heuberger, Peter S.C., et al.
(författare)
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Modelling and Identification with Rational Orthogonal Basis Functions
- 2005. - 1
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Bok (refereegranskat)abstract
- Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing.Nine international experts have contributed to this work to produce thirteen chapters that can be read independently or as a comprehensive whole with a logical line of reasoning:Construction and analysis of generalized orthogonal basis function model structure;System Identification in a time domain setting and related issues of variance, numerics, and uncertainty bounding;System identification in the frequency domain;Design issues and optimal basis selection;Transformation and realization theory.Modelling and Identification with Rational Orthogonal Basis Functions affords a self-contained description of the development of the field over the last 15 years, furnishing researchers and practising engineers working with dynamical systems and stochastic processes with a standard reference work.
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| 2. |
- Heuberger, Peter S. C., et al.
(författare)
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Orthonormal basis functions in time and frequency domain : Hambo transform theory
- 2004
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Ingår i: SIAM Journal of Control and Optimization. - 0363-0129 .- 1095-7138. ; 42:4, s. 1347-1373
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Tidskriftsartikel (refereegranskat)abstract
- The class of finite impulse response (FIR), Laguerre, and Kautz functions can be generalized to a family of rational orthonormal basis functions for the Hardy space H2 of stable linear dynamical systems. These basis functions are useful for constructing efficient parameterizations and coding of linear systems and signals, as required in, e.g., system identification, system approximation, and adaptive filtering. In this paper, the basis functions are derived from a transfer function perspective as well as in a state space setting. It is shown how this approach leads to alternative series expansions of systems and signals in time and frequency domain. The generalized basis functions induce signal and system transforms (Hambo transforms), which have proved to be useful analysis tools in various modelling problems. These transforms are analyzed in detail in this paper, and a large number of their properties are derived. Principally, it is shown how minimal state space realizations of the system transform can be obtained from minimal state space realizations of the original system and vice versa.
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| 3. |
- Lyzell, Christian, et al.
(författare)
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Order and Structural Dependence Selection of LPV-ARX Models using a Nonnegative Garrote Approach
- 2009
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Ingår i: Proceedings of the 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference. - 9781424438716 - 9781424438723 ; , s. 7406-7411
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Konferensbidrag (refereegranskat)abstract
- In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.
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| 4. |
- Toth, Roland, et al.
(författare)
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Order and Structural Dependence Selection of LPV-ARX Models using a Nonnegative Garrote Approach
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.
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