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Subspace Identification for Linear Systems focuses on the theory, implementation and applications of subspace identification algorithms for linear time-invariant finite- dimensional dynamical systems. These algorithms allow for a fast, straightforward and accurate determination of linear multivariable models from measured input-output data.
The theory of subspace identification algorithms is presented in detail. Several chapters are devoted to deterministic, stochastic and combined deterministic-stochastic subspace identification algorithms. For each case, the geometric properties are stated in a main 'subspace' Theorem. Relations to existing algorithms and literature are explored, as are the interconnections between different subspace algorithms. The subspace identification theory is linked to the theory of frequency weighted model reduction, which leads to new interpretations and insights.
The implementation of subspace identification algorithms is discussed in terms of the robust and computationally efficient RQ and singular value decompositions, which are well-established algorithms from numerical linear algebra. The algorithms are implemented in combination with a whole set of classical identification algorithms, processing and validation tools in Xmath's ISID, a commercially available graphical user interface toolbox. The basic subspace algorithms in the book are also implemented in a set of Matlab files accompanying the book.
An application of ISID to an industrial glass tube manufacturing process is presented in detail, illustrating the power and user-friendliness of the subspace identification algorithms and of their implementation in ISID. The identified model allows for an optimal control of the process, leading to a significant enhancement of the production quality. The applicability of subspace identification algorithms in industry is further illustrated with the application of the Matlab files to ten practical problems. Since all necessary data and Matlab files are included, the reader can easily step through these applications, and thus get more insight in the algorithms.
Subspace Identification for Linear Systems is an important reference for all researchers in system theory, control theory, signal processing, automization, mechatronics, chemical, electrical, mechanical and aeronautical engineering.

Inhaltsverzeichnis

Frontmatter

1. Introduction, Motivation and Geometric Tools

Abstract
In this Chapter, we summarize the main contributions of the book. In Section 1.1, we first give a short motivation for dealing with the multivariable system identification problem. In Section 1.2, we discuss in some more detail the main contributions which make that subspace identification algorithms are excellent tools to work with in an industrial environment. We also provide some historical background and compare our achievements to previously existing approaches to find black box mathematical models of systems. Notes on the organization of the book and a Chapter by Chapter overview can be found in Section 1.3. Finally, Section 1.4 introduces the main geometric and statistical tools, used for the development of, and the insights in subspace identification algorithms.
Peter Van Overschee, Bart De Moor

2. Deterministic Identification

Abstract
In this Chapter we treat the subspace identification of purely deterministic systems, with no measurement nor process noise (vk ≡ wk ≡ 0 in Figure 1.4). We treat this problem for two reasons:
  • Most of the conceptual ideas and geometric concepts, which will also be used in the Chapters to follow, are introduced by means of this simple identification problem.
  • We treat the problem from a different point of view as in the literature, which makes it easier to assimilate it as a special case in the Chapters to follow. Similarities between the presented algorithm and the literature are pointed out.
Peter Van Overschee, Bart De Moor

3. Stochastic Identification

Abstract
In this Chapter, we treat the subspace identification of purely stochastic systems with no external input (uk ≡ 0). The stochastic identification problem thus consists of computing the stochastic system matrices from given output data only. We show how this can be done using geometric operations.
Peter Van Overschee, Bart De Moor

4. Combined Deterministic-Stochastic Identification

Abstract
In this Chapter we describe the subspace identification of combined deterministic-stochastic systems. For these systems, both the external input uk and the process and measurement noise wk and vk are different from zero. We use the results and ideas of the two previous Chapters to derive the main Theorem, which indicates how the combined deterministic-stochastic Kalman filter states can be extracted from the input-output data.
Peter Van Overschee, Bart De Moor

5. State Space Bases and Model Reduction

Abstract
In this Chapter we describe how the state space basis of models identified with subspace identification algorithms can be determined. It is shown that this basis is determined by the input spectrum and by user defined input and output weights (the weights introduced in the three main Theorems of the previous Chapters).
Peter Van Overschee, Bart De Moor

6. Implementation and Applications

Without Abstract
Peter Van Overschee, Bart De Moor

7. Conclusions and Open Problems

Abstract
In this book we have treated the theory, implementation and application of subspace identification algorithms for linear time-invariant systems.
Peter Van Overschee, Bart De Moor

Backmatter

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