This thesis is concerned with the choice of the uncertainty structure in robust control problems. This choice affects the optimization carried out to obtain a robust feedback controller, and determines how robust a feedback loop will be to discrepancies in the parameters or dynamics of the plant model. Firstly, it presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for several commonly used uncertainty structures for linear time-invariant systems (additive, multiplicative, inverse multiplicative, inverse additive, right coprime factor uncertainty).Secondly, the thesis discusses the robust stabilization problem for linear plants with a coprime factor uncertainty structure where the coprime factors of the plant are not necessarily normalized. The problem considered here is a generalization of the normalized coprime factor robust stabilization problem. It is shown that the minimum of the ratio of (non-normalized) coprime factor distance over (non-normalized) coprime factor robust stability margin, termed the robustness ratio, is an important bound in robust stability and performance results. A synthesis method is proposed which maintains a lower bound on the normalized coprimefactor robust stability margin (as a proxy for nominal performance) while also robustly stabilizing a particular perturbed plant, potentially far outside a normalized coprime factor neighbourhood of the nominal plant. The coprime factor synthesis problem is also considered in a state-space framework. It is shown that it admits a simple and intuitive controller implementation in observer form. Via the solution of one Riccati equation, an optimally robust observer gain L can be obtained for any state-feedback matrix F. One particular method for obtaining a suitable F is also proposed, ensuring that the feedback loop is particularly robust to uncertain lightly damped poles and zeros.

This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory --- that of observing the system and then applying feedback --- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and disturbance, and is seen to have several applications in quantum information. In order to characterize the optimality of our tracking procedures, some figure-of-merit has to be specified. Naturally, distance measures for quantum states are the ideal candidates for this purpose. We investigated several possibilities, and found that there is usually a compromise between physically motivated and mathematically tractable measures. We also introduce an alternative to the Uhlmann-Jozsa fidelity for mixed quantum states, which besides reproducing a number of properties of the standard fidelity, is especially attractive because it is simpler to compute. We employ some ideas of convex analysis to construct optimal control schemes analytically. In particular, we obtain analytic forms of optimal controllers for stabilizing and tracking any pair of states of a single-qubit. In the case of stabilization, we find that feedback control is always useful, but because of the trade-off between information gain and disturbance, somewhat different from the type of feedback performed in classical systems. In the case of tracking, we find that feedback is not always useful, meaning that depending on the choice of states one wants to achieve, it may be better not to introduce any noise by the application of quantum measurements. We also demonstrate that our optimal controllers are immediately applicable in several quantum information applications such as state-dependent cloning, purification, stabilization, and discrimination. In all of these cases, we were able to recover and extend previously known optimal strategies and performances. Finally we show how optimal single-step control schemes can be concatenated to provide multi-step strategies that usually over-perform optimal control protocols based on a single interaction between the controller and the system.

This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory --- that of observing the system and then applying feedback --- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and disturbance, and is seen to have several applications in quantum information. In order to characterize the optimality of our tracking procedures, some figure-of-merit has to be specified. Naturally, distance measures for quantum states are the ideal candidates for this purpose. We investigated several possibilities, and found that there is usually a compromise between physically motivated and mathematically tractable measures. We also introduce an alternative to the Uhlmann-Jozsa fidelity for mixed quantum states, which besides reproducing a number of properties of the standard fidelity, is especially attractive because it is simpler to compute. We employ some ideas of convex analysis to construct optimal control schemes analytically. In particular, we obtain analytic forms of optimal controllers for stabilizing and tracking any pair of states of a single-qubit. In the case of stabilization, we find that feedback control is always useful, but because of the trade-off between information gain and disturbance, somewhat different from the type of feedback performed in classical systems. In the case of tracking, we find that feedback is not always useful, meaning that depending on the choice of states one wants to achieve, it may be better not to introduce any noise by the application of quantum measurements. We also demonstrate that our optimal controllers are immediately applicable in several quantum information applications such as state-dependent cloning, purification, stabilization, and discrimination. In all of these cases, we were able to recover and extend previously known optimal strategies and performances. Finally we show how optimal single-step control schemes can be concatenated to provide multi-step strategies that usually over-perform optimal control protocols based on a single interaction between the controller and the system.

This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory --- that of observing the system and then applying feedback --- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and disturbance, and is seen to have several applications in quantum information. In order to characterize the optimality of our tracking procedures, some figure-of-merit has to be specified. Naturally, distance measures for quantum states are the ideal candidates for this purpose. We investigated several possibilities, and found that there is usually a compromise between physically motivated and mathematically tractable measures. We also introduce an alternative to the Uhlmann-Jozsa fidelity for mixed quantum states, which besides reproducing a number of properties of the standard fidelity, is especially attractive because it is simpler to compute. We employ some ideas of convex analysis to construct optimal control schemes analytically. In particular, we obtain analytic forms of optimal controllers for stabilizing and tracking any pair of states of a single-qubit. In the case of stabilization, we find that feedback control is always useful, but because of the trade-off between information gain and disturbance, somewhat different from the type of feedback performed in classical systems. In the case of tracking, we find that feedback is not always useful, meaning that depending on the choice of states one wants to achieve, it may be better not to introduce any noise by the application of quantum measurements. We also demonstrate that our optimal controllers are immediately applicable in several quantum information applications such as state-dependent cloning, purification, stabilization, and discrimination. In all of these cases, we were able to recover and extend previously known optimal strategies and performances. Finally we show how optimal single-step control schemes can be concatenated to provide multi-step strategies that usually over-perform optimal control protocols based on a single interaction between the controller and the system.

