In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.

Abstract Date: 2017-06-05 Level: Master thesis in Business Administration, 15 cr Institution: School of Business, Society and Engineering, Mälardalen University Authors:                             Nilsson, Isabella                  Ulriksson, Jennifer                                            920507                                930119 Title: Connection versus Recovery? Communication technology in the modern working life.  Tutor: Magnus Hoppe Keywords: Smartphones, Information and communication technology, Boundary control, Psychological detachment, Work-Life Conflict, Stress, Job-Demand-Control. Research question: How do managers handle the positive and negative effects of communication technology? Purpose: The aim of this study is to critically analyse how managers in Sweden regulate the use of communication technology and how they perceive the effects of communication technology on the modern workplace. This contributes to an understanding regarding whether communication technology should be handled based on individuals being either digitally connected or able to mentally recover from work. Method: This study is of a qualitative approach, where semi-structured interviews were conducted with eight managers who is/ or has been, in charge of personnel. The study has a deductive approach and thus has its base in theory. Theories have consequently been used in the construction of the interview questions as well as in the creation of Modell 1.0. Conclusion: Policies restricting the use of communication technology is not desirable according to managers, this is due to it being a prerequisite for the working life of 2017. ‘Connection’ and ‘recovery’ are not dichotomies for all employees. Policies can be of use for employees who need help managing the boundaries between work and family. However, to reach a solution regarding the negative effects of communication technology, efforts should be put into the organizational culture rather than policies, which is depicted in Model 2.0. In that way, negative effects of communication technology can be fought off without risking the positive effects. Communication technology should not be handled based on the assumption that individuals are either digitally connected or able to mentally recover from work.

We present a linear-quadratic regulator (LQR) design for a heat transfer model describing the cooling process of steel profiles in a rolling mill. Primarily we consider a feedback control approach for a linearization of the nonlinear model given there, but we will also present first ideas how to use local (in time) linearizations to treat the nonlinear equation with a regulator approach. Numerical results based on a spatial finite element discretization and a numerical algorithm for solving large-scale algebraic Riccati equations are presented both for the linear and nonlinear models.

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.

Doctor of Philosophy / Psychological Sciences / Patrick A. Knight / Satisfaction with work-family balance is a relatively new construct that differs from other work-life constructs in several ways: it is not focused on conflict between work/family domains, does not include cross-domain transfer processes, has no directional implications, and is not multidimensional. The current study has three purposes: 1. Examine work-family balance issues for both blue-collar and white-collar employees, as the literature has focused mainly on white-collar employees. 2. Examine relationship between technology and satisfaction with work-family balance. 3. Assess how role salience influences satisfaction with work-family balance. Participants were recruited and compensated for completing a 60 item online survey via Qualtrics. Blue-collar participants were recruited from manufacturing industries, while no industry was specified for white-collar employees. The sample consisted of 210 participants (105 blue-collar, 105 white-collar). Several checks were included throughout the survey to ensure data quality. Two hierarchical regression analyses were conducted. The first regression revealed that boundary control and autonomy predict satisfaction with work-family balance, while employee type and boundary interruptions do not. Boundary control, family identity, and stress significantly predicted satisfaction with work-family balance in the second regression, while boundary interruptions, work identity, hours worked, and technology use did not. Results indicate white-collar workers have higher satisfaction with work-family balance, lower stress, and lower turnover intentions compared to blue-collar workers. Results also reveal that technology use to complete work outside of work hours is significantly and positively related to stress. Nearly half of participants report feeling expected to utilize technology to complete work outside of work hours. In addition, while it was hypothesized that those higher on family identity would have lower satisfaction with work-family balance when they used technology outside of work hours, worked longer hours, and had more frequent boundary interruptions than would those lower on family identity, the opposite effect was found for each of these variables. Implications of the study include: 1. Organizations may improve employee satisfaction with work-family balance by increasing autonomy and boundary control. 2. Employees may improve satisfaction with work-family balance by taking time to de-stress from work and limiting use of technology to complete work outside of work hours.

In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.

