Control of Coupled Partial Differential Equations

ISBN-13: 9783764377205 / Angielski / Twarda / 2007 / 382 str.

G. Leugering; G]nter Leugering; Karl Kunisch

Opis

The international Conference on Optimal Control of Coupled Systems of Partial Di?erential Equations was held at the Mathematisches Forschungsinstitut Ob- wolfach (www.mfo.de) from April, 17 to 23, 2005. The scienti?c program included 30 talks coveringvarious topics as controllability,feedback-control,optimality s- tems, model-reduction techniques, analysis and optimal control of ?ow problems and ?uid-structure interactions, as well as problems of shape and topology op- mization. The applications discussed during the conference range from the op- mization and control of quantum mechanical systems, the design of piezo-electric acoustic micro-mechanical devices, optimal control of crystal growth, the control of bodies immersed into a ?uid to airfoil design and much more. Thus the app- cations are across all time and length scales. Optimization and control of systems governed by partial di?erential eq- tions and more recently by variational inequalities is a very active ?eld of research in Applied Mathematics, in particular in numerical analysis, scienti?c comp- ing and optimization. In order to able to handle real-world applications, scalable and parallelizable algorithms have to be designed, implemented and validated. This requires an in-depth understanding of both the theoretical properties and the numerical realization of such structural insights. Therefore, a 'core' devel- ment within the ?eld of optimization with PDE-constraints such as the analysis of control-and-state-constrained problems, the role of obstacles, multi-phases etc. and an interdisciplinary 'diagonal' bridging regarding applications and numerical simulation are most important.

Spis treści

Preface.- A Sharp Geometric Condition for the Boundary Exponential Stabilizability of a Square Plate by Moment Feedbacks only.- Local Exponential Stabilization Strategies of the Navier-Stokes Equations, d = 2, 3, via Feedback Stabilization of its Linearization.- Convergence Analysis of an Adaptive Finite Element Method for Distributed Control Problems with Control Constraints.- Optimal Boundary Control in Flood Management.- On Two Numerical Approaches for the Boundary Control Stabilization of Semi-linear Parabolic Systems: A Comparison.- Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation.- Optimal and Model Predictive Control of the Boussinesq Approximation.- Applications of Semi-smooth Newton Methods to Variational Inequalities.- Identification of Nonlinear Coefficients in Hyperbolic PDEs, with Application to Piezoelectricity.- An SQP Active Set Method for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions.- Shape Optimization for Navier-Stokes Equations .- A Family of Stabilization Problems for the Oseen Equations.- Beyond Bilinear Controllability: Applications to Quantum Control.- Optimal Control Problems with Convex Control Constraints.- Control of Moving Domains, Shape Stabilization and Variational Tube Formulations

Blurb

This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005.

With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal control of flow problems, and fluid-structure interactions, as well as problems of shape and topology optimization. Applications affected by these findings are distributed over all time and length scales starting with optimization and control of quantum mechanical systems, the design of piezoelectric acoustic micro-mechanical devices, or optimal control of crystal growth to the control of bodies immersed into a fluid, airfoil design, and much more.

The book addresses advanced students and researchers in optimization and control of infinite dimensional systems, typically represented by partial differential equations. Readers interested either in theory or in numerical simulation of such systems will find this book equally appealing.