With the advent of telecommunication technology, the need to transport multimedia content is increasing day by day. Successful video transmission over the wireless network faces a lot of challenges because of the limited resource and error prone nature of the wireless environment. To deal with these two challenges, not only the video needs to be compressed very efficiently but also the compression scheme needs to provide some error resilient features to deal with the high packet loss probability. In this thesis, we have worked with the H.264/ Advanced Video Coding (AVC) video compression standard since this is the most recent and most efficient video compression scheme. Also H.264 provides novel error resilient features e.g. slicing of the frame, Flexible Macroblock Ordering (FMO), data partitioning etc. In this thesis, we investigate how to utilize the error resilient schemes of H.264 to ensure a good quality picture at the receiving end. In the first part of the thesis, we find the optimum slice size that will enhance the quality of video transmission in a 3G environment. In the second part, we jointly optimize the data partitioning property and partial reliability extension property of the new transport layer protocol, Stream Control Transmission Protocol (SCTP). In the third and last part, we focus more on the network layer issues. We obtain the optimum point of application layer Forward Error Correction (FEC) and Medium Access Control (MAC) layer retransmission in a capacity constrained network. We assume that the bit rate assigned for the video application is more than the video bit rate so that the extra capacity available can be used for error correction. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Legged locomotion has several interesting challenges that need to be addressed, such as the ability of dynamically walk over rough terrain like stairs or stepping stones, as well as the ability to adapt to unexpected changes in the environment and the dynamic model of the robot. This thesis is driven towards solving these challenges and makes contributions on theoretical and experimental aspects to address: dynamic walking, model uncertainty, and rough terrain. On the theoretical front, we introduce and develop a unified robust and adaptive control framework that enables the ability to enforce stability and safety-critical constraints arising from robotic motion tasks under a high level of model uncertainty. We also present a novel method of walking gait optimization and gait library to address the challenge of dynamic robotic walking over stochastically generated stepping stones with significant variations in step length and step height, and where the robot has knowledge about the location of the next discrete foothold only one step ahead. On the experimental front, our proposed methods are successfully validated on ATRIAS, an underactuated, human-scale bipedal robot. In particular, experimental demonstrations illustrate our controller being able to dynamically walk at 0.6 m/s over terrain with step length variation of 23 to 78 cm, as well as simultaneous variation in step length and step height of 35 to 60cm and -22 to 22cm respectively. In addition to that, we also successfully implemented our proposed adaptive controller on the robot, which enables the ability to carry an unknown load up to 68 lb (31 kg) while maintaining very small tracking errors of about 0.01 deg (0.0017 rad) at all joints. To be more specific, we firstly develop robust control Lyapunov function based quadratic program (CLFQP) controller and L1 adaptive control to handle model uncertainty for bipedal robots. An application is dynamic walking while carrying an unknown load. The robust CLF-QP controller can guarantee robustness via a quadratic program that can be extended further to achieve robust safety-critical control. The L1 adaptive control can estimate and adapt to the presence of model uncertainty in the system dynamics. We then present a novel methodology to achieve dynamic walking for underactuated and hybrid dynamcal bipedal robots subject to safety-critical constraints. The proposed controller is based on the combination of control Barrier functions (CBFs) and control Lyapunov functions (CLFs) implemented as a state-based online quadratic program to achieve stability under input and state constraints. The main contribution of this work is the control design to enable stable dynamical bipedal walking subject to strict safety constraints that arise due to walking over a terrain with randomly generated discrete footholds. We next introduce Exponential Control Barrier Functions (ECBFs) as means to enforce high relativedegree safety constraints for nonlinear systems. We also develop a systematic design method that enables creating the Exponential CBFs for nonlinear systems making use of tools from linear control theory. Our method creates a smooth boundary for the safety set via an exponential function, therefore is called Exponential CBFs. Similar to exponential stability and linear control, the exponential boundary of our proposed method helps to have smoother control inputs and guarantee the robustness under model uncertainty. The proposed control design is numerically validated on a relative degree 4 nonlinear system (the two-link pendulum with elastic actuators and experimentally validated on a relative degree 6 linear system (the serial cart-spring system). Thanks to these advantages of Exponential CBFs, we then can apply the method to the problem of 3D dynamic walking with varied step length and step width as