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

Tóth, Roland; Heuberger, P.S.C.; Hof, Paul M.J. Van den

doi:10.1109/cdc.2006.377063

Cited by 6 publications

(18 citation statements)

References 14 publications

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“…To use them in the identification of general LPV systems, we introduce a model structure, that 1 In terms of m, the fuzziness parameter of the clustering algorithm. If m → ∞, optimality is guaranteed (see [15]). consists of an OBF filter bank, connected to a weighting function set with dynamic dependence on p. For reasons of clarity we describe the model structure for the SISO case.…”

Section: Lpv Obf Model Structuresmentioning

confidence: 99%

“…For this property, generally infinitely many functions, n e = ∞, are required, so using a finite number of basis functions restricts the class of realizable LPV systems. In practice however, careful selection of the basis can ensure almost error free representation of F P with a limited number of OBFs (see [15]). …”

Section: Lpv Obf Model Structuresmentioning

confidence: 99%

“…As mentioned in Section I, a key problem of OBFs based identification is the choice of the basis functions Φ ne n b . For completeness, first a practically applicable basis selection mechanism based on [15] is briefly discussed. Then, assuming that a set of basis functions is given, the WF-LPV identification approach based on a separable least squares algorithm is presented.…”

Section: Lpv Identificationmentioning

confidence: 99%

“…Then the basis selection procedure is as follows: 1) Determination of pole samples of the pole functionals of S by LTI identification of each Fp ∈ F P . 2) Determination of the optimal OBF set Φ ne n b for S based on FKcM clustering [15]. The procedure also copes with the uncertainty of the pole estimates.…”

Section: A Obf Selectionmentioning

confidence: 99%

“…The first is to choose an OBF set Φ n , "sufficiently rich" to describe F P . In [15] a FuzzyKolmogorov c-Max (FKcM) approach was proposed to solve this selection problem through the fusion of Kolmogorov nwidth theory for OBFs [16] and Fuzzy c-Means clustering [17] of sample poles of F P . This approach guarantees in an asymptotic 1 sense the least worst-case local modeling error for F P with the resulting OBFs [15], [14].…”

Section: Introductionmentioning

confidence: 99%

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Flexible model structures for LPV identification with static scheduling dependency

Tóth

Heuberger

Hof

2008

2008 47th IEEE Conference on Decision and Control

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A discrete-time linear parameter-varying (LPV) model can be seen as the combination of local LTI models together with a scheduling signal dependent function set, that selects one of the models to describe the continuation of the signal trajectories at every time instant. An identification strategy of LPV models is proposed that consists of the separate approximation of the local model set and the scheduling functions. The local model set is represented as a linear combination (series expansion) of orthonormal basis functions (OBFs). The expansion coefficients are dynamically dependent (weighting) functions of the scheduling parameters (depending on time shifted scheduling). To approximate this dependency class with a static one (non-shifted scheduling), a feedback-based structure of the weighting functions is introduced. The proposed model structure is identified in a two step procedure. First the OBFs, that guarantee the least asymptotic worst-case modeling error for the local models, are selected through the fuzzy Kolmogorov c-Max approach. With the resulting OBFs, the weighting functions are identified through a separable least-squares algorithm. The method is demonstrated by means of simulation examples and analyzed in terms of applicability, convergence, and consistency of the model estimates

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Section: Lpv Obf Model Structuresmentioning

confidence: 99%

Section: Lpv Obf Model Structuresmentioning

confidence: 99%

Section: Lpv Identificationmentioning

confidence: 99%

Section: A Obf Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Flexible model structures for LPV identification with static scheduling dependency

Tóth

Heuberger

Hof

2008

2008 47th IEEE Conference on Decision and Control

Self Cite

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Modeling and Identification of Linear Parameter-Varying Systems

Tóth

2010

Lecture Notes in Control and Information Sciences

455

573

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so swiftly that it feels like yesterday when I first walked the corridors of the Delft Center for Systems and Control (DCSC). At the same time, I cherish all the countless memories that bound my heart to this place and to the people whom I worked with and walked those corridors with day by day. I owe many people a lot for their support, encouragement, and advice, which have contributed directly or indirectly to this thesis and the scientific research associated with it.Besides these general words of gratitude, a number of people deserves special attention. First, I would like to express my thanks towards my supervisors Paul Van den Hof and Peter Heuberger for their excellent guidance and friendship over the years. They were always there helping to find the missing wheel or rejoicing in the success of a breakthrough. Their support both in terms of research and personal matters made my life a lot easier. I also would like to thank Carsten Scherer for many discussions. His ability to understand abstract ideas sharply from half words or bad notation always amazes me.However, my greatest thanks go to my wife Andrea, whose tender love has been a miracle in my life. She was always there in these years, in every moment, supporting me to accomplish all that I was aiming at. She is more than I could ever wish for, as she is all that I would ever need. Last but not least, I thank our son Sándor for all the drawings and stamps he made on my manuscripts to make his father happy and also our daughter Lujza for the smiles to warm my heart. They always worked. It is to them whom I dedicate this thesis.

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Identification of LPV system using locally weighted technique

Zeng

Gao

2010

Appl. Math. J. Chin. Univ.

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The problem of linear parameter varying (LPV) system identification is considered based on the locally weighted technique which provides estimation of the LPV model parameters at each distinct data time point by giving large weights to measurements that are "close" to the current time point and small weights to measurements "far" from the current time point. Issues such as choice of distance function, weighting function and bandwidth selection are discussed.The developed method is easy to implement and simulation results illustrate its efficiency. §1 IntroductionRecently, the identification problem of linear parameter varying (LPV) system [13] has received considerable attention, motivated by problems confronted in robust control [1,11] and gain scheduling control [7,10]. Work on the identification of LPV system can be roughly divided into 2 classes: global approaches which obtain a single parameter dependent model [3,5,14,15,17,21] and local approaches which identify many linear time invariant (LTI) models [10,16,20]. The global approaches rely on the assumption that both the control input and the scheduling variables are persistently excited simultaneously in one global identification experiment, which may not be reasonable in many applications. The local approaches supply attractive alternatives. However, both the global and local approaches need some kind of a priori information of the system, which may not be available in practice [9].In this paper, an attempt is made to identify the LPV system based on locally weighted technique [12], which provides estimation of the LPV model parameters at each distinct data time point by giving large weights to measurements that are "close" to the current time point and small weights to measurements "far" from the current time point. This technique uses available data and does not require much a priori information of the system, which makes it suitable for many practical applications.

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

Cited by 6 publications

References 14 publications

Flexible model structures for LPV identification with static scheduling dependency

Flexible model structures for LPV identification with static scheduling dependency

Modeling and Identification of Linear Parameter-Varying Systems

Identification of LPV system using locally weighted technique

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