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.

Nodal variations and long-term changes in the main tides on the coasts of China

The long-term changes in the main tidal constituents (O1, K1, M2, N2, and S2) along the coasts of China and in adjacent seas are investigated based on 17 tide-gauge records covering the period 1954–2012. The observed 18.61 year nodal modulations of the diurnal constituents O1 and K1 are in agreement with the equilibrium tidal theory, except in the South China Sea. The observed modulations of the M2 and N2 amplitudes are smaller than theoretically predicted at the northern stations and larger at the southern stations. The discrepancies between the theoretically predicted nodal variations and the observations are discussed. The 8.85 year perigean cycle is identifiable in the N2 parameters at most stations, except those in the South China Sea. The radiational component of S2 contributes on average 16% of the observed S2 except in the Gulf of Tonkin, on the south coast, where it accounts for up to 65%. We confirmed the existence of nodal modulation in S2, which is stronger on the north coast. The semidiurnal tidal parameters show significant secular trends in the Bohai and Yellow Seas, on the north coast, and in the Taiwan Strait. The largest increase is found for M2 for which the amplitude increases by 4–7 mm/yr in the Yellow Sea. The potential causes for the linear trends in tidal constants are discussed.

A description of the FAMOUS (version XDBUA) climate model and control run

FAMOUS is an ocean-atmosphere general circulation model of low resolution, capable of simulating approximately 120 years of model climate per wallclock day using current high performance computing facilities. It uses most of the same code as HadCM3, a widely used climate model of higher resolution and computational cost, and has been tuned to reproduce the same climate reasonably well. FAMOUS is useful for climate simulations where the computational cost makes the application of HadCM3 unfeasible, either because of the length of simulation or the size of the ensemble desired. We document a number of scientific and technical improvements to the original version of FAMOUS. These improvements include changes to the parameterisations of ozone and sea-ice which alleviate a significant cold bias from high northern latitudes and the upper troposphere, and the elimination of volume-averaged drifts in ocean tracers. A simple model of the marine carbon cycle has also been included. A particular goal of FAMOUS is to conduct millennial-scale paleoclimate simulations of Quaternary ice ages; to this end, a number of useful changes to the model infrastructure have been made.

Influence of temperature on the motility of Pseudomonas oryzihabitans and control of Globodera rostochiensis

The motility and efficacy of Pseudomonas oryzihabitans as a biocontrol agent against the potato cyst nematode Globodera rostochiensis were studied with respect to temperature. The influence of soil moisture on bacterial movement was also tested. In a closed container trial, P. oryzihabitans significantly reduced invasion of second stage juveniles (J2) of G. rostochiensis in potato roots, its effect being more marked at 25 and 21 degreesC than at 17 degreesC. P. oryzihabitans motility in vitro was optimal at 26 degreesC and inhibited at temperatures below 18 degreesC. In soil, both temperature and matric potential affected bacterial movement. At 16 degreesC its movement and survival were suppressed, but they were unaffected at 25 degreesC. At both temperatures the biocontrol agent moved faster in the wetter (- 0.03 MPa) than in the drier soil (- 0.1 MPa). These results suggest that temperature is a key factor in determining the potential of P. or.yzihabitans as a biocontrol agent. (C) 2003 Elsevier Science Ltd. All rights reserved.

Sex-dependent age modulation of frontostriatal and temporo-parietal activation during cognitive control

Developmental functional imaging studies of cognitive control show progressive age-related increase in task-relevant fronto-striatal activation in male development from childhood to adulthood. Little is known, however, about how gender affects this functional development. In this study, we used event related functional magnetic resonance imaging to examine effects of sex, age, and their interaction on brain activation during attentional switching and interference inhibition, in 63 male and female adolescents and adults, aged 13 to 38. Linear age correlations were observed across all subjects in task-specific frontal, striatal and temporo-parietal activation. Gender analysis revealed increased activation in females relative to males in fronto-striatal areas during the Switch task, and laterality effects in the Simon task, with females showing increased left inferior prefrontal and temporal activation, and males showing increased right inferior prefrontal and parietal activation. Increased prefrontal activation clusters in females and increased parietal activation clusters in males furthermore overlapped with clusters that were age-correlated across the whole group, potentially reflecting more mature prefrontal brain activation patterns for females, and more mature parietal activation patterns for males. Gender by age interactions further supported this dissociation, revealing exclusive female-specific age correlations in inferior and medial prefrontal brain regions during both tasks, and exclusive male-specific age correlations in superior parietal (Switch task) and temporal regions (Simon task). These findings show increased recruitment of age-correlated prefrontal activation in females, and of age-correlated parietal activation in males, during tasks of cognitive control. Gender differences in frontal and parietal recruitment may thus be related to gender differences in the neurofunctional maturation of these brain regions.

