## Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy ModelsThe 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 opti mization 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 ap proach for a broad variety of systems. |

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### Contents

23 | |

3 | 35 |

Nonlinear Local Optimization 79 | 78 |

Nonlinear Global Optimization | 113 |

Unsupervised Learning Techniques | 137 |

Model Complexity Optimization | 157 |

9 | 207 |

Advanced Aspects | 391 |

Dynamic Local Linear NeuroFuzzy Models | 601 |

Neural Networks with Internal Dynamics | 645 |

Applications of Static Models | 655 |

Applications of Dynamic Models 677 | 676 |

Applications of Advanced Methods | 709 |

Vectors and Matrices | 735 |

757 | |

779 | |

### Other editions - View all

Nonlinear System Identification: From Classical Approaches to Neural ... Oliver Nelles Limited preview - 2001 |

Nonlinear System Identification: From Classical Approaches to Neural ... Oliver Nelles No preview available - 2010 |

Nonlinear System Identification: From Classical Approaches to Neural ... Oliver Nelles No preview available - 2014 |

### Common terms and phrases

adaptation algorithm applied approximation ARMAX ARX model basis functions chosen clustering computational constraints convergence curse of dimensionality data samples data set depends dynamic models errorbars evaluation evolution strategies example extrapolation behavior filter fuzzy models fuzzy systems Gaussian genetic algorithms global global optimization gradient hidden layer input space interpolation iteration layer weights least squares linear models linear neuro-fuzzy models LLMs LOLIMOT look-up table loss function matrix membership functions method MLP network model architectures model complexity model error model output model structure MSFs NARX neural network neurons nonlinear optimization number of parameters OE model one-step prediction operating point optimization techniques parameter estimation performance polynomial prediction error prior knowledge process output RBF networks regression regressors rule consequents Sect shown in Fig signal simulation static step step responses strategy structure optimization system identification tion training data typically unsupervised learning utilized validity functions values variables variance error vector