| System identification is the field of mathematical modeling of dynamic systems from experimental data. Generally, the methods of identification can be classified into two main classes: the prediction error methods (PEM) and subspace methods. While PEM methods have better statistical properties, subspace methods are known to have remarkable advantages such as being numerically robust, non-iterative, and suitable for multi-input multi-output (MIMO) systems. In this thesis, two problems are studied within the framework of subspace identification. The first is the incorporation of prior system information in subspace identification and the second is the extension of the method to two-dimensional (2-D) systems.;In many situations in system identification, the data available are not informative enough due to highly noise-corrupted measurements or lack of sufficient input excitation. This may lead to the identification of low-quality models. To improve the quality of identified models, some a priori known information, from process operator experience or first principles, can be incorporated in the identification process. The prior information can include stability, dc gain, time constant, frequency response, and system structure. In this work, based on the interpretation of subspace identification as a multistep ahead predictor, it is proposed to combine the equality constrained least-squares (CLS) with subspace identification to incorporate prior information. This yields computationally efficient alternatives to the available nonlinear optimization-based methods. Using the proposed algorithms, different types of prior information are incorporated in subspace identification leading to more accurate models. Furthermore, a recursive CLS-based subspace algorithm is developed so that the method can be used for online applications and time-varying systems.;The second part of the thesis is dedicated to 2-D systems in which the variables vary along two dimensions, which may be time and space or two spatial variables. To list a few, batch processes, image processing applications, and discretized partial differential equations modeling distributed parameter systems can be treated as 2-D systems. In this work, extending the ideas of subspace identification to 2-D state-space systems is investigated. In particular, subspace identification is used to identify a special class of 2-D systems termed causal, recursive, and separable-in-denominator (CRSD) filters which are usually used in image processing. The algorithm is based upon a recently proposed formulation which makes use of all 2-D input-output deterministic data to identify CRSD models in Roesser form. The applicability of the algorithm is validated with the aid of a simulation example. |
