Nonlinear Identification: Extended State Affine Systems
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The aim of this thesis is to investigate the nonlinear identification using Extended State Affine Systems (ESA systems). In the first part of this thesis, the basics of the ESA systems are de-scribed. Furthermore, it is shown how data equations can be obtained for different approxima-tion approaches. The author focuses the exact identification and its approximations. Also, the notation of the system class is described.
Another part is the development of regularization methods. To solve the identification prob-lem it is necessary to solve an inverse problem. In the case of ESA, it the problem is usually ill posed. Using the different regularization methods the solution of the inverse problem can be found in a numerically more stable way. Three different groups of regularization methods are developed. First, the Tikhonov regularization methods; second, the truncation regulariza-tion methods and finally the iterative methods. For each group, different possibilities for pa-rameter choice rules are described. At the end of this part, the presented methods are com-pared and evaluated. Hereby, the relevance of the Kernel method is investigated.
The last part of the thesis deals with the comparison of the ESA identification with other iden-tification methods. Therefore, two other methods are used: the ARMAX identification and the Neural Networks. Under these conditions, different examples will be investigated. Several validation values are introduced and defined to compare the various methods on the examples. The extrapolation behaviour of the different methods is important. Furthermore, the examples are chosen in a way using a linear, a weak nonlinear and a nonlinear example. Also, the nonlinear example is compared to results in the literature.
Finally, advantages and disadvantages of the ESA identification are stated.