In this dissertation, we present a H-infinity based multivariable control design methodology that can be used to systematically address design specifications at distinct feedback loop-breaking points. It is well understood that for multivariable systems, obtaining good/acceptable closed loop properties at one loop-breaking point does not mean the same at another. This is especially true for multivariable systems that are ill-conditioned (having high condition number and/or relative gain array and/or scaled condition number). We analyze the tradeoffs involved in shaping closed loop properties at these distinct loop-breaking points and illustrate through examples the existence of pareto optimal points associated with them. Further, we study the limitations and tradeoffs associated with shaping the properties in the presence of right half plane poles/zeros, limited available bandwidth and peak time-domain constraints. To address the above tradeoffs, we present a methodology for designing multiobjective constrained H-infinity based controllers, called Generalized Mixed Sensitivity (GMS), to effectively and efficiently shape properties at distinct loop-breaking points. The methodology accommodates a broad class of convex frequency- and time-domain design specifications. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera parameterization that transforms the nonlinear problem in the controller to an affine one in the Youla et al. parameter. Basis parameters that result in efficient approximation (using lesser number of basis terms) of the infinite-dimensional parameter are studied. Three state-of-the-art subgradient-based non-differentiable constrained convex optimization solvers, namely Analytic Center Cutting Plane Method (ACCPM), Kelley's CPM and SolvOpt are implemented and compared.

The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency.

Multi-label learning, which deals with data associated with multiple labels simultaneously, is ubiquitous in real-world applications. To overcome the curse of dimensionality in multi-label learning, in this thesis I study multi-label dimensionality reduction, which extracts a small number of features by removing the irrelevant, redundant, and noisy information while considering the correlation among different labels in multi-label learning. Specifically, I propose Hypergraph Spectral Learning (HSL) to perform dimensionality reduction for multi-label data by exploiting correlations among different labels using a hypergraph. The regularization effect on the classical dimensionality reduction algorithm known as Canonical Correlation Analysis (CCA) is elucidated in this thesis. The relationship between CCA and Orthonormalized Partial Least Squares (OPLS) is also investigated. To perform dimensionality reduction efficiently for large-scale problems, two efficient implementations are proposed for a class of dimensionality reduction algorithms, including canonical correlation analysis, orthonormalized partial least squares, linear discriminant analysis, and hypergraph spectral learning. The first approach is a direct least squares approach which allows the use of different regularization penalties, but is applicable under a certain assumption; the second one is a two-stage approach which can be applied in the regularization setting without any assumption. Furthermore, an online implementation for the same class of dimensionality reduction algorithms is proposed when the data comes sequentially. A Matlab toolbox for multi-label dimensionality reduction has been developed and released. The proposed algorithms have been applied successfully in the Drosophila gene expression pattern image annotation. The experimental results on some benchmark data sets in multi-label learning also demonstrate the effectiveness and efficiency of the proposed algorithms.