well as dynamic walking on time-varying stepping stones. For the work of using CBF for stepping stones, we use only one nominal walking gait. Therefore the range of step length variation is limited ([25 : 60](cm)). In order to improve the performance, we incorporate CBF with gait library and increase the step length range significantly ([10 : 100](cm)). While handling physical constraints and step transition via CBFs appears to work well, these constraints often become active at step switching. In order to resolve this issue, we introduce the approach of 2-step periodic walking. This method not only gives better step transitions but also offers a solution for the problem of changing both step length and step height. Experimental validation on the real robot was also successful for the problem of dynamic walking on stepping stones with step lengths varied within [23 : 78](cm) and average walking speed of 0:6(m=s). In order to address the problems of robust control and safety-critical control in a unified control framework, we present a novel method of optimal robust control through a quadratic program that offers tracking stability while subject to input and state-based constraints as well as safety-critical constraints for nonlinear dynamical robotic systems under significant model uncertainty. The proposed method formulates robust control Lyapunov and barrier functions to provide guarantees of stability and safety in the presence of model uncertainty. We evaluate our proposed control design on different applications ranging from a single-link pendulum to dynamic walking of bipedal robot subject to contact force constraints as well as safety-critical precise foot placements on stepping stones, all while subject to significant model uncertainty. We conduct preliminary experimental validation of the proposed controller on a rectilinear spring-cart system under different types of model uncertainty and perturbations. To solve this problem, we also present another solution of adaptive CBF-CLF controller, that enables the ability to adapt to the effect of model uncertainty to maintain both stability and safety. In comparison with the robust CBF-CLF controller, this method not only can handle a higher level of model uncertainty but is also less aggressive if there is no model uncertainty presented in the system.

In this thesis, higher derivative theories and constrained dynamics are investigated in detail. In the first part of the thesis, we discuss how the Ostrogradski instability emerges in non-degenerate higher derivative theories in the context of a one-dimensional point particle where the position of the particle is a function only dependent on time. We show that the instabilities can only be removed by the addition of constraints if the original theory’s phase space is reduced. We then generalize this formalism to the most general higher derivative gravity theory where the action is not only linearly dependent on the Ricci scalar but also the quadratic curvature invariants in four-dimensional spacetime. We find that the instabilities can be removed by the judicious addition of constraints at the quadratic level of metric fluctuations around Minkowski and de Sitter backgrounds while the dimensionality of the original phase space is reduced. The constrained higher derivative gravity theory is ghost free as well as preserves the renormalization properties of higher derivative gravity, at the price of giving up the Lorentz invariance. In the second part of the thesis, we study the spherically symmetric static solution of a class of two scalar-field theory, where one of them is a Lagrange multiplier enforcing a constraint relating the value of the other scalar field to the norm of its derivative. We find the spherically symmetric static solution of the theory with an exponential potential. However, when we investigate the stability issue of the solution, the perturbation with the odd type symmetry is stable, while the even modes always contain one ghostlike degree of freedom.

The regular waterfilling(WF) policy maximizes the mutual information of parallel channels, when the inputs are Gaussian. However, Gaussian input is ideal, which does not exist in reality. Discrete constellations are usually used instead, such as $ M $-PAM and $ M $-QAM. As a result, the mercury/waterfilling (MWF) policy is introduced, which is a generalization of the regular WF. The MWF applies to inputs with arbitrary distributions, while the regular WF only applies to Gaussian inputs. The MWF-based optimal power allocation (OPA) is presented, for which an algorithm called the internal/external bisection method is introduced. The constellation-constrained capacity is discussed in the thesis, where explicit expressions are presented. The expression contains an integral, which does not have a closed-form solution. However, it can be evaluated via the Monte Carlo method. An approximation of the constellation-constrained capacity based on the sphere packing method is introduced, whose OPA is a convex optimization problem. The CVX was used initially, but it did not generate satisfactory results. Therefore, the bisection method is used instead. Capacities of the MWF and its sphere packing approximation are evaluated for various cases, and compared with each other. It turns out the sphere packing approximation has similar performances to the MWF, which validates the approximation. Unlike the MWF, the sphere packing approximation does not suffer from the loss of precision due to the structure of MMSE functions, which demonstrates its robustness.

