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Dynamic system identification. Experiment design and data analysis. (English) Zbl 0578.93060
Mathematics in Science and Engineering, 136. New York - London: Academic Press (Harcourt Brace Jovanovich, Publishers). X, 291 p. (1977).
This book is devoted to the process of building mathematical models of physical systems by using experimental data. The authors attempt to present a state-of-the-art description of design and analysis of experiments for dynamical systems and include many results not previously published in book form.
There are seven chapters with a set of problems and their solutions in the book. In Chapter 1 the authors review a number of key results and establish notation from probability theory, point estimation theory, sufficient statistics, hypothesis testing and Bayesian decision theory; they also discuss some commonly used estimators: least squares (LS), maximum likelihood (ML), maximum a posteriori (MAP), minimum risk (MR), minimax entropy (ME). In Chapter 2 the authors discuss the simplest LS estimation procedure and study the properties of the estimator both with and without the assumption of Gaussian modelling errors. They also describe briefly a robust numerical procedure for solving LS problems. Chapter 3 introduces the ML approach and considers a more general class of problems. Chapter 4 deals with the development of mathematical models describing the input/output behavior of deterministic and stochastic dynamical systems. The parameter estimation procedures described in the first three chapters are extended for this purpose.
In Chapter 5 the authors turn to the problem of estimating the parameters within a model of a dynamical system, using observations made on the input/output over some specified time period. The algorithms for these models are direct analogues of the algorithms from Chapters 2 and 3. The authors discuss asymptotic properties of the resulting estimators and the problem of closed loop estimation. In Chapter 6 the authors study the design of experimental conditions so that an experiment will be maximally informative. $$\{$$ They consider the question of achievable accuracy in identification.$$\}$$ Finally, in Chapter 7 recursive estimation and experimental design techniques are described.
The authors’ approach to the problem is basically of a statistical nature. They assume that the reader will have met many of these results previously, but for completeness they summarize them in the appendices. The authors intend that the book be useful as a starting point for researchers and as a guide for persons who wish to apply identification methods in practice.

MSC:
 93E12 Identification in stochastic control theory 93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 62K05 Optimal statistical designs 62C10 Bayesian problems; characterization of Bayes procedures 62F10 Point estimation 62F35 Robustness and adaptive procedures (parametric inference) 93E10 Estimation and detection in stochastic control theory 93E25 Computational methods in stochastic control (MSC2010)