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The problem addressed is the evaluation of a school and the study conducts a philosophical analysis of the normative and political presuppositions of educational evaluation. This involves the articulation of a comprehensive theory of education, integrating social and political philosophy and a vision of the good for man. This integration is achieved through an examination of the related ideas of an existential perspective on the good of the individual, the grounding of normative judgments in the human existential predicament, the primacy of practice and the importance of "democratic" communications and power relations. It is argued that educational evaluation should be grounded in a conception of man's good - in both individual and social terms, and Chapter I addresses the individual aspect. Chapter II analyses the social perspective and articUlates a democratic social principle based on equal consideration of the good of all individuals. Chapter III argues that power relations and communications processes are crucial for individuals and groups realizing their good. Chapter IV articulates principles for the shaping of power relations and communications by the basic structure of society; it addresses the reconciliation of popular political accountability, worker autonomy and cultural pluralism. Chapter V uses the preceding analyses to articulate two basic aims for education, one existential, the other social. It is argued that these aims should be elaborated in terms of the power relations and communications processes of the participants before considering specific educational objectives, curriculum,pedagogy or evaluation procedures. The overarching importance of the system of political control over education is stressed. Throughout, and especially in Chapter VI, the thesis addresses major policy issues in the political control of education, e.g., educational evaluation, curriculum control, teacher accountability, local versus central control. It also raises basic questions concerning the research programme of educational theorists and philosophers of education.

The kinematics and dynamics of many robotic systems evolve on differential manifolds, rather than strictly in Euclidean space. Lie groups, a class of differential manifold with a group structure, arise naturally in the study of rigid-body kinematics. This dissertation studies the design of state observers for systems whose state evolves on a Lie group. State observers, or state estimators, are a crucial part of the guidance, navigation, and control algorithms necessary for autonomous operation of many ground, air, and marine vehicles. The design of state observers on Lie groups is therefore a highly practical exercise. One such nonlinear observer, the gradient-based observer, has generated significant interest in the literature due to its computational simplicity and stability guarantees. The first part of this dissertation explores several applications of the gradient-based observer, including both the attitude estimation problem and the simultaneous localization and mapping (SLAM) problem. By modifying the cost function associated with the observer, several novel attitude estimators are introduced that provide faster convergence when the initial attitude error is large. Further, a SLAM algorithm with guaranteed convergence is introduced and tested in both simulation and experiment. In the second part of this dissertation, the state of the art in Lie group observer design is extended by the development of a higher-order filter on a Lie group. By analogy to the classical linear complementary filter, the proposed method can be interpreted as a nonlinear complementary filter on a Lie group. A disturbance observer that accounts for constant and harmonic disturbances in the group velocity measurements is also considered. Local asymptotic stability about the desired equilibrium point is demonstrated. In addition, an H2-optimal filter synthesis method is derived and disturbance rejection via the internal model principle is considered. A numerical example that demonstrates the desirable properties of the higher-order nonlinear complementary filter, as well as the synthesis techniques, is presented in the context of rigid-body attitude estimation.