In this thesis we present a method for detecting planar targets in real-time on power-constrained, or low-powered, hand-held devices such as mobile phones. We adopt the feature recognition (also referred to as feature matching) approach and employ fast-to-compute local feature descriptors to establish point correspondences. To obtain a satisfactory localization accuracy, most local feature descriptors seek a transformation of the input intensity patch that is invariant to various geometric and photometric deformations. Generally, such transformations are computationally intensive, hence are not ideal for real-time applications on limited hardware platforms. On the other hand, descriptors which are fast to compute are typically limited in their ability to provide invariance to a vast range of deformations. To address these shortcomings, we have developed a learning-based approach which can be applied to any local feature descriptor to increase the system’s robustness to both affine and perspective deformations. The motivation behind applying a learning-based approach is to transfer as much of the computational burden (as possible) onto an offline training phase, allowing a reduction in cost during online matching. The approach comprises of identifying keypoints which remain stable under artificially induced perspective transformations, extracting the corresponding feature vectors, and finally aggregating the feature vectors of coincident keypoints to obtain the final descriptors. We strictly focus on objects which are planar, thus allowing us to synthesize images of the object in order to capture the appearance of keypoint patches under several perspectives.

Most practical control problems must deal with constraints imposed by equipment limitations, safety considerations or environmental regulations. While it is often beneficial to maintain operation close to the limits in order to maximize profit or meet stringent product specifications, the violation of actuator constraints during normal operation can result in serious performance degradation (sometimes instability) and economic losses. This thesis is concerned with the development of control strategies for multivariable systems which systematically account for actuator constraints while guaranteeing closed-loop stability as well as graceful degradation of non-linear performance. A novel anti-windup structure is proposed which combines the efficiency of conventional anti-windup schemes with the optimality of model predictive control (MPC) algorithms. In particular, the classical internal model control (IMC) law is enhanced for optimal performance by incorporating an on-line optimization. The resulting control scheme offers both stability and performance guarantees with moderate computational expense. The proposed optimizing scheme has prospects for industrial applications as it can be implemented easily and efficiently on programmable logic controllers (PLC).

The current descriptions of bricolage largely present it as a behaviour in new businesses in richer contexts. Therefore, more diverse context-specific explanations are needed in order to deepen our understanding of bricolage. While Bricolage behaviour has been largely explained in new businesses, in extremely constrained environments, even established firms use bricolage to mobilise resources. This study set out to contribute to the understanding of bricolage by exploring it in an extremely constrained context. Using an interpretivist paradigm, empirical evidence from 8 case studies was collected through in-depth interviews and each is presented in a rich, ‘thick’ description. Through inductive coding, data-driven themes that highlight the nuances of bricolage when settings are extremely poor were derived. The study examines the idiosyncrasies of bricolage behaviour in small established firms, found in poor settings, it finds that, everything is a resource that can be bricolaged. It also finds that there is varied intensity with which underlying constructs of bricolage- making do, using resources at hand and recombining resources are manifested throughout the entrepreneurial process. In the starting phases, making do dominates, in the surviving phase, using resources at hand becomes more prominent, while in the growing phase, recombining resources is prioritised. This suggests that in poor contexts, bricolage manifests as a process that occurs throughout the life of the business. Additionally, the study highlights the sub-processes of bricolage,-scavenging, buttressing and refining. It explains how they interact by showing that scavenging precedes making do, buttressing precedes using resources at hand and refining precedes recombination of resources. Moreover different resources are used varyingly along the bricolage process. Furthermore, it integrates bricolage with two concepts of adaptive persistence and community embeddedness. Adaptive persistence is an active and dynamic experimentation to meet new challenges with the aim of finally solving them. It is exhibited as continuous adjustment to absorb emerging environmental shocks. On the other hand, community embeddedness highlights the firms’ close connection and interface with its local community on activities beyond its core role. In turn, the community becomes both an active advocate and a customer of the firm. These behaviours facilitate firm development. This work contributes to the understanding of bricolage behaviour by showing that the sub processes are more elaborate in poor settings and that established firms adopt these sub-processes varyingly as they develop. / Thesis (PhD)--University of Pretoria, 2018. / Gordon Institute of Business Science (GIBS) / PhD / Unrestricted

