OPTIMAL POLE SELECTION FOR LPV SYSTEM IDENTIFICATION WITH OBFs, A CLUSTERING APPROACH

Tóth, Roland; Heuberger, Psc Peter; Hof, van den Pmj Paul

doi:10.3182/20060329-3-au-2901.00052

Cited by 6 publications

(9 citation statements)

References 11 publications

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“…In Figure 2, the membership function of a cluster is presented for m = 2 and 25. Based on these and the previous results of [8], the following observations can be made: [8], the magnitude of N av is the same, however the bisection based solution of (13) results in a significantly increased computational time.…”

Section: Results Of Applicationmentioning

confidence: 52%

“…However, χ is not comparable for different m. The results in [8] used m = 2, thus comparison only to m2c5 is available, giving that m2c5 performs worse. Explanation lies in the peaking value of the m2c5 associated membership functions, like in Figure 2.a.…”

Section: Results Of Applicationmentioning

confidence: 99%

“…As an example, we consider an asymptotically stable LPV system S, also considered in [8], given in a parameter-affine controller canonical form:…”

Section: Results Of Applicationmentioning

confidence: 99%

“…In [8], 3 different metrics-based FcM solutions were given which clustered the same pole set into 5 fuzzy sets. This number agrees with the number of sets by visual inspection and the order of the local LTI systems.…”

Section: Results Of Applicationmentioning

confidence: 99%

“…In this paper we aim at a well applicable solution, based on the joint application of the KnW result and FcM clustering, which is capable of determining such region Ω and its associated asymptotically optimal basis in the KnW sense. This solution, which is an improved version of the algorithms presented in [8] and [9], is developed to solve the first two steps of a proposed approach for identifying LPV systems. This approach consists of the following steps:…”

Section: Introductionmentioning

confidence: 99%

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Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

Tóth

Heuberger

Hof

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-A fuzzy clustering approach is developed to select pole locations for Orthonormal Basis Functions (OBFs), used for identification of Linear Parameter Varying (LPV) systems. The identification approach is based on interpolation of locally identified Linear Time Invariant (LTI) models, using globally fixed OBFs. Selection of the optimal OBF structure, that guarantees the least worst-case local modelling error in an asymptotic sense, is accomplished through the fusion of the Kolmogorov n-width (KnW) theory and Fuzzy c-Means (FcM) clustering of observed sample system poles. I. INTRODUCTIONIn general, many physical systems and control problems suffer from parameter variations due to non-stationarity, nonlinear behavior, or dependence on independent variables, such as space coordinates. These systems vary in size and complexity from highly advanced aircrafts [1] to induction motors [2], but they share the common need for accurate and efficient control of the relevant process variables, which has to satisfy the rapidly increasing industrial performance demands. However, accurate modelling of such systems is in general a complex and tedious task, involving the use of non-linear partial differential equations, leading to models with many parameters and high computational complexity.For processes with mild non-linearities, the theory of LPV systems offers an attractive framework for modelling and handling non-linear or time-varying dynamics. These systems are generally described in a state-space representation (SSR), where the state-space matrices are usually affine functions of a time-varying parameter vector ζ : Z → Γ. Here Γ denotes the parameter space. Furthermore, control design in the LPV framework can be carried out by using LTI control theory via gain scheduling [3]. Therefore, the LPV approach can offer a useful venue to meet recent industrial demands. However, existing methods for identification of such systems often produce models with high complexity or -for instance with subspace techniques -with substantial computational load. Because most control design methods require low-order models and fast iterations in the identification process, it is a challenge to develop efficient methods for LPV system identification that yield models with limited complexity and computation time. An additional point of concern is that the McMillan degree of the system may change due to variations of ζ, especially when the approach is based on interpolation of local models. One way to overcome these

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Section: Results Of Applicationmentioning

confidence: 52%

Section: Results Of Applicationmentioning

confidence: 99%

“…As an example, we consider an asymptotically stable LPV system S, also considered in [8], given in a parameter-affine controller canonical form:…”

Section: Results Of Applicationmentioning

confidence: 99%

Section: Results Of Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

Tóth

Heuberger

Hof

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Robust identification/invalidation in an LPV framework

Bianchi¹,

Peña²

2009

Intl J Robust & Nonlinear

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SUMMARYA robust linear parameter varying (LPV) identification/invalidation method is presented. Starting from a given initial model, the proposed method modifies it and produces an LPV model consistent with the assumed uncertainty/noise bounds and the experimental information. This procedure may complement existing nominal LPV identification algorithms, by adding the uncertainty and noise bounds which produces a set of models consistent with the experimental evidence. Unlike standard invalidation results, the proposed method allows the computation of the necessary changes to the initial model in order to place it within the consistency set. Similar to previous LPV identification procedures, the initial parameter dependency is fixed in advance, but here a methodology to modify this dependency is presented. In addition, all calculations are made on state-space matrices which simplifies further controller design computations. The application of the proposed method to the identification of nonlinear systems is also discussed.

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Asymptotically optimal orthonormal basis functions for LPV system identification

2009

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OPTIMAL POLE SELECTION FOR LPV SYSTEM IDENTIFICATION WITH OBFs, A CLUSTERING APPROACH

Cited by 6 publications

References 11 publications

Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

Robust identification/invalidation in an LPV framework

Asymptotically optimal orthonormal basis functions for LPV system identification

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