On the structured distance to uncontrollability

This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the μ-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate that the structured distance can differ from the standard, unstructured distance to uncontrollability by an arbitrary amount. It is also shown how systems of higher order can be addressed. © 2008 Elsevier B.V. All rights reserved

Approximate controllability and observability measures in control systems design

The selection of systems of inputs and outputs (input and output structure) forms part of early system design, which is important since it preconditions the potential for control design. Existing methodologies for input, output structure selection rely on criteria expressing distance from uncontrollability (unobservability). The thesis introduces novel measures for evaluating and estimating the distance to uncontrollability and relatively unobservability. At first, the modal measuring approach is studied in detail, providing a framework for the ”best” structure selection. Although controllability (observability) is invariant under state feedback (output injection), the corresponding degrees expressing distance from uncontrollability (unobservability) are not. Hence, the thesis introduces new criteria for the distance problem from uncontrollability (unobservability) which is invariant under feedback transformations. The approach uses the restricted input-state (state-output) matrix pencil and then deploys exterior algebra that reduces the overall problem to the standard problem of distance of a set of polynomials from non-coprimeness. Results on the distance of the Sylvester Resultants from singularity provide the new measures. Since distance to singularity of the corresponding Sylvester matrix is the key in evaluating the distance to uncontrolability it is of the particular interest in the present work. In order to find the solution two novel methods are introduced in the thesis, namely the alternating projection algorithm and a structured singular value approach. A least-squares alternating projection algorithm, motivated by a factorisation result involving the Sylvester resultant matrix, is proposed for calculating the ”best” approximate GCD of a coprime polynomial set. The properties of the proposed algorithm are investigated and the method is compared with alternative optimisation techniques which can be employed to solve the problem. It is also shown that the problem of an approximate GCD calculation is equivalent tothe solution of a structured singular value (µ) problem arising in robust control for which numerous techniques are available. Motivated by the powerful concept of the structured singular values, the proposed method is extended to the special case of an implicit system that has a wide application in the behavioural analysis of complex systems. Moreover, µ-value approach has a potential application for the general distance problem to uncontrollability that is numerically hard to obtain. Overall, the proposed framework significantly simplifies and generalises the input-output structure selection procedure and evaluates alternative solutions for a variety of distance problems that appear in Control Theory

Decay rate estimations for linear quadratic optimal regulators

Let $u(t)=-Fx(t)$ be the optimal control of the open-loop system $x'(t)=Ax(t)+Bu(t)$ in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the closed-loop system $x'(t)=(A-BF)x(t)$. Main attention is given to the case of a skew-Hermitian matrix $A$. Given an operator $A$, for a class of cases, we find a matrix $B$ that provides an almost optimal decay rate. We show how our results can be applied to the problem of optimizing the decay rate for a large finite collection of control systems $(A, B_j)$, $j=1, \dots, N$, and illustrate this on an example of a concrete mechanical system. At the end of the article, we pose several questions concerning the decay rates in the context of linear quadratic optimization and in a more general context of the pole placement problem.Comment: 25 pages, 1 figur

The Moderating Role of Service Design Attributes in Females’ Fear of Crime in the Underground

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonA great number of female passengers appear to feel fear of crime in underground railways and appear to be affected by the problem in terms of their frequency of use of the underground service, compared to males. However, although it has been dealt with as a problem to be ameliorated in the underground by Transport for London (TFL), how the service is designed to affect their fear and what factors should be taken into account in underground service design to alleviate fear of crime have not been fully answered to date. This research, therefore, aims to identify the influential factors of service design of the underground on female users’ fear of crime by investigating the features and their configurations of the London Underground service, which mediate the user groups’ fear. In order to identify the influential design attributes of the London Underground, which mediate female users’ fear of crime in situations, first, literature on emotion and fear, gender and sex, and service design and the elements of service are reviewed to find the intersection among the research domains. Based on the theoretical foundation, two user studies are designed to identify the role of female users’ gender in the underground and the influential factors of the underground service on the groups’ fear. Thirty one female user interviews are accordingly conducted and analysed in an ‘abductive’ manner. As a result, the mechanisms of female users’ fear of crime in the underground are revealed and the service design attributes in the mechanism are identified. Consequently, a conceptual model of the influential factors of service design on female users’ fear of crime is developed

Gateway to offending behaviour: permission-giving thoughts of online users of child sexual exploitation material.

