Item – Theses Canada

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OCLC number
1019465910
Link(s) to full text
LAC copy
Author
Rasouli, Mohammad.
Title
Term Selection for Nonlinear Systems and Convexity Analysis of the Hammerstein Model.
Degree
Ph. D. -- University of Calgary, 2011
Publisher
Ottawa : Library and Archives Canada = Bibliothèque et Archives Canada, 2012.
Description
1 online resource
Notes
Includes bibliographical references.
Abstract
<?Pub Inc> The convexity of an optimization problem is an important property that guarantees the global and local minima are identical. Thus, formulating system identification problems as convex optimizations may drastically simplify their solution, for example, by eliminating the need to find a good starting point, since convergence to the global optimum is guaranteed. This research investigated two applications of convex optimization to system identification problems. A key step in formulating a system identification problem is determining the structure of the model that approximates a real system. Thus, a term selection approach is proposed for nonlinear system model structure selection based on the Least absolute shrinkage and selection operator (Lasso) that has been developed for linear regression models. Lasso, in a linear regression context, results in a constrained optimization that can be recast as a convex optimization. Thus, the main idea involves incorporating the Lasso constraint in an iterative solution approach. The proposed method is then modified so that it is applicable to systems with parameters that represent physical quantities. This method is applied to experimental and simulated data collected from an induction motor as well as simulated data for a Hammerstein model to demonstrate the steps of the proposed method. The second problem that is addressed is the quasiconvexity of the Hammerstein model identification problem with respect to its parameters. In comparison to the work done to date, a much less restrictive condition under which the optimization problem will be quasiconvex is derived. Along that direction, convexity of the Hammerstein model identification is proven for a constrained optimization formulation with an Independent and Identically Distributed (IID) input. The numerical results presented give more insights to the problem and the methodology taken for the solution.
ISBN
9780494818527
0494818522