In order to be worldwide competitive, the automotive industry is constantly challenged to produce higher quality vehicles in the shortest time possible and with the minimum costs of production. Most of the problems with new products derive from poor quality design processes, which often leads to undesired issues in a stage where changes are extremely expensive. During the preliminary design phase, designers have to deal with complex parametric problems where material and geometric characteristics of the car components are unknown. Any change in these parameters might significantly affect the global behaviour of the car. A target which is very sensitive to small variations of the parameters is the noise and vibration response of the vehicle (NVH study), which strictly depends on its global static and dynamic stiffness. In order to find the optimal solution, a lot of configurations exploring all the possible parametric combinations need to be tested. The current state of the art in the automotive design context is still based on standard numerical simulations, which are computationally very expensive when applied to this kind of multidimensional problems. As a consequence, a limited number of configurations is usually analysed, leading to suboptimal products. An alternative is represented by reduced order method (ROM) techniques, which are based on the idea that the essential behaviour of complex systems can be accurately described by simplified low-order models. This thesis proposes a novel extension of the proper generalized decomposition (PGD) method to optimize the design process of a car structure with respect to its global static and dynamic stiffness properties. In particular, the PGD method is coupled with the inertia relief (IR) technique and the inverse power method (IPM) to solve, respectively, the parametric static and dynamic stiffness analysis of an unconstrained car structure and extract its noise and vibrations properties. A main advantage is that, unlike many other ROM methods, the proposed approach does not require any pre-processing phase to collect prior knowledge of the solution. Moreover, the PGD solution is computed with only one offline computation and presents an explicit dependency on the introduced design variables. This allows to compute the solutions at a negligible computational cost and therefore opens the door to fast optimisation studies and real-time visualisations of the results in a pre-defined range of parameters. A novel algebraic approach is also proposed which allows to involve both material and complex geometric parameters, such that shape optimisation studies can be performed. In addition, the method is developed in a nonintrusive format, such that an interaction with commercial software is possible, which makes it particularly interesting for industrial applications. Finally, in order to support the designers in the decision-making process, a graphical interface app is developed which allows to visualise in real-time how changes in the design variables affect pre-defined quantities of interest.

Magnetic Resonance Imaging (MRI) scanners have become an essential tool in the medical industry due to their ability to produce high resolution images of the human body. To generate an image of the body, MRI scanners combine strong static magnetic fields with transient gradient magnetic fields. The interaction of these magnetic fields with the conducting components present in superconducting MRI scanners gives rise to an important problem in the design of new MRI scanners. The transient magnetic fields give rise to the appearance of eddy currents in conducting components. These eddy currents, in turn, result in electromagnetic stresses, which cause the conducting components to deform and vibrate. The vibrations are undesirable as they lead to a deterioration in image quality (with image artefacts) and to the generation of noise, which can cause patient discomfort. The eddy currents, in addition, lead to heat being dissipated and deposited into the cryostat, which is filled with helium in order to maintain the coils in a superconducting state. This deposition of heat can cause helium boil off and potentially result in a costly magnet quench. Understanding the mechanisms involved in the generation of these vibrations and the heat being deposited into the cryostat are, therefore, key for a successful MRI scanner design. This involves the solution of a coupled magneto-mechanical problem, which is the focus of this work. In this thesis, a new computational methodology for the solution of three-dimensional (3D) magneto-mechanical coupled problems with application to MRI scanner design is presented. To achieve this, first an accurate mathematical description of the magneto-mechanical coupling is presented, which is based on a Lagrangian formulation and the assumption of small displacements. Then, the problem is linearised using an AC-DC splitting of the fields, and a variational formulation for the solution of the linearised problem in a time-harmonic setting is presented. The problem is then discretised using high order finite elements, where a combination of hierarchical H1 and H(curl) basis functions is used. An efficient staggered algorithm for the solution of the coupled system is proposed, which combines the DC and AC stages and makes use of preconditioned iterative solvers when appropriate. This finite element methodology is then applied to a set of challenging academic and industrially relevant problems in order to demonstrate its accuracy and efficiency. This finite element methodology results in the accurate and efficient solution of the magneto-mechanical problem of interest. However, in the design stage of a new MRI scanner, this coupled problem must be solved repeatedly for varying model parameters such as frequency or material properties. Thus, even if an efficient finite element solver is available for the solution of the coupled problem, the need for these repeated simulations result in a bottleneck in terms of computational cost, which leads to an increase in design time and its associated financial implications. Therefore, in order to optimise this process, the application of Reduced Order Modelling (ROM) techniques is considered. A ROM based on the Proper Orthogonal Decomposition (POD) method is presented and applied to a series of challenging MRI configurations. The accuracy and efficiency of this ROM is demonstrated by performing comparisons against the full order or high fidelity finite element software, showing great performance in terms of computational speed-up, which has major benefits in the optimisation of the design process of new MRI scanners.