Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

An example of active circulation control of the unsteady separated flow past a semi-infinite plate

Active circulation control of the two-dimensional unsteady separated flow past a semiinfinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented

Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information

In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved

A receding horizon generalization of pointwise min-norm controllers

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Measuring device Patent

Expulsion and measuring device for determining quantity of liquid in tank under conditions of weightlessnes

A Dynamical Analysis of the Proposed Circumbinary HW Virginis Planetary System

In 2009, the discovery of two planets orbiting the evolved binary star system HW Virginis was announced, based on systematic variations in the timing of eclipses between the two stars. The planets invoked in that work were significantly more massive than Jupiter, and moved on orbits that were mutually crossing - an architecture which suggests that mutual encounters and strong gravitational interactions are almost guaranteed. In this work, we perform a highly detailed analysis of the proposed HW Vir planetary system. First, we consider the dynamical stability of the system as proposed in the discovery work. Through a mapping process involving 91,125 individual simulations, we find that the system is so unstable that the planets proposed simply cannot exist, due to mean lifetimes of less than a thousand years across the whole parameter space. We then present a detailed re-analysis of the observational data on HW Vir, deriving a new orbital solution that provides a very good fit to the observational data. Our new analysis yields a system with planets more widely spaced, and of lower mass, than that proposed in the discovery work, and yields a significantly greater (and more realistic) estimate of the uncertainty in the orbit of the outermost body. Despite this, a detailed dynamical analysis of this new solution similarly reveals that it also requires the planets to move on orbits that are simply not dynamically feasible. Our results imply that some mechanism other than the influence of planetary companions must be the principal cause of the observed eclipse timing variations for HW Vir. If the sys- tem does host exoplanets, they must move on orbits differing greatly from those previously proposed. Our results illustrate the critical importance of performing dynamical analyses as a part of the discovery process for multiple-planet exoplanetary systems.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ

The Diagnostic Potential of Transition Region Lines under-going Transient Ionization in Dynamic Events

We discuss the diagnostic potential of high cadence ultraviolet spectral data when transient ionization is considered. For this we use high cadence UV spectra taken during the impulsive phase of a solar flares (observed with instruments on-board the Solar Maximum Mission) which showed excellent correspondence with hard X-ray pulses. The ionization fraction of the transition region ion O V and in particular the contribution function for the O V 1371A line are computed within the Atomic Data and Analysis Structure, which is a collection of fundamental and derived atomic data and codes which manipulate them. Due to transient ionization, the O V 1371A line is enhanced in the first fraction of a second with the peak in the line contribution function occurring initially at a higher electron temperature than in ionization equilibrium. The rise time and enhancement factor depend mostly on the electron density. The fractional increase in the O V 1371A emissivity due to transient ionization can reach a factor of 2--4 and can explain the fast response in the line flux of transition regions ions during the impulsive phase of flares solely as a result of transient ionization. This technique can be used to diagnostic the electron temperature and density of solar flares observed with the forth-coming Interface Region Imaging Spectrograph.Comment: 18 pages, 6 figure

Community experiences of organised crime in Scotland

The research explored community experiences of serious organised crime in Scotland (SOC). The report provides information on the nature and extent of the impact of SOC on everyday life in the community, as well as offering suggestions for policy development. The study sought to answer the following questions: 1)What are the relationships that exist between SOC and communities in Scotland? 2)What are the experiences and perceptions of residents, stakeholders and organisations of the scope and nature of SOC within their local area? and 3)How does SOC impact on community wellbeing, and to what extent can the harms associated with SOC be mitigated

A Prototype for the PASS Permanent All Sky Survey

A prototype system for the Permanent All Sky Survey (PASS) project is presented. PASS is a continuous photometric survey of the entire celestial sphere with a high temporal resolution. Its major objectives are the detection of all giant-planet transits (with periods up to some weeks) across stars up to mag 10.5, and to deliver continuously photometry that is useful for the study of any variable stars. The prototype is based on CCD cameras with short focal length optics on a fixed mount. A small dome to house it at Teide Observatory, Tenerife, is currently being constructed. A placement at the antarctic Dome C is also being considered. The prototype will be used for a feasibility study of PASS, to define the best observing strategies, and to perform a detailed characterization of the capabilities and scope of the survey. Afterwards, a first partial sky surveying will be started with it. That first survey may be able to detect transiting planets during its first few hundred hours of operation. It will also deliver a data set around which software modules dealing with the various scientific objectives of PASS will be developed. The PASS project is still in its early phase and teams interested in specific scientific objectives, in providing technical expertise, or in participating with own observations are invited to collaborate.Comment: Accepted for Astronomische Nachrichten (special issue for 3rd Potsdam Thinkshop 'Robotic Astronomy' in July 2004). 4 pages, 4 fig