The endorsement of permission-giving thoughts, or so-called cognitive distortions, has been discussed as a contributing factor in sexually abusive behaviour. The current study set out to explore the thinking patterns of offenders who have used/downloaded child sexual exploitation material (CSEM), based on a survey of professionals. A thematic analysis elicited four overarching themes, namely the Perceived Nature of Children (perception of children portrayed in CSEM, as well as children in general), Non-sexual Engagement with CSEM (motivating factors that are not inherently sexual in nature), Denial of Harm (perception of the level of harm caused by CSEM), and Expression of a General Sexual Preference (general interest in deviant sexual behaviour). These themes aid to explore the differences and similarities between contact and non-contact offenders and to improve the understanding of the role of permission-giving thoughts in this offending. Results are discussed in terms of their theoretical significance and future implications

Approximate zero polynomials of polynomial matrices and linear systems

This paper introduces the notions of approximate and optimal approximate zero polynomial of a polynomial matrix by deploying recent results on the approximate GCD of a set of polynomials Karcaniaset al. (2006) 1 and the exterior algebra Karcanias and Giannakopoulos (1984) 4 representation of polynomial matrices. The results provide a new definition for the "approximate", or "almost" zeros of polynomial matrices and provide the means for computing the distance from non-coprimeness of a polynomial matrix. The computational framework is expressed as a distance problem in a projective space. The general framework defined for polynomial matrices provides a new characterization of approximate zeros and decoupling zeros Karcanias et al. (1983) 2 and Karcanias and Giannakopoulos (1984) 4 of linear systems and a process leading to computation of their optimal versions. The use of restriction pencils provides the means for defining the distance of state feedback (output injection) orbits from uncontrollable (unobservable) families of systems, as well as the invariant versions of the "approximate decoupling polynomials". The overall framework that is introduced provides the means for introducing measures for the distance of a system from different families of uncontrollable, or unobservable systems, which may be feedback dependent, or feedback invariant as well as the notion of "approximate decoupling polynomials"

The role of metacognition in self-critical rumination: an investigation in individuals presenting with low self-esteem

Background: No research, to date, has directly investigated the role of metacognition in self-critical rumination and low self-esteem. Aim: To investigate the presence of metacognitive beliefs about self-critical rumination; the goal of self-critical rumination and its stop signal; and the degree of detachment from intrusive self-critical thoughts. Method: Ten individuals reporting both a self-acknowledged tendency to judge themselves critically and having low self-esteem were assessed using metacognitive profiling, a semi-structured interview. Results: All participants endorsed both positive and negative metacognitive beliefs about self-critical rumination. Positive metacognitive beliefs concerned the usefulness of self-critical rumination as a means of improving cognitive performance and enhancing motivation. Negative metacognitive beliefs concerned the uncontrollability of self-critical rumination and its negative impact on mood, motivation and perception of self-worth. The primary goal of engaging in self-critical rumination was to achieve a better or clearer understanding of a given trigger situation or to feel more motivated to resolve it. However, only four participants were able to identify when this goal had been achieved, which was if the trigger situation were not to occur again. Participants unanimously stated that they were either unable to detach from their self-critical thoughts or could do so some of the time with varying degrees of success. More often than not, though, self-critical thoughts were viewed as facts, would rarely be seen as distorted or biased, and could take hours or days to dissipate. Conclusions: These findings provide preliminary evidence that specific facets of metacognition play a role in the escalation and perseveration of self-critical rumination