System identification: theory for the user.

*(English)*Zbl 0615.93004This book is a valuable addition to the literature on system identification and parameter estimation. Its rigorous treatment of the main topics in the system identification field should appeal to the mathematically-minded reader. The book addresses to all of those who want to get a firm grip on the basic system identification techniques that are currently available. The book contains 17 chapters and 2 appendices, which are briefly reviewed in the following.

Part i: Systems and models

Chapter 1 introduces, in an informal way, the basic entities of an identification exercise. Chapter 2 discusses time-invariant linear systems described by impulse responses and transfer functions, and introduces some basic notions on signal spectra and description of the disturbances. Chapter 3 discusses three main applications in which a system description is useful: simulation, prediction and control. Chapter 4 introduces a general family of transfer-function and state-space models and derives a number of results on their identifiability properties. Chapter 5 contains a brief discussion about time-varying and nonlinear models.

Part ii: Methods

Chapter 6 presents several nonparametric time- and frequency-domain methods, such as transient analysis, correlation analysis, Fourier and spectral analysis. Chapter 7 describes two general methods for parameter estimation: the prediction error method (PEM) and the correlation method (CM), which are shown to contain many other estimation methods as special cases. Chapter 8 establishes the consistency and identifiability properties of PEM and CM, and Chapter 9 derives the asymptotic distributions of the parameter estimates provided by these two general methods. Chapters 10 and 11 discuss various off-line and, respectively, on-line techniques to compute the PEM and CM estimates, and analyse the main problems associated with these techniques (such as convergence, numerical accuracy and fast implementation).

Part iii: User’s choice

Chapter 12 discusses the options and objectives that a user of system identification methods may have. Chapters 13, 14 and 15 attempt to provide some general answers to such important problems as experiment design and choice of an identification criterion. Chapter 16 discusses various techniques for model structure selection and model validation, and Chapter 17 presents two identification exercises. Finally, Appendix I contains a brief discussion of some concepts from the probability theory, and Appendix II presents the basic results on linear regressions.

Part i: Systems and models

Chapter 1 introduces, in an informal way, the basic entities of an identification exercise. Chapter 2 discusses time-invariant linear systems described by impulse responses and transfer functions, and introduces some basic notions on signal spectra and description of the disturbances. Chapter 3 discusses three main applications in which a system description is useful: simulation, prediction and control. Chapter 4 introduces a general family of transfer-function and state-space models and derives a number of results on their identifiability properties. Chapter 5 contains a brief discussion about time-varying and nonlinear models.

Part ii: Methods

Chapter 6 presents several nonparametric time- and frequency-domain methods, such as transient analysis, correlation analysis, Fourier and spectral analysis. Chapter 7 describes two general methods for parameter estimation: the prediction error method (PEM) and the correlation method (CM), which are shown to contain many other estimation methods as special cases. Chapter 8 establishes the consistency and identifiability properties of PEM and CM, and Chapter 9 derives the asymptotic distributions of the parameter estimates provided by these two general methods. Chapters 10 and 11 discuss various off-line and, respectively, on-line techniques to compute the PEM and CM estimates, and analyse the main problems associated with these techniques (such as convergence, numerical accuracy and fast implementation).

Part iii: User’s choice

Chapter 12 discusses the options and objectives that a user of system identification methods may have. Chapters 13, 14 and 15 attempt to provide some general answers to such important problems as experiment design and choice of an identification criterion. Chapter 16 discusses various techniques for model structure selection and model validation, and Chapter 17 presents two identification exercises. Finally, Appendix I contains a brief discussion of some concepts from the probability theory, and Appendix II presents the basic results on linear regressions.

Reviewer: P.Stoica

##### MSC:

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

93B30 | System identification |

93E12 | Identification in stochastic control theory |

62F12 | Asymptotic properties of parametric estimators |

62G05 | Nonparametric estimation |

62J05 | Linear regression; mixed models |

62Kxx | Design of statistical experiments |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M15 | Inference from stochastic processes and spectral analysis |

62M20 | Inference from stochastic processes and prediction |

93C05 | Linear systems in control theory |

93E10 | Estimation and detection in stochastic control theory |

93E25 | Computational methods in stochastic control (MSC2010) |