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A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, April 2016 / A Rotary Wing Unmanned Aerial Vehicle (RW UAV) as a platform and its payload consisting of sophisticated sensors would be costly items. Hence, a RW UAV in the 500 kg class designed to fulfil a number of missions would represent a considerable capital outlay for any customer. Therefore, in the event of an engine failure, a means should be provided to get the craft safely back on the ground without incurring damage or causing danger to the surrounding area. The aim of the study was to design a controller for autorotative landing of a RW UAV in the event of engine failure. In order to design a controller for autorotative landing, an acceleration model was used obtained from a study by Stanford University. FLTSIM helicopter flight simulation package yielded necessary RW UAV response data for the autorotation regimes. The response data was utilized in identifying the unknown parameters in the acceleration model. A Differential Dynamic Programming (DDP) control algorithm was designed to compute the main and tail rotor collective pitch and the longitudinal and lateral cyclic pitch control inputs to safely land the craft. The results obtained were compared to the FLTSIM flight simulation response data. It was noted that the mathematical model could not accurately model the pitch dynamics. The main rotor dynamics were modelled satisfactorily and which are important in autorotation because without power from the engine, the energy in main rotor is critical in a successful execution of an autorotative landing. Stanford University designed a controller for RC helicopter, XCell Tempest, which was deemed successful. However, the DDP controller was designed for autonomous autorotative landing of RW UAV weighing 560 kg, following engine failure. The DDP controller has the ability to control the RW UAV in an autorotation landing but the study should be taken further to improve certain aspects such as the pitch dynamics and which can possibly be achieved through online parameter estimation. / MT 2017

Merton’s Optimal Investment-Consumption Problem is a classic optimization problem in finance. It aims to find the optimal controls for a portfolio with both risky and risk-less assets, inorder to maximize an investor’s utility function. One of the controls is the optimal allocationof wealth invested in a risky asset and the other control is the consumption rate. The problemis solved by using Dynamic Programming and the related Hamilton-Jacobi-Bellman equation.One of the disadvantages of the original problem is the consideration of constant volatility. Inthis thesis, we extend Merton’s problem considering the Grzelak-Oosterlee-Van Veeren modelthat describes the dynamics of a risky asset with stochastic volatility and stochastic interestrate. We derive the related Hamilton-Jacobi-Bellman for Merton’s problem considering theGrzelak-Oosterlee-Van Veeren model. We simulate the controls from Merton’s problem intwo different cases, one case where the volatility and interest rate are stochastic, following theGOVV-model. In the other case, the volatility and interest rate are assumed to be constant, asin Merton’s problem. The results obtained from simulations show that the case with stochasticvolatility and interest gave the same results as the case where the volatility and the interest ratewere assumed to be constant.

Decision diagrams have recently emerged as a promising approach for difficult scheduling problems, along with other challenging discrete optimization problems. Decision diagrams can offer a compact representation of the solution space, and has the ability to capture complex constraints that are hard to model or express in other techniques. This thesis explores two standard construction methods for relaxed decision diagrams, top-down construction and incremental refinement. The techniques are compared on their ability to handle scheduling problems with multiple time windows and precedence constraints. The construction methods are evaluated on several metrics, including generated bound, execution time, and the size of the diagram, on instances of the problem with up to 200 tasks. The results show that incremental refinement generates smaller diagrams with good bounds when compared to the top-down compilation algorithm; the reduction in diagram size and increase in bounds for incremental refinement comes at the expense of execution time compared to top-down compilation.

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The National Library of Medicine (NLM), an institute in the National Institutes of Health (NIH), maintains a collection of 17,000 digitized spine X-ray images obtained from the second National Health and Nutrition Examination Survey (NHANES II). Research effort has been devoted to develop a web-accessible retrieval system that allows retrieval of images from the NHANES II database on relevant and frequently found pathologies. A comprehensive and successful image retrieval system requires effective image representation and matching methods, relevance feedback algorithms to incorporate user opinions, and efficient indexing schemes for fast access to image databases. This dissertation studies and develops approaches for all of the above areas within the context of content-Based Image Retrieval (CBIR) of spine X-ray images from the NHANES II collection. Shape is an important characteristic for describing pertinent pathologies in various types of medical images, including spine X-ray images. Retrieving images with shapes similar to a specific user query can be useful for finding pathologies exhibited in images in large survey collections. In this work, vertebral outlines are extracted for image retrieval using shape matching methods to detect the presence of anterior osteophytes. The Multiple Open Triangle (MOT) shape representation method is proposed for partial shape matching (PSM), and a Corner-Guided Dynamic Programming (DP) strategy is developed to search partial intervals for matching comparison based on a 9-point model marked by a board-certified radiologist. The MOT method demonstrates higher retrieval accuracy compared to other approaches and the retrieval speed is improved significantly through the use of Corner-Guided DP. Computer-calculated low-level image features fall short when imitating high-level human visual perception. Relevance Feedback (RF) attempts to bridge the gap between the two by analyzing and employing user feedback. The need for overcoming this gap is more evident in medical image retrieval. Existing RF approaches are analyzed and a weight-updating formula for RF is developed. A hybrid retrieval approach is proposed that utilizes both CBIR with RF and RF history. This hybrid approach uses short-term memory to store the feedback history, which contributes to the retrieval results and helps select images for user feedback. An approximate 20% average increase in retrieval recall percentage is achieved within two RF iterations. Efficient indexing methods are desired for fast database access. An agglomerative clustering algorithm is adopted to pre-index the database based on pre-calculated pair-wise distances between indexed parts. Retrieval with this pre-indexing procedure is shown to offer faster retrieval and maintain a comparable recall percentage.

Many applications use multiple cameras to simultaneously capture imagery of a scene from different vantage points on a rigid, moving camera system over time. Multiple cameras often provide unique viewing angles but also additional levels of detail of a scene at different spatio-temporal resolutions. However, in order to benefit from this added information the sources must be temporally aligned. As a result of cost and physical limitations it is often impractical to synchronize these sources via an external clock device. Most methods attempt synchronization through the recovery of a constant scale factor and offset with respect to time. This limits the generality of such alignment solutions. We present an unsupervised method that utilizes a content-based clustering mechanism in order to temporally align multiple non-synchronized image sequences of different and varying spatio-temporal resolutions. We show that the use of temporal constraints and dynamic programming adds robustness to changes in capture rates, field of view, and resolution.