Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.

Redistribution of Soil Organic Matter by Permafrost Disturbance in the Canadian High Arctic

With increased warming in the Arctic, permafrost thaw may induce localized physical disturbance of slopes. These disturbances, referred to as active layer detachments (ALDs), redistribute soil across the landscape, potentially releasing previously unavailable carbon (C). In 2007–2008, widespread ALD activity was reported at the Cape Bounty Arctic Watershed Observatory in Nunavut, Canada. Our study investigated organic matter (OM) composition in soil profiles from ALD-impacted and undisturbed areas. Solid-state 13C nuclear magnetic resonance (NMR) and solvent-extractable biomarkers were used to characterize soil OM. Throughout the disturbed upslope profile, where surface soils and vegetation had been removed, NMR revealed low O-alkyl C content and biomarker analysis revealed low concentrations of solvent-extractable compounds suggesting enhanced erosion of labile-rich OM by the ALD. In the disturbed downslope region, vegetation remained intact but displaced material from upslope produced lateral compression ridges at the surface. High O-alkyl content in the surface horizon was consistent with enrichment of carbohydrates and peptides, but low concentrations of labile biomarkers (i.e., sugars) suggested the presence of relatively unaltered labile-rich OM. Decreased O-alkyl content and biomarker concentrations below the surface contrasted with the undisturbed profile and may indicate the loss of well-established pre-ALD surface drainage with compression ridge formation. However, pre-ALD profile composition remains unknown and the observed decreases may result from nominal pre-ALD OM inputs. These results are the first to establish OM composition in ALD-impacted soil profiles, suggesting reallocation of permafrost-derived soil C to areas where degradation or erosion may contribute to increased C losses from disturbed Arctic soils.

Remote Sensing of Vegetation Change Across a Latitudinal Gradient in the Canadian Arctic

Global air surface temperatures and precipitation have increased over the last several decades resulting in a trend of greening across the Circumpolar Arctic. The spatial variability of warming and the inherent effects on plant communities has not proven to be uniform or homogeneous on global or local scales. We can apply remote sensing vegetation indices such as the Normalized Difference Vegetation Index (NDVI) to map and monitor vegetation change (e.g., phenology, greening, percent cover, and biomass) over time. It is important to document how Arctic vegetation is changing, as it will have large implications related to global carbon and surface energy budgets. The research reported here examined vegetation greening across different spatial and temporal scales at two disparate Arctic sites: Apex River Watershed (ARW), Baffin Island, and Cape Bounty Arctic Watershed Observatory (CBAWO), Melville Island, NU. To characterize the vegetation in the ARW, high spatial resolution WorldView-2 data were processed to create a supervised land-cover classification and model percent vegetation cover (PVC) (a similar process had been completed in a previous study for the CBAWO). Meanwhile, NDVI data spanning the past 30 years were derived from intermediate resolution Landsat data at the two Arctic sites. The land-cover classifications at both sites were used to examine the Landsat NDVI time series by vegetation class. Climate variables (i.e., temperature, precipitation and growing season length (GSL) were examined to explore the potential relationships of NDVI to climate warming. PVC was successfully modeled using high resolution data in the ARW. PVC and plant communities appear to reside along a moisture and altitudinal gradient. The NDVI time series demonstrated an overall significant increase in greening at the CBAWO (High Arctic site), specifically in the dry and mesic vegetation type. However, similar overall greening was not observed for the ARW (Low Arctic site). The overall increase in NDVI at the CBAWO was attributed to a significant increase in July temperatures, precipitation and GSL.