This dissertation explores a unique automated approach to map one phoneme set to another, based on the acoustic distances between the individual phonemes. Although the focus of this investigation is on cross-language applications, this automated approach can be extended to same-language but different-database applications as well. The main goal of this investigation is to be able to use the data of a source language, to train the initial acoustic models of a target language for which very little speech data may be available. To do this, an automatic technique for mapping the phonemes of the two data sets must be found. Using this technique, it would be possible to accelerate the development of a speech recognition system for a new language. The current research in the cross-language speech recognition field has focused on manual methods to map phonemes. This investigation has considered an English-to-Afrikaans phoneme mapping, as well as an Afrikaans-to-English phoneme mapping. This has been previously applied to these language instances, but utilising manual phoneme mapping methods. To determine the best phoneme mapping, different acoustic distance measures are compared. The distance measures that are considered are the Kullback-Leibler measure, the Bhattacharyya distance metric, the Mahalanobis measure, the Euclidean measure, the L2 metric and the Jeffreys-Matusita distance. The distance measures are tested by comparing the cross-database recognition results obtained on phoneme models created from the TIMIT speech corpus and a locally-compiled South African SUN Speech database. By selecting the most appropriate distance measure, an automated procedure to map phonemes from the source language to the target language can be done. The best distance measure for the mapping gives recognition rates comparable to a manual mapping process undertaken by a phonetic expert. This study also investigates the effect of the number of Gaussian mixture components on the mapping and on the speech recognition system’s performance. The results indicate that the recogniser’s performance increases up to a limit as the number of mixtures increase. In addition, this study has explored the effect of excluding the Mel Frequency delta and acceleration cepstral coefficients. It is found that the inclusion of these temporal features help improve the mapping and the recognition system’s phoneme recognition rate. Experiments are also carried out to determine the impact of the number of HMM recogniser states. It is found that single-state HMMs deliver the optimum cross-language phoneme recognition results. After having done the mapping, speaker adaptation strategies are applied on the recognisers to improve their target-language performance. The models of a fully trained speech recogniser in a source language are adapted to target-language models using Maximum Likelihood Linear Regression (MLLR) followed by Maximum A Posteriori (MAP) techniques. Embedded Baum-Welch re-estimation is used to further adapt the models to the target language. These techniques result in a considerable improvement in the phoneme recognition rate. Although a combination of MLLR and MAP techniques have been used previously in speech adaptation studies, the combination of MLLR, MAP and EBWR in cross-language speech recognition is a unique contribution of this study. Finally, a data pooling technique is applied to build a new recogniser using the automatically mapped phonemes from the target language as well as the source language phonemes. This new recogniser demonstrates moderate bilingual phoneme recognition capabilities. The bilingual recogniser is then further adapted to the target language using MAP and embedded Baum-Welch re-estimation techniques. This combination of adaptation techniques together with the data pooling strategy is uniquely applied in the field of cross-language recognition. The results obtained using this technique outperform all other techniques tested in terms of phoneme recognition rates, although it requires a considerably more time consuming training process. It displays only slightly poorer phoneme recognition than the recognisers trained and tested on the same language database. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

Scientific phenomena are often studied through collections of related scalar fields such as data generated by simulation experiments that are parameter or time dependent . Exploration of such data requires robust measures to compare them in a feature aware and intuitive manner. Topological data analysis is a growing area that has had success in analyzing and visualizing scalar fields in a feature aware manner based on the topological features. Various data structures such as contour and merge trees, Morse-Smale complexes and extremum graphs have been developed to study scalar fields. The extremum graph is a topological data structure based on either the maxima or the minima of a scalar field. It preserves local geometrical structure by maintaining relative locations of extrema and their neighborhoods. It provides a suitable abstraction to study a collection of datasets where features are expressed by descending or ascending manifolds and their proximity is of importance. In this thesis, we design a measure to understand the similarity between scalar fields based on the extremum graph abstraction. We propose a topological structure called the complete extremum graph and define a distance measure on it that compares scalar fields in a feature aware manner. We design an algorithm for computing the distance and show its applications in analyzing time varying data such as understanding periodicity, feature correspondence and tracking, and identifying key frames.

In the automotive sector, engine testing generates vast data volumes that are mainly beneficial to requesting engineers. However, these tests are often not revisited for further analysis due to inconsistent data quality and a lack of structured assessment methods. Moreover, the absence of a tailored knowledge discovery process hinders effective preprocessing, transformation, analytics, and visualization of data, restricting the potential for historical data insights. Another challenge arises from the heterogeneous nature of test structures, resulting in varying measurements, data types, and contextual requirements across different engine test datasets. This thesis aims to overcome these obstacles by introducing a specialized knowledge discovery approach for the distinctive Multiple Inconsistent Heterogeneous Data (MIHData) format characteristic of engine testing. The proposed methods include adapting data quality assessment and reporting, classifying engine types through compositional features, employing modified dendrogram similarity measures for classification, performing customized feature extraction, transformation, and structuring, generating and manipulating synthetic images to enhance data visualization, and applying adapted list-based indexing for multivariate engine test summary data searches. The thesis demonstrates how these techniques enable exploratory analysis, visualization, and classification, presenting a practical framework to extract meaningful insights from historical data within the engineering domain. The ultimate objective is to facilitate the reuse of past data resources, contributing to informed decision-making processes and enhancing comprehension within the automotive industry. Through its focus on data quality, heterogeneity, and knowledge discovery, this research establishes a foundation for optimized utilization of historical Engine Test Data (ETD) for improved insights. / Soroptimist International Bradford