In this study, neural networks are developed under conditions of nonnormality as alternatives to standard control charts, and their performance is compared with those of standard ‾x and CUSUM control charts.

We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under which circumstances a given number of controllers can successfully stabilize a given system.

This dissertation discusses the predictability of the atmosphere-ocean climate system on interannual and decadal timescales. We investigate the extent to which the atmospheric internal variability (weather noise) can cause climate prediction to lose skill; and we also look for the oceanic processes that contribute to the climate predictability via interaction with the atmosphere. First, we develop a framework for assessing the predictability of a linear stochastic system. Based on the information of deterministic dynamics and noise forcing, various predictability measures are defined and new predictability-analysis tools are introduced. For the sake of computational efficiency, we also discuss the formulation of a low-order model within the context of four reduction methods: modal, EOF, most predictable pattern, and balanced truncation. Subsequently, predictabilities of two specific physical systems are investigated within such framework. The first is a mixed layer model of SST with focus on the effect of oceanic advection.Analytical solution of a one-dimensional model shows that even though advection can give rise to a pair of low-frequency normal modes, no enhancement in the predictability is found in terms of domain averaged error variance. However, a Predictable Component Analysis (PrCA) shows that advection can play a role in redistributing the predictable variance. This analytical result is further tested in a more realistic two-dimensional North Atlantic model with observed mean currents. The second is a linear coupled model of tropical Atlantic atmosphere-ocean system. Eigen-analysis reveals that the system has two types of coupled modes: a decadal meridional mode and an interannual equatorial mode. The meridional mode, which manifests itself as a dipole pattern in SST, is controlled by thermodynamic feedback between wind, latent heat flux, and SST, and modified by ocean heat transport. The equatorial mode, which manifests itself as an SST anomaly in the eastern equatorial basin, is dominated by dynamic feedback between wind, thermocline, upwelling, and SST. The relative strength of thermodynamic vs dynamic feedbacks determines the behavior of the coupled system, and enables the tropical Atlantic variability to be more predictable than the passive-ocean scenario.