In the Swedish labor market, it has become more common that employees, with an office-based workplace, themselves decide when, where and how their work takes place. This flexibility results in a situation where the borders between work and private life become blurred and the work can therefore be described as flexible. The purpose of the study was to examine and analyze flexible work-life from a coworker perspective, its' perceived possibilities and challenges and consequences for work life balance. A qualitative study with semi-structured interviews was conducted among coworkers in different trades in the Swedish labor market. The results showed a wide range of possibilities and challenges with flexible work conditions. Flexible work-life opportunities revealed to promote those with family responsibility, not least single parents. The flexible work-way also opened up the possibility to recover and enhanced wellbeing, but could also result in negative consequences such as perceived stress. The wellbeing and the experienced work-life balance has shown to be affected by work demands, the degree of control and the work experience. Therefore, has it been of great importance that the coworkers get enough support and help to find functional strategies to be able to draw a line between work and leisure. / På den svenska arbetsmarknaden är det allt mer vanligt att medarbetare med kontorsbaserade yrken själva får utforma när, var och hur arbetet ska utföras. Den flexibiliteten medför att gränserna mellan arbete och privatliv suddas ut och arbetet kan därmed beskrivas som gränslöst. Syftet med studien var att undersöka och analysera gränslöst arbete ur ett medarbetarperspektiv. Studien utgick från frågeställningar som berör medarbetares erfarenheter av gränslöst arbete, dess möjligheter och utmaningar samt hur det påverkar balansen mellan arbete och fritid. En kvalitativ ansats med semistrukturerade intervjuer som datainsamlingsmetod användes bland medarbetare inom olika branscher på den svenska arbetsmarknaden. Studiens resultat visade på en rad olika möjligheter och utmaningar med gränslösa arbetsförhållanden. Det flexibla arbetssättet visade sig bland annat underlätta för de med familjeansvar, inte minst för ensamstående föräldrar. Det gränslösa arbetssättet visade sig också främja möjligheten till återhämtning och ökat välmående, men riskerade även att resultera i negativa följder såsom upplevd stress. Välmåendet och den upplevda balansen mellan arbete och privatliv, även kallat work-life balance, påverkades av arbetskrav, graden av kontroll och arbetslivserfarenhet. Därför har det varit av stor vikt att medarbetarna har stöd och får vägledning att hitta fungerande strategier för att kunna dra en gräns mellan arbete och privatliv.

Dans cette thèse, nous étudions la synchronisation, qui est un phénomène bien répandu dans la nature. Elle a été observée pour la première fois par Huygens en 1665. En se basant sur les résultats de la contrôlabilité frontière exacte, pour un système couplé d’équations des ondes avec des contrôles frontières de Neumann, nous considérons la synchronisation frontière exacte (par groupes), ainsi que la détermination de l’état de synchronisation. Ensuite, nous considérons la contrôlabilité exacte et la synchronisation exacte (par groupes) pour le système couplé avec des contrôles frontières couplés de Robin. A cause du manque de régularité de la solution, nous rencontrons beaucoup plus de difficultés. Afin de surmonter ces difficultés, on obtient un résultat sur la trace de la solution faible du problème de Robin grâce aux résultats de régularité optimale de Lasiecka-Triggiani sur le problème de Neumann. Ceci nous a permis d’établir la contrôlabilité exacte, et, par la méthode de la perturbation compacte, la non-contrôlabilité exacte du système. De plus, nous allons étudier la détermination de l’état de synchronisation, ainsi que la nécessité des conditions de compatibilité des matrices de couplage. / This thesis studies the widespread natural phenomenon of synchronization, which was first observed by Huygens en 1665. On the basis of the results on the exact boundary controllability, for a coupled system of wave equations with Neumann boundary controls, we consider its exact boundary synchronization (by groups), as well as the determination of the state of synchronization. Then, we consider the exact boundary controllability and the exact boundary synchronization (by groups) for the coupled system with coupled Robin boundary controls. Due to difficulties from the lack of regularity of the solution, we have to face a bigger challenge. In order to overcome this difficulty, we take advantage of the regularity results for the mixed problem with Neumann boundary conditions (Lasiecka and Triggiani) to discuss the exact boundary controllability, and by the method of compact perturbation, to obtain the non-exact controllability for the system.