A cooperative multi-agent system is a collection of interacting agents deployed in a mission space where each agent is allowed to control its local state so that the fleet of agents collectively optimizes a common global objective. While optimization problems associated with multi-agent systems intend to determine the fixed set of globally optimal agent states, control problems aim to obtain the set of globally optimal agent controls. Associated non-convexities in these problems result in multiple local optima. This dissertation explores systematic techniques that can be deployed to either escape or avoid poor local optima while in search of provably better (still local) optima. First, for multi-agent optimization problems with iterative gradient-based solutions, a distributed approach to escape local optima is proposed based on the concept of boosting functions. These functions temporarily transform gradient components at a local optimum into a set of boosted non-zero gradient components in a systematic manner so that it is more effective compared to the methods where gradient components are randomly perturbed. A novel variable step size adjustment scheme is also proposed to establish the convergence of this distributed boosting process. Developed boosting concepts are successfully applied to the class of coverage problems. Second, as a means of avoiding convergence to poor local optima in multi-agent optimization, the use of greedy algorithms in generating effective initial conditions is explored. Such greedy methods are computationally cheap and can often exploit submodularity properties of the problem to provide performance bound guarantees to the obtained solutions. For the class of submodular maximization problems, two new performance bounds are proposed and their effectiveness is illustrated using the class of coverage problems. Third, a class of multi-agent control problems termed Persistent Monitoring on Networks (PMN) is considered where a team of agents is traversing a set of nodes (targets) interconnected according to a network topology aiming to minimize a measure of overall node state. For this class of problems, a gradient-based parametric control solution developed in a prior work relies heavily on the initial selection of its `parameters' which often leads to poor local optima. To overcome this initialization challenge, the PMN system's asymptotic behavior is analyzed, and an off-line greedy algorithm is proposed to systematically generate an effective set of initial parameters. Finally, for the same class of PMN problems, a computationally efficient distributed on-line Event-Driven Receding Horizon Control (RHC) solution is proposed as an alternative. This RHC solution is parameter-free as it automatically optimizes its planning horizon length and gradient-free as it uses explicitly derived solutions for each RHC problem invoked at each agent upon each event of interest. Hence, unlike the gradient-based parametric control solutions, the proposed RHC solution does not force the agents to converge to one particular behavior that is likely to be a poor local optimum. Instead, it keeps the agents actively searching for the optimum behavior. In each of these four parts of the thesis, an interactive simulation platform is developed (and made available online) to generate extensive numerical examples that highlight the respective contributions made compared to the state of the art.

Connaître en temps réel la réponse et le comportement des cellules et organismes modèles suite à des changements de leur environnement, ou à des modulations de leurs fonctions biologiques est devenu essentiel dans les sciences du vivant. Ces réponses nous permettent ensuite de comprendre les mécanismes qui régissent le fonctionnement des cellules vivantes, avec des implications en recherche fondamentale, appliquée et biomédicale. Un des plus gros défis technologiques reste le contrôle des paramètres environnementaux en microscopie haute résolution. De nos jours, aucun système ne permet de réguler un ensemble complexe de paramètres de manière précise, dynamique et simultanée tout en observant les cellules dans leur environnement. L’objectif de ma thèse est de mettre au point un tel dispositif permettant a minima une régulation fine de la température, de la composition du milieu, et notamment de la concentration de divers drogues. Ce système doit être compatible avec les applications les plus poussées en microscopie photonique. Mon approche au cours de ma thèse pour élaborer un tel système est l’utilisation de la microfluidique. En effet, c’est la seule technologie qui puisse de réaliser un tel multiplexage. Elle permet de manipuler des petites quantités de fluide à travers un système contenant des canaux de dimensions allant du micromètre au centimètre. Cet ordre de grandeur des canaux constitue un atout majeur (réduction de la consommation des réactifs, réduction des couts, cinétiques des réactions chimiques et biologiques élevées, temps de diffusion court, etc.) et permet d’allier les expériences biologiques à la microscopie. Mon objectif est de concevoir une puce microfluidique qui représentera un pas technologique majeur et ouvrira de nouvelles possibilités de recherche. / Monitoring in real-time the response of cells and model organisms to the changes in their environment or to modulations of their biological functions has become essential in life sciences. One of the main technical challenges for biologists is the precise and dynamic control of various environmental parameters while doing high-resolution microscopy. My thesis consists of building a robust and versatile system, dedicated to live-cell imaging that will be compatible with adherent and non adherent models, that could provide a precise and simultaneous control of 1) the temperature, 2) the media exchanges and 3) the drug concentration while doing photonic microscopy. My approach is to use microfluidics, which is the best candidate in order to achieve this system and provides all the necessary controls of micro-scaled volumes for culturing, maintaining or analyzing cells. It produces miniaturized systems used as tools for biological experiments, in which channels of a micro-scaled dimension are used for the fluid circulation. The laminar flow in these chips allows fast molecule diffusion as well as fast temperature diffusion. Because of the high surface to volume ratio, the consumption of reagents is reduced, and media switches can be fast. This system will represent a major technical and beneficial step and will open new possibilities of research in biology.

