Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs - and the requirement for rapid solution - pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Despite difficulties, there is a pressing need to capitalize on continuing advances in computing power to develop optimization methods that will replace simple rule-based decision making with optimized decisions based on complex PDE simulations.
Lorenz T. Biegler is the Bayer Professor of Chemical Engineering at Carnegie Mellon University. Omar Ghattas is the John A. and Katherine G. Jackson Chair in Computational Geosciences at the University of Texas at Austin. Matthias Heinkenschloss is Professor of Computational and Applied Mathematics at Rice University. David E. Keyes is the Fu Foundation Professor of Applied Mathematics at Columbia University. Bart van Bloemen Waanders is Principal Member of the Technical Staff at Sandia National Laboratories.
Preface; Part I. Concepts and Properties of Real-Time, Online Strategies: 1. Constrained optimal feedback control for DAE; 2. A stabilizing real-time implementation of NMPC; 3. Numerical feedback controller design for PDE systems using model reduction: techniques and case studies; 4. Least-squares methods for optimization; Part II. Fast PDE-Constrained Optimization Solvers: 5. Space-time multigrid methods for solving unsteady optimal control problem; 6. A time-parallel implicit methodology for the near-real-time solution of systems of linear oscillators; 7. Generalized SQP-methods with 'parareal' time-domain decomposition for time-dependent PDE-constrained optimization; 8. Simultaneous pseudo-timestepping for state constrained optimization problems in aerodynamics; 9. The effect of the digital filter stepsize control on control optimization performance; Part III. Reduced Order Modeling: 10. Certified rapid solution of partial differential equations for real-time parameter estimation and optimization