In the study of multi-agent systems (MASs), cooperative control is one of the most fundamental issues. As it covers a broad spectrum of applications in many industrial areas, there is a desire to design cooperative control protocols for different system and network setups. Motivated by this fact, in this thesis we focus on elaborating consensus protocol design, via model predictive control (MPC), under two different scenarios: (1) general constrained linear MASs with bounded additive disturbance; (2) linear MASs with input constraints underlying distributed communication networks. In Chapter 2, a tube-based robust MPC consensus protocol for constrained linear MASs is proposed. For undisturbed linear MASs without constraints, the results on designing a centralized linear consensus protocol are first developed by a suboptimal linear quadratic approach. In order to evaluate the control performance of the suboptimal consensus protocol, we use an infinite horizon linear quadratic objective function to penalize the disagreement among agents and the size of control inputs. Due to the non-convexity of the performance function, an optimal controller gain is difficult or even impossible to find, thus a suboptimal consensus protocol is derived. In the presence of disturbance, the original MASs may not maintain certain properties such as stability and cooperative performance. To this end, a tube-based robust MPC framework is introduced. When disturbance is involved, the original constraints in nominal prediction should be tightened so as to achieve robust constraint satisfaction, as the predicted states and the actual states are not necessarily the same. Moreover, the corresponding robust constraint sets can be determined offline, requiring no extra iterative online computation in implementation. In Chapter 3, a novel distributed MPC-based consensus protocol is proposed for general linear MASs with input constraints. For the linear MAS without constraints, a pre-stabilizing distributed linear consensus protocol is developed by an inverse optimal approach, such that the corresponding closed-loop system is asymptotically stable with respect to a consensus set. Implementing this pre-stabilizing controller in a distributed digital setting is however not possible, as it requires every local decision maker to continuously access the state of their neighbors simultaneously when updating the control input. To relax these requirements, the assumed neighboring state, instead of the actual state of neighbors, is used. In our distributed MPC scheme, each local controller minimizes a group of control variables to generate control input. Moreover, an additional state constraint is proposed to bound deviation between the actual and the assumed state. In this way, consistency is enforced between intended behaviors of an agent and what its neighbors believe it will behave. We later show that the closed-loop system converges to a neighboring set of the consensus set thanks to the bounded state deviation in prediction. In Chapter 4, conclusions are made and some research topics for future exploring are presented. / Graduate / 2021-03-31

Social activity data sets are increasing in number and volume. Finding community structure in such data is valuable in many applications. For example, understand- ing the community structure of social networks may reduce the spread of epidemics or boost advertising revenue; discovering partitions in tra c networks can help to optimize routing and to reduce congestion; finding a group of users with common interests can allow a system to recommend useful items. Among many aspects, qual- ity of inference and e ciency in finding community structures in such data sets are of paramount concern. In this thesis, we propose several approaches to improve com- munity detection in these aspects. The first approach utilizes the concept of K-cores to reduce the size of the problem. The K-core of a graph is the largest subgraph within which each node has at least K connections. We propose a framework that accelerates community detection. It first applies a traditional algorithm that is relatively slow to the K-core, and then uses a fast heuristic to infer community labels for the remaining nodes. The second approach is to scale the algorithm to multi-processor systems. We de- vise a scalable community detection algorithm for large networks based on stochastic block models. It is an alternating iterative algorithm using a maximum likelihood ap- proach. Compared with traditional inference algorithms for stochastic block models, our algorithm can scale to large networks and run on multi-processor systems. The time complexity is linear in the number of edges of the input network. The third approach is to improve the quality. We propose a framework for non- negative matrix factorization that allows the imposition of linear or approximately linear constraints on each factor. An example of the applications is to find community structures in bipartite networks, which is useful in recommender systems. Our algorithms are compared with the results in recent papers and their quality and e ciency are verified by experiments.

