The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

A new perspective on warming of the global oceans

Changes in ocean circulation associated with internal climate variability have a major influence on upper ocean temperatures, particularly in regions such as the North Atlantic, which are relatively well-observed and therefore over-represented in the observational record. As a result, global estimates of upper ocean heat content can give misleading estimates of the roles of natural and anthropogenic factors in causing oceanic warming. We present a method to quantify ocean warming that filters out the natural internal variability from both observations and climate simulations and better isolates externally forced air-sea heat flux changes. We obtain a much clearer picture of the drivers of oceanic temperature changes, being able to detect the effects of both anthropogenic and volcanic influences simultaneously in the observed record. Our results show that climate models are capable of capturing in remarkable detail the externally forced component of ocean temperature evolution over the last five decades.

Failure of a control strategy for a hybrid air-conditioning and wind catchers/towers system at Bluewater shopping malls in Kent

Purpose – To evaluate the control strategy for a hybrid natural ventilation wind catchers and air-conditioning system and to assess the contribution of wind catchers to indoor air environments and energy savings if any. Design/methodology/approach – Most of the modeling techniques for assessing wind catchers performance are theoretical. Post-occupancy evaluation studies of buildings will provide an insight into the operation of these building components and help to inform facilities managers. A case study for POE was presented in this paper. Findings – The monitoring of the summer and winter month operations showed that the indoor air quality parameters were kept within the design target range. The design control strategy failed to record data regarding the operation, opening time and position of wind catchers system. Though the implemented control strategy was working effectively in monitoring the operation of mechanical ventilation systems, i.e. AHU, did not integrate the wind catchers with the mechanical ventilation system. Research limitations/implications – Owing to short-falls in the control strategy implemented in this project, it was found difficult to quantify and verify the contribution of the wind catchers to the internal conditions and, hence, energy savings. Practical implications – Controlling the operation of the wind catchers via the AHU will lead to isolation of the wind catchers in the event of malfunctioning of the AHU. Wind catchers will contribute to the ventilation of space, particularly in the summer months. Originality/value – This paper demonstrates the value of POE as indispensable tool for FM professionals. It further provides insight into the application of natural ventilation systems in building for healthier indoor environments at lower energy cost. The design of the control strategy for natural ventilation and air-conditioning should be considered at the design stage involving the FM personnel.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Housing supply and planning controls: the impact of development control processing times on housing supply in England

The National Housing and Planning Advice Unit commissioned Professor Michael Ball of Reading University to undertake empirical research into how long it was taking to obtain planning consent for major housing sites in England. The focus on sites as opposed to planning applications is important because it is sites that generate housing.

The impact of maternal control on children’s anxious cognitions, behaviours and affect: an experimental study

Controlling parenting is associated with child anxiety however the direction of effects remains unclear. The present study implemented a Latin-square experimental design to assess the impact of parental control on children’s anxious affect, cognitions and behaviour. A non-clinical sample of 24 mothers of children aged 4-5 years were trained to engage in (a) controlling and (b) autonomy-granting behaviours in interaction with their child during the preparation of a speech. When mothers engaged in controlling parenting behaviours, children made more negative predictions about their performance prior to delivering their speech and reported feeling less happy about the task, and this was moderated by child trait anxiety. In addition, children with higher trait anxiety displayed a significant increase in observed child anxiety in the controlling condition. The pattern of results was maintained when differences in mothers’ levels of negativity and habitual levels of control were accounted for. These findings are consistent with theories that suggest that controlling parenting is a risk factor in the development of childhood anxiety.