Hinging hyperplane trees for approximation and identification

Ernst, Susanne

doi:10.1109/cdc.1998.758452

Cited by 47 publications

(35 citation statements)

References 11 publications

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“…(27) can be converted to a model that is separable and linear in the binary variables as in Eq. (9). We demonstrate this idea using an example.…”

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

“…These models constitute the identified models for a hybrid system described by Eq. (9). An advantage of the reduced mode method is that the models for all locations are consistent with the a priori knowledge of the structure of the hybrid system embodied in Eq.…”

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

“…They assumed a structure of the model and formulated an optimization problem which minimizes an appropriately defined criterion function in order to obtain all partition and parameters of the location models simultaneously. In contrast, Breiman [7], Heredia and Arce [8], Ernst [9] and Hush & Horne [10] avoided solving a single complex optimization problem as above but solved several simple optimization problems in order to achieve the same goal of identifying partition and parameters of all locations. They initially assumed a single location with simple structure and added more locations by fitting the residual of previous models.…”

Section: A Brief Review On Hybrid System Identificationmentioning

confidence: 99%

“…An advantage of the reduced mode method is that the models for all locations are consistent with the a priori knowledge of the structure of the hybrid system embodied in Eq. (9). Thus, this approach makes lesser demands on the data set used for identification by exploiting the knowledge of the structure of the system.…”

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

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Hybrid system identification using a structural approach and its model based control: An experimental validation

Nandola

Bhartiya

2009

Nonlinear Analysis: Hybrid Systems

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“…(27) can be converted to a model that is separable and linear in the binary variables as in Eq. (9). We demonstrate this idea using an example.…”

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

Section: A Brief Review On Hybrid System Identificationmentioning

confidence: 99%

Section: Identification Of Hybrid Systems Using a Reduced Mode Approachmentioning

confidence: 99%

See 2 more Smart Citations

Hybrid system identification using a structural approach and its model based control: An experimental validation

Nandola

Bhartiya

2009

Nonlinear Analysis: Hybrid Systems

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“…In other words, instead to be solved at once, the overall identification problem is divided into several steps, each consisting in an easier problem to solve. The algorithms proposed in [14,22,35,37,39] fall into this category. The algorithm [14] has been analyzed in [59].…”

Section: Remark 31mentioning

confidence: 99%

Identification of Hybrid Systems A Tutorial

Paoletti

Juloski

Ferrari-Trecate

et al. 2007

European Journal of Control

358

271

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Nonlinear System Identification

Nelles

2001

1,117

447

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PrefaceThe goal of this book is to provide engineers and scientIsts in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. The reader will be able to apply the discussed models and methods to real problems with the necessary confidence and the awareness of potential difficulties that may arise in practice. This book is self-contained in the sense that it requires merely basic knowledge of matrix algebra, signals and systems, and statistics. Therefore, it also serves as an introduction to linear system identification and gives a practical overview on the major optimization methods used in engineering. The emphasis of this book is on an intuitive understanding of the subject and the practical application of the discussed techniques. It is not written in a theorem/proof style; rather the mathematics is kept to a minimum and the pursued ideas are illustrated by numerous figures, examples, and real-world applications.Fifteen years ago, nonlinear system identification was a field of several ad-hoc approaches, each applicable only to a very restricted class of systems. With the advent of neural networks, fuzzy models, and modern structure optimization techniques a much wider class of systems can be handled. Although one major characteristic of nonlinear systems is that almost every nonlinear system is unique, tools have been developed that allow the use of the same approach for a broad variety of systems. Certainly, a more problem-specific procedure typically promises superior performance, but from an industrial point of view a good tradeoff between development effort and performance is the decisive criterion for success. This book presents neural networks and fuzzy models together with major classical approaches in a unified framework. The strict distinction between the model architectures on the one hand (Part II) and the techniques for fitting these models to data on the other hand (Part I) tries to overcome the confusing mixture between both that is frequently encountered in the neuro and fuzzy literature. Nonlinear system identification is currently a field of very active research; many new methods will be developed and old methods will be refined. Nevertheless, I am confident that the underlying principles will continue to be valuable in the future.This book offers enough material for a two-semester course on optimization and nonlinear system identification. A higher level one-semester graduate course can focus on Chap. 7, the complete Part II, and Chaps. 17 to 21 in VI Preface Part III. For a more elementary one-semester course without prerequisites in optimization and linear system identification Chaps. 1 to 4 and 16 might be covered, while Chaps. 10, 14, 18, and 21 can be skipped. Alternatively, a course might omit the dynamic systems in Part III and instead emphasize the optimization techniques and nonlinear static modeling treated in Parts I and II. The applications presented in Part IV focus on a certain model architecture, and will convince th...

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Hinging hyperplane trees for approximation and identification

Cited by 47 publications

References 11 publications

Hybrid system identification using a structural approach and its model based control: An experimental validation

Hybrid system identification using a structural approach and its model based control: An experimental validation

Identification of Hybrid Systems A Tutorial

Nonlinear System Identification

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