Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Energy decay for the linear Klein-Gordon equation and boundary control

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

A note on the controllability for the wave equation in nonsmooth plane domains

We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved part of the boundary, while in the straight part we impose homogeneous Dirichlet boundary condition. The initial state has finite energy and the control is square integrable. (c) 2005 Elsevier B.V. All rights reserved.

Focus on opportunities as a boundary condition of the relationship between job control and work engagement: A multi-sample, multi-method study

The concept of focus on opportunities describes how many new goals, options, and possibilities employees believe to have in their personal future at work. In this multi-sample, multi-method study, the authors investigated relationships between focus on opportunities and general and daily work engagement and the moderating role of focus on opportunities on between- and within-person relationships between job control and work engagement. Based on a social cognitive theory framework on the motivating potential of a future temporal focus, it was hypothesized that focus on opportunities is positively related to work engagement. Further, consistent with the notion of compensatory resources, it was expected that job control is not related to work engagement among employees with a high focus on opportunities, whereas job control, as an external resource of the work environment, is positively related to work engagement among employees with a low focus on opportunities. Both a cross-sectional survey study (N=174) and a daily diary study (N=64) supported the hypotheses. The study contributes to research on the job demands-resources model as it emphasizes the role of focus on opportunities as a motivational factor in the relationship between job control and work engagement.

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Shock tunnel experiments on control of shock induced large separation bubble using boundary layer bleed

Shock-Boundary Layer Interaction (SBLI) often occurs in supersonic/hypersonic flow fields. Especially when accompanied by separation (termed strong interaction), the SBLI phenomena largely affect the performance of the systems where they occur, such as scramjet intakes, thus often demanding the control of the interaction. Experiments on the strong interaction between impinging shock wave and boundary layer on a flat plate at Mach 5.96 are carried out in IISc hypersonic shock tunnel HST-2. The experiments are performed at moderate flow total enthalpy of 1.3 MJ/kg and freestream Reynolds number of 4 million/m. The strong shock generated by a wedge (or shock generator) of large angle 30.96 degrees to the freestream is made to impinge on the flat plate at 95 mm (inviscid estimate) from the leading edge, due to which a large separation bubble of length (75 mm) comparable to the distance of shock impingement from the leading edge is generated. The experimental simulation of such large separation bubble with separation occurring close to the leading edge, and its control using boundary layer bleed (suction and tangential blowing) at the location of separation, are demonstrated within the short test time of the shock tunnel (similar to 600 mu s) from time resolved schlieren flow visualizations and surface pressure measurements. By means of suction - with mass flow rate one order less than the mass flow defect in boundary layer - a reduction in separation length by 13.33% was observed. By the injection of an array of (nearly) tangential jets in the direction of mainstream (from the bottom of the plate) at the location of separation - with momentum flow rate one order less than the boundary layer momentum flow defect - 20% reduction in separation length was observed, although the flow field was apparently unsteady. (C) 2014 Elsevier Masson SAS. All rights reserved.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2010 by Sang Lee.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2011 Elsevier Ltd.