Statistical process control (SPC) is a collection of scientific tools developed and engineered to diagnose unnecessary variation in the output of a production process and eliminate it or perhaps accommodate it by adjusting process settings. The task of quality control (QC) is of fundamental importance in manufacturing processes when a change in the process causes misleading results, this alteration should be detected and corrected as soon as possible. Statistical QC charts originated in the late 1920s by Dr. W. A. Shewhart provide a powerful tool for monitoring production lines in manufacturing industries. They are also have been implemented in various disciplines, such as sequential monitoring of internet traffic flows, health care systems, and more. Shewhart-type charts are effective in detecting large shifts in the process but ineffective in detecting small to moderate shifts. This blind spot allows small shifts (smaller than one standard deviation) to continue undetected in the process, thereby incurring larger total costs for manufacturers. This thesis addresses this issue by augmenting current time-weighted charts (charts that use all the information from the start of a process until the most recent sample/observation) with a Double Generally Weighted Moving Average (DGWMA) chart, leading to more effective process monitoring. The objective of this thesis is to provide the fundamentals and introduce the researcher/practitioner to the essentials of the univariate DGWMA chart from both parametric and nonparametric perspectives. Numerous concepts and characteristics of proposed DGWMA charts are discussed comprehensively. Theoretical expressions and detailed calculations have been provided to aid the interested reader to familiarize and study the topic more thoroughly. This thesis paints a bigger picture of the DGWMA chart in a sense that other time-weighted charts such as the Generally Weighted Moving Average (GWMA), Exponentially Weighted Moving Average (EWMA), Double Exponentially Weighted Moving Average (DEWMA) and Cumulative Sum (CUSUM) fall under this umbrella. Both real-life data and simulated examples have been embedded throughout the thesis. We make use of R and Mathematica software packages to calculate numerical results related to the run length distribution and its associated characteristics in this thesis. We only consider control charts for monitoring the process location parameter. However, our conclusions and recommendations are extendable for the process dispersion parameter. In this thesis, we consider the DGWMA chart as the main chart and the EWMA, DEWMA, GWMA, and CUSUM charts as special cases. The thesis consists of the following chapters with a short description for each chapter as follows: Chapter 1 provides a brief introduction to SPC concepts and gives a literature review in terms of background information for the research conducted in this thesis. The scope and objectives of the present research are highlighted in detail. Chapter 2 provides an overview and a theoretical background on the design and implementation of the DGWMA chart derived from the SPC literature review. The properties of the DGWMA chart, including the plotting statistic, the structure for the weights, the control limits (exact/steady-state), etc. are considered in detail. The weighting structure of the DGWMA chart and its special case are discussed and pictured to emphasize the impact of weights in increasing the detection capability of time-weighted charts. Three approaches are described and investigated for calculating the run length distribution and its associated characteristics for the DGWMA chart and its special case the DEWMA chart; this includes: (i) exact approach; (ii) Markov chain approach; (iii) Monte Carlo simulation. In Chapter 3 we develop a one-sided generalized parametric chart (denoted by DGWMA-TBE) for monitoring the time between events (TBE) of nonconformities items originating from the high-yield processes when the underlying process distribution is gamma and the parameter of interest is known (Case K) and unknown (Case U). A Markov chain approach is implemented to derive the run length distribution and its associated characteristics for the DGWMA and DEWMA charts. An exact approach is also used to derive closed-form expressions for the run length distribution of the proposed chart. Performance analysis has been undertaken to execute a comparative study with several existing time-weighted charts. The proposed chart encompasses one-sided GWMA-TBE, EWMA-TBE, DEWMA-TBE, and Shewhart-type charts as limiting or special cases. The CUSUM-TBE chart is also included in the performance comparison. The necessary design parameters are provided to aid the implementation of the proposed chart and finding the optimal design and near optima design that is useful for practitioners. Alternative discrete distributions are considered for the weights of the GWMA-TBE chart and a discussion is provided to address the connection between new weights originating from the suggested distributions and the chart’s capability in detecting shifts. As a result, one can design an optimal GWMA-TBE chart by replacing weights from the discrete Weibull distribution without the implementation of the double exponential smoothing technique. Chapter 4 focuses on developing a two-sided nonparametric (distribution-free) DGWMA control chart based on the exceedance (EX) statistic, denoted as DGWMA-EX when the parameter of interest is unknown (Case U) and the underlying process distribution is continuous and symmetric. An exact approach and a Markov chain approach are considered to calculate the run length distribution and its associated characteristics for the proposed chart. A performance comparison has been undertaken to execute analysis with other nonparametric time-weighted charts available in the SPC literature. The proposed chart en-compasses two-sided GWMA-EX, EWMA-EX, DEWMA-EX, and Shewhart-type charts as limiting or special cases. The CUSUM-EX chart is also included in the performance comparison Also, the performance of the proposed DGWMA-EX chart has been evaluated under different symmetric and skewed distributions in comparison with its main counterparts, and the necessary results and recommendations are provided for practitioners to design an optimal chart. Chapter 5 encloses this thesis with a summary of the research conducted and provides concluding remarks concerning future research opportunities. / Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2020. / This research was supported in part by the National Research Foundation (NRF) under Grant Number 71199 and the postgraduate research bursary supported by the University of Pretoria. Any findings, opinions, and conclusions expressed in this thesis are those of the author and do not necessarily reflect the views of the parties. / Statistics / PhD (Mathematical Statistics) / Unrestricted