The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Turbulent flow at 190 m height above London during 2006-2008: A climatology and the applicability of similarity theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ_i/u_* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.

Livestock vaccine adoption among poor farmers in Bolivia: Remembering innovation diffusion theory

The paper explores the low uptake of livestock vaccination among poor farming communities in Bolivia utilising core elements of the original innovation diffusion theory. Contrary to the recent literature, we found that vaccination behaviour was strongly Linked to social and cultural, rather than economic, drivers. While membership in a group increased uptake, the 'hot' and 'cold' distinctions which dictate health versus illness within Andean cosmology also played a role, with vaccination viewed as a means of addressing underlying imbalances. We concluded that uptake of livestock vaccination was unlikely to improve without knowledge transfer that acknowledges local. epistemologies for Livestock disease. (C) 2008 Elsevier Ltd. All rights reserved.

The impact of harvesting on a formerly endangered tropical bird: insights from life-history theory

1. Life-history theory assumes that trade-offs exist between an individual's life-history components, such that an increased allocation of a resource to one fitness trait might be expected to result in a cost for a conflicting fitness trait. Recent evidence from experimental manipulations of wild individuals supports this assumption. 2. The management of many bird populations involves harvesting for both commercial and conservation purposes. One frequently harvested life-history stage is the egg, but the consequences of repeated egg harvesting for the individual and the long-term dynamics of the population remain poorly understood. 3. We used a well-documented restored population of the Mauritius kestrel Falco punctatus as a model system to explore the consequences of egg harvesting (and associated management practices) for an individual within the context of life-history theory. 4. Our analysis indicated that management practices enhanced both the size and number of clutches laid by managed females, and improved mid-life male and female adult survival relative to unmanaged adult kestrels. 5. Although management resulted in an increased effort in egg production, it reduced parental effort during incubation and the rearing of offspring, which could account for these observed changes. 6. Synthesis and applications. This study demonstrates how a commonly applied harvesting strategy, when examined within the context of life-history theory, can identify improvements in particular fitness traits that might alleviate some of the perceived negative impact of harvesting on the long-term dynamics of a managed population.

Managing threatened species – the ecological toolbox, evolutionary theory and the declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviourbased models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley’s declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.

Identifying and understanding factors influencing the uptake of new technologies on dairy farms in SW England using the theory of reasoned action

Whilst much is known of new technology adopters, little research has addressed the role of their attitudes in adoption decisions; particularly, for technologies with evident economic potential that have not been taken up by farmers. This paper presents recent research that has used a new approach which examines the role that adopters' attitudes play in identifying the drivers of and barriers to adoption. The study was concerned with technologies for livestock farming systems in SW England, specifically oestrus detection, nitrogen supply management, and, inclusion of white clover. The adoption behaviour is analysed using the social-psychology theory of reasoned action to identify factors that affect the adoption of technologies, which are confirmed using principal components analysis. The results presented here relate to the specific adoption behaviour regarding the Milk Development Council's recommended observation times for heat detection. The factors that affect the adoption of this technology are: cost effectiveness, improved detection and conception rates as the main drivers, whilst the threat to demean the personal knowledge and skills of a farmer in 'knowing' their cows is a barrier. This research shows clearly that promotion of a technology and transfer of knowledge for a farming system need to take account of the beliefs and attitudes of potential adopters. (C) 2006 Elsevier Ltd. All rights reserved.

Managing threatened species: the ecological toolbox, evolutionary theory and declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviour-based models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley's declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.