Nonlinear optimization approaches to H2-norm based LPV modelling and control
Sammanfattning: To be able to analyze certain classes of non-linear systems, it is necessary to try to represent them as linear parameter varying systems or even as linear fractional representations. For linear parameter varying systems and linear fractional representations of systems there exists many advanced analysis methods such as IQC-analysis and μ-analysis. This means that an important intermediate step in all this is to generate a linear parameter varying model that describes these non-linear system sufficiently well.The first contribution in this thesis is a novel method that tries, through nonlinear programming and a quasi-Newton framework, to generate a linear parameter varying model given linearized state space models. The idea behind the method is to preserve the input-output relations of the given linearized systems and, in an H2-measure, find the best one. To handle uncertainties in data an extension of the proposed method is presented. It is shown how the computationally hard robust optimization approach to the uncertain case can be approximated using a problem specific regularization.The second contribution in this thesis is a method for synthesizing output-feedback H2 controllers of arbitrary order. This method also uses non-linear programming and a quasi-Newton framework to achieve this. One great benefit with this method is that it also possible to impose structure in the controller.Both of the methods described above tries to solve non-linear and non-convex problems, which means that the problem of finding a good initial estimate is an important problem. For both methods an initialization procedure is proposed to try to find an initial estimate.The methods are evaluated on several examples and show promising results. A contributing factor is that significant effort has been spent on utilizing the structure of the optimization problems to make the methods efficient.
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