Object displays and control of dynamic systems

Recent work has suggested that for some tasks, graphical displays which visually integrate information from more than one source offer an advantage over more traditional displays which present the same information in a separated format. Three experiments are described which investigate this claim using a task which requires subjects to control a dynamic system. In the first experiment, the integrated display is compared to two separated displays, one an animated mimic diagram, the other an alphanumeric display. The integrated display is shown to support better performance in a control task, but experiment 2 shows that part of this advantage may be due to its analogue nature. Experiment 3 considers performance on a fault detection task, and shows no difference between the integrated and separated displays. The paper concludes that previous claims made for integrated displays may not generalize from monitoring to control tasks.

Diagnosis of variability and trends in a global precipitation dataset using a physically motivated statistical model

A physically motivated statistical model is used to diagnose variability and trends in wintertime ( October - March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasi-geostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount. The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity q(s) has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

The diurnal cycle of convection and atmospheric tides in an aquaplanet

The diurnal cycle of tropical convection and its relationship to the atmospheric tides is investigated using an aquaplanet GCM. The diurnal and semidiurnal harmonics of precipitation are both found to contribute significantly to the total diurnal variability of precipitation in the model, which is broadly consistent with observations of the diurnal cycle of convection over the open ocean. The semidiurnal tide is found to be the dominant forcing for the semidiurnal harmonic of precipitation. In contrast the diurnal tide plays only a small role in forcing the diurnal harmonic of precipitation, which is dominated by the variations in shortwave and longwave heating. In both the diurnal and semidiurnal harmonics, the feedback onto the convection by the humidity tendencies due to the convection is found to be important in determining the phase of the harmonics. Further experiments show that the diurnal cycle of precipitation is sensitive to the choice of closure in the convection scheme. While the surface pressure signal of the simulated atmospheric tides in the model agree well with both theory and observations in their magnitude and phase, sensitivity experiments suggest that the role of the stratospheric ozone in forcing the semidiurnal tide is much reduced compared to theoretical predictions. Furthermore, the influence of the cloud radiative effects seems small. It is suggested that the radiative heating profile in the troposphere, associated primarily with the water vapor distribution, is more important than previously thought for driving the semidiurnal tide. However, this result may be sensitive to the vertical resolution and extent of the model.

How soccer players head the ball: a test of optic acceleration cancellation theory with virtual reality

We measured the movements of soccer players heading a football in a fully immersive virtual reality environment. In mid-flight the ball’s trajectory was altered from its normal quasi-parabolic path to a linear one, producing a jump in the rate of change of the angle of elevation of gaze (α) from player to ball. One reaction time later the players adjusted their speed so that the rate of change of α increased when it had been reduced and reduced it when it had been increased. Since the result of the player’s movement was to regain a value of the rate of change close to that before the disturbance, the data suggest that the players have an expectation of, and memory for, the pattern that the rate of change of α will follow during the flight. The results support the general claim that players intercepting balls use servo control strategies and are consistent with the particular claim of Optic Acceleration Cancellation theory that the servo strategy is to allow α to increase at a steadily decreasing rate.

Influence of temperature on the motility of Pseudomonas oryzihabitans and control of Globodera rostochiensis

The motility and efficacy of Pseudomonas oryzihabitans as a biocontrol agent against the potato cyst nematode Globodera rostochiensis were studied with respect to temperature. The influence of soil moisture on bacterial movement was also tested. In a closed container trial, P. oryzihabitans significantly reduced invasion of second stage juveniles (J2) of G. rostochiensis in potato roots, its effect being more marked at 25 and 21 degreesC than at 17 degreesC. P. oryzihabitans motility in vitro was optimal at 26 degreesC and inhibited at temperatures below 18 degreesC. In soil, both temperature and matric potential affected bacterial movement. At 16 degreesC its movement and survival were suppressed, but they were unaffected at 25 degreesC. At both temperatures the biocontrol agent moved faster in the wetter (- 0.03 MPa) than in the drier soil (- 0.1 MPa). These results suggest that temperature is a key factor in determining the potential of P. or.yzihabitans as a biocontrol agent. (C) 2003 Elsevier Science Ltd. All rights reserved.

The value of badger populations and control of tuberculosis in cattle in England and Wales: A note

This note reports on the results of a choice experiment survey of 400 people in England and Wales, conducted to estimate the value that society places on changes to the size of the badger population. The study was undertaken in the context of the possible need to reduce the badger population by culling to help control bovine tuberculosis in cattle. The study found that people were concerned about the problem of bovine tuberculosis in cattle, which was reflected in their willingness to pay to control the disease, and gave a relatively low value to changes in the size of the badger population (within limits). However, people did not like the idea of a policy that intentionally killed large numbers of badgers and had a relatively very high willingness to pay not to have such a policy.