Two robust control strategies are proposed in this dissertation for a class of multi-input multi-output dynamic systems with matched and mismatched perturbations. First of all, a novel design methodology of switching variables is proposed for solving the regulation problems. A serial state transformations are needed in order to design pseudo feedback gains and adaptive mechanisms. By utilizing the pseudo control input gain embedded in each of the switching variable, the proposed controller can not only suppress the mismatched perturbations when the controlled systems are in the sliding mode, but also attain locally asymptotic stability. The design of a robust output tracking controller is presented next for solving the tracking problems. Without utilizing the information of state variable, the proposed output feedback tracking controllers are capable of driving the state tracking errors into a small bounded region whose size can be adjusted through the designed parameters, and guarantee the stability of controlled systems. These two robust control schemes are designed by means of the variable structure control technique with sliding mode and Lyapunov stability theorem. Each controller contains three parts. The first part is for eliminating measurable feedback signals. The second part is used for adjusting the convergent rate of state variables (or tracking errors) of the controlled system. The third part is an adaptive control mechanism, which is to adapt some unknown constants of the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations are not required. Several numerical examples and an application of controlling aircraft's velocity are demonstrated for showing the feasibility of the proposed control methodologies.

In this dissertation, four nonlinear controllers are proposed for different class of multi-input multi-output (MIMO) systems with matched and mismatched perturbations. All the plants to be controlled contains input uncertainty. The technique of the adaptive sliding mode control (ASMC) scheme is first introduced in order to solve the regulation or tracking problems. By applying adaptive techniques to the design of a novel sliding surface as well as to the design of sliding mode controller, one can not only enable the fulfillment of reaching mode in fi- nite time, but also suppress the mismatched perturbations when system is in the sliding mode. Secondly, the design methodology of block backstepping is proposed to solve the regulation problem in chapter 5. Some adaptive mechanisms are employed in the virtual input controller, so that the mismatched perturbations can be tackled and the proposed robust controller can guarantee stability of the controlled systems. All these control schemes are designed by means of Lyapunov stability theorem. Each robust controller contains two parts. The first part is for eliminating measurable feedback signals of the plant, and the second part is an adaptive control mechanism, which is capable of adapting some unknown constants embedded in the least upper bounds of perturbations, so that the knowledge of the least upper bounds of matched and mismatched perturbations is not required and can achieve asymptotic stability. Several numerical examples and industrial applications are demonstrated for showing the feasibility of the proposed control schemes.

Based on the Lyapunov stability theorem, an adaptive variable structure observer and a controller are proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems with unmeasurable states to solve regulation and tracking problems. In order to estimate the unmeasurable states, a design methodology of variable structure observers is presented first. Then the controller is designed so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. Some adaptive mechanisms are embedded in the sliding surface function and sliding mode controllers, so that not only the mismatched perturbations are suppressed effectively during the sliding mode, but also the information of upper bounds of some perturbations are not required. When the controlled system is the sliding mode, the stability or asymptotical stability is guaranteed. A numerical example and a practical example are given to demonstrate the feasibility of the proposed design technique.

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping controller is proposed in this thesis for a class of multi-input systems with mismatched perturbations to solve regulation problems. According to the number of block (m) in the plant to be controlled, m-1 virtual input controllers are designed from the first block to the (m-1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, so that the knowledge of the least upper bounds of mismatched perturbations is not required. The resultant control system can achieve asymptotic stability. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control scheme.

The overall objective of this thesis was to compare compensatory reactions in young and older adults following unexpected platform perturbations in the frontal and sagittal planes during gait. Eleven young (aged 18-30) and ten community-dwelling older adults (aged 65+) completed a general health questionnaire, Mini BESTest, hip strength tests, and 45 walking trials on a motion platform. The walking trials were completed in a randomized block design on a 5 m pathway that moved following right heel contact after at least two steps. Young adults had stronger hips and performed better on the Mini BESTest than older adults. Compensatory reactions (measured through gait parameters and centre of mass motion) indicated that lateral perturbations were more difficult for both groups. These measures showed that young adults were able to recover more quickly than older adults. This could be attributed to altered base of support changes that occurred immediately following platform motions. / Ontario Graduate Scholarship

