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Abstract
This dissertation proposes algorithms for data-driven nonparametric identification, model reduction, and control synthesis of linear parameter-varying (LPV) models in the state-space form. We make use of kernelized machine learning (ML) and multivariate analysis (MVA) tools to develop model reduction techniques that reduce the scheduling dependency in LPV state-space (LPV-SS) models, thereby reducing exponentially, the computation complexity of LPV controller synthesis. Further, we formulate a regularized least squares support vector machine (LS-SVM)-based algorithm to identify LPV-SS models using inputs, outputs, states, and scheduling variables measurements. The technique is further extended to an instrumental variable support vector machine (IV-SVM) approach that is able to identify LPV-SS models under generic noise conditions, including cases where noise not only is colored, but is also correlated with the scheduling variables. The proposed technique seeks to obtain an unbiased estimator of the scheduling dependency functions in the face of noise-induced bias. In case the state variables are not directly measurable, a kernelized canonical correlation analysis (CCA)-based routine is proposed to estimate the states from past and future inputs, outputs, and scheduling variables measurements. This provides a non-unique estimate of the states up to a similarity transform. Once the states are estimated, previously-proposed LS-SVM-based algorithm is used in tandem with the estimated states to identify an LPV-SS model. All techniques proposed in this work exploit the use of the so-called kernel trick, giving extra degrees of freedom to choose different kernel functions and tune their associated hyper-parameters. Different applications including a robotic manipulator and chemical process models are used to verify the different algorithms developed as part of this dissertation.