This thesis is concerned with a certain class of algorithms for the solution of constrained optimization problems and generalized Nash equilibrium problems in Hilbert spaces. This class of algorithms is inspired by the alternating direction method of multipliers (ADMM) and eliminates the constraints using an augmented Lagrangian approach. The alternating direction method consists of splitting the augmented Lagrangian subproblem into smaller and more easily manageable parts. Before the algorithms are discussed, a substantial amount of background material, including the theory of Banach and Hilbert spaces, fixed-point iterations as well as convex and monotone set-valued analysis, is presented. Thereafter, certain optimization problems and generalized Nash equilibrium problems are reformulated and analyzed using variational inequalities and set-valued mappings. The analysis of the algorithms developed in the course of this thesis is rooted in these reformulations as variational inequalities and set-valued mappings. The first algorithms discussed and analyzed are one weakly and one strongly convergent ADMM-type algorithm for convex, linearly constrained optimization. By equipping the associated Hilbert space with the correct weighted scalar product, the analysis of these two methods is accomplished using the proximal point method and the Halpern method. The rest of the thesis is concerned with the development and analysis of ADMM-type algorithms for generalized Nash equilibrium problems that jointly share a linear equality constraint. The first class of these algorithms is completely parallelizable and uses a forward-backward idea for the analysis, whereas the second class of algorithms can be interpreted as a direct extension of the classical ADMM-method to generalized Nash equilibrium problems. At the end of this thesis, the numerical behavior of the discussed algorithms is demonstrated on a collection of examples. / Die vorliegende Arbeit behandelt eine Klasse von Algorithmen zur Lösung restringierter Optimierungsprobleme und verallgemeinerter Nash-Gleichgewichtsprobleme in Hilberträumen. Diese Klasse von Algorithmen ist angelehnt an die Alternating Direction Method of Multipliers (ADMM) und eliminiert die Nebenbedingungen durch einen Augmented-Lagrangian-Ansatz. Im Rahmen dessen wird in der Alternating Direction Method of Multipliers das jeweilige Augmented-Lagrangian-Teilproblem in kleinere Teilprobleme aufgespaltet. Zur Vorbereitung wird eine Vielzahl grundlegender Resultate präsentiert. Dies beinhaltet entsprechende Ergebnisse aus der Literatur zu der Theorie von Banach- und Hilberträumen, Fixpunktmethoden sowie konvexer und monotoner mengenwertiger Analysis. Im Anschluss werden gewisse Optimierungsprobleme sowie verallgemeinerte Nash-Gleichgewichtsprobleme als Variationsungleichungen und Inklusionen mit mengenwertigen Operatoren formuliert und analysiert. Die Analysis der im Rahmen dieser Arbeit entwickelten Algorithmen bezieht sich auf diese Reformulierungen als Variationsungleichungen und Inklusionsprobleme. Zuerst werden ein schwach und ein stark konvergenter paralleler ADMM-Algorithmus zur Lösung von separablen Optimierungsaufgaben mit linearen Gleichheitsnebenbedingungen präsentiert und analysiert. Durch die Ausstattung des zugehörigen Hilbertraums mit dem richtigen gewichteten Skalarprodukt gelingt die Analyse dieser beiden Methoden mit Hilfe der Proximalpunktmethode und der Halpern-Methode. Der Rest der Arbeit beschäftigt sich mit Algorithmen für verallgemeinerte Nash-Gleichgewichtsprobleme, die gemeinsame lineare Gleichheitsnebenbedingungen besitzen. Die erste Klasse von Algorithmen ist vollständig parallelisierbar und es wird ein Forward-Backward-Ansatz für die Analyse genutzt. Die zweite Klasse von Algorithmen kann hingegen als direkte Erweiterung des klassischen ADMM-Verfahrens auf verallgemeinerte Nash-Gleichgewichtsprobleme aufgefasst werden. Abschließend wird das Konvergenzverhalten der entwickelten Algorithmen an einer Sammlung von Beispielen demonstriert.