<p>This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.</p>

In this thesis we study certain singular Sturm-Liouville differential expressions from an operator theoretic point of view.In particular we are interested in expressions that involve strongly singular potentials as introduced by Gesztesy and Zinchenko.On the ODE side, analyzing these expressions involves the so-called $m$-functions, often generalized Nevanlinna functions, who encapsulate spectral information of the underlying problem.The aim of the two papers in this thesis is to further understanding on the operator theory side.In the first paper, we use a model for super singular perturbations to describe a family of induced self-adjoint realizations of a perturbed Schr\"o\-din\-ger operator, i.e., with a potential of the form $c/x^2 + q$ where $q$ is a perturbation.Following the unperturbed example of Kurasov and Luger, we find that the so-called $Q$-function appearing in this approach is in good agreement with the above named $m$-function.Furthermore, we show that the operator model can be chosen such that $Q \equiv m$.In the second paper, we present a negative result in this area, namely that the supersingular perturbations model cannot be used for all strongly singular potentials.For a potential with a stronger singularity at the origin, namely $1/x^4$, we discuss the asymptotic behaviour of the Weyl solution at zero.It turns out that this function cannot be regularized appropriately and the operator model breaks down.

Coral reef environments have been degrading steadily over the last few decades. It is generally accepted now that coral reefs are one of the first marine ecosystems to show measurable perturbations driven by global warming. Some of theses perturbations are consequence of extreme stochastic disturbances like hurricanes or extreme thermal anomalies and therefore, can be easily identified using broad indicators like coral cover. These indicators are easy to measure and provide a general description of the system in question. The detection and interpretation of more subtle perturbation in coral communities is more complicated, both logistically and conceptually. However, detecting chronic perturbations at an early stage can increase significantly the success of early mitigating management strategies. This thesis focuses on the development and application of highly sensitive indicators that can detect subtle perturbations in coral communities. It also studies the ecological interpretation of mild perturbations and their effect on the future structure of coral reef environments. The mild thermal disturbance experienced by the Heron Island reef in the south of the Great Barrier Reef during the 2005-2006 summer, and an environmental gradient along the central coast of Venezuela (south Caribbean Sea), were used as models to test the sensitivity of coral reefs to mild disturbances at different organisation levels (organism, population, and community). At the organismal level my results showed that the intensity of bleaching that a colony shows during a mild thermal disturbance is affected by the morphology of the colony as well as the substrates surrounding the colony. Colonies surrounded by sand bleached more than colonies surrounded by dead coral or rubble. I propose that reef specific information on the relative cover of sand, rubble, and dead coral can improve the fine scale accuracy of bleaching predicting models. Studying the same mild thermal disturbance at Heron Island, I showed how demographic parameters of some populations are more sensitive to mild thermal disturbances than coral cover (the most widely used response variable in coral monitoring programs around the world). Furthermore, my results suggest that the response of coral populations to mild thermal disturbance is different in nature and intensity to the respond observed during extreme thermal disturbances. Some taxa like Stylophora pistillata, are highly sensitive to extreme thermal disturbances, and tend to be the first to die under these conditions. In contrast, this taxon was extremely tolerant to the mild thermal disturbance of early 2006 in comparison to other taxa identified previously as more tolerant than S. pistillata. This difference in the response of coral environments to milder more common disturbances can have great influence in the trajectory that coral reefs follow in a rapidly changing world. Finally at a community level, I demonstrated how the power to detect the effect of environmental conditions on coral environments is drastically increased when the coral host-endosymbiotic algae relationship is interpreted holistically. The percentage of the variability of the community structure that can be explained by environmental variables in the central coast of Venezuela is doubled when the unit of selection considered is the holobiont instead of the coral host or the endosymbiont independently. This approach can be crucial for the detection of subtle changes in coral communities as the frequency and intensity of disturbances increase rapidly. The increase in detection power provided by the different approaches developed in this project can both improve our understanding of the structuring role of mild disturbances in coral communities as well as help identify the effect of disturbances in an early stage before the perturbation reaches catastrophic proportions. This early identification of perturbations can be used for the development of adaptive management strategies that can increase the resistance and resilience of coral reefs in the future.

Thesis (M.S.)--Ohio University, November, 2008. / Title from PDF t.p. Includes bibliographical references.

Thesis (M.Sc. (Dept. of Mathematics, Faculty of Natural Sciences))--University of the Western Cape, 2009. / Bibliography: leaves 180-195.