Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl

A multi-model ensemble Kalman filter for data assimilation and forecasting

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi-model ensemble Kalman filter (MM-EnKF) based on this framework. The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner; it uses adaptive model error estimation to provide matrix-valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi-model ensemble, with respect to both probabilistic and deterministic error metrics.Comment: 23 pages, 10 figure

Optimal Collision Avoidance Trajectories for Unmanned/Remotely Piloted Aircraft

The post-911 environment has punctuated the force-multiplying capabilities that Remotely Piloted Aircraft (RPA) provides combatant commanders at all echelons on the battlefield. Not only have unmanned aircraft systems made near-revolutionary impacts on the battlefield, their utility and proliferation in law enforcement, homeland security, humanitarian operations, and commercial applications have likewise increased at a rapid rate. As such, under the Federal Aviation Administration (FAA) Modernization and Reform Act of 2012, the United States Congress tasked the FAA to provide for the safe integration of civil unmanned aircraft systems into the national airspace system (NAS) as soon as practicable, but not later than September 30, 2015. However, a necessary entrance criterion to operate RPAs in the NAS is the ability to Sense and Avoid (SAA) both cooperative and noncooperative air traffic to attain a target level of safety as a traditional manned aircraft platform. The goal of this research effort is twofold: First, develop techniques for calculating optimal avoidance trajectories, and second, develop techniques for estimating an intruder aircraft\u27s trajectory in a stochastic environment. This dissertation describes the optimal control problem associated with SAA and uses a direct orthogonal collocation method to solve this problem and then analyzes these results for different collision avoidance scenarios

Efficient Reinforcement Learning using Gaussian Processes

This book examines Gaussian processes (GPs) in model-based reinforcement learning (RL) and inference in nonlinear dynamic systems. First, we introduce PILCO, a fully Bayesian approach for efficient RL in continuous-valued state and action spaces when no expert knowledge is available. PILCO learns fast since it takes model uncertainties consistently into account during long-term planning and decision making. Thus, it reduces model bias, a common problem in model-based RL. Due to its generality and efficiency, PILCO is a conceptual and practical approach to jointly learning models and controllers fully automatically. Across all tasks, we report an unprecedented degree of automation and an unprecedented speed of learning. Second, we propose principled algorithms for robust filtering and smoothing in GP dynamic systems. Our methods are based on analytic moment matching and clearly advance state-of-the-art methods

Enhancing the information content of geophysical data for nuclear site characterisation

Our knowledge and understanding to the heterogeneous structure and processes occurring in the Earth’s subsurface is limited and uncertain. The above is true even for the upper 100m of the subsurface, yet many processes occur within it (e.g. migration of solutes, landslides, crop water uptake, etc.) are important to human activities. Geophysical methods such as electrical resistivity tomography (ERT) greatly improve our ability to observe the subsurface due to their higher sampling frequency (especially with autonomous time-lapse systems), larger spatial coverage and less invasive operation, in addition to being more cost-effective than traditional point-based sampling. However, the process of using geophysical data for inference is prone to uncertainty. There is a need to better understand the uncertainties embedded in geophysical data and how they translate themselves when they are subsequently used, for example, for hydrological or site management interpretations and decisions. This understanding is critical to maximize the extraction of information in geophysical data. To this end, in this thesis, I examine various aspects of uncertainty in ERT and develop new methods to better use geophysical data quantitatively. The core of the thesis is based on two literature reviews and three papers. In the first review, I provide a comprehensive overview of the use of geophysical data for nuclear site characterization, especially in the context of site clean-up and leak detection. In the second review, I survey the various sources of uncertainties in ERT studies and the existing work to better quantify or reduce them. I propose that the various steps in the general workflow of an ERT study can be viewed as a pipeline for information and uncertainty propagation and suggested some areas have been understudied. One of these areas is measurement errors. In paper 1, I compare various methods to estimate and model ERT measurement errors using two long-term ERT monitoring datasets. I also develop a new error model that considers the fact that each electrode is used to make multiple measurements. In paper 2, I discuss the development and implementation of a new method for geoelectrical leak detection. While existing methods rely on obtaining resistivity images through inversion of ERT data first, the approach described here estimates leak parameters directly from raw ERT data. This is achieved by constructing hydrological models from prior site information and couple it with an ERT forward model, and then update the leak (and other hydrological) parameters through data assimilation. The approach shows promising results and is applied to data from a controlled injection experiment in Yorkshire, UK. The approach complements ERT imaging and provides a new way to utilize ERT data to inform site characterisation. In addition to leak detection, ERT is also commonly used for monitoring soil moisture in the vadose zone, and increasingly so in a quantitative manner. Though both the petrophysical relationships (i.e., choices of appropriate model and parameterization) and the derived moisture content are known to be subject to uncertainty, they are commonly treated as exact and error‐free. In paper 3, I examine the impact of uncertain petrophysical relationships on the moisture content estimates derived from electrical geophysics. Data from a collection of core samples show that the variability in such relationships can be large, and they in turn can lead to high uncertainty in moisture content estimates, and they appear to be the dominating source of uncertainty in many cases. In the closing chapters, I discuss and synthesize the findings in the thesis within the larger context of enhancing the information content of geophysical data, and provide an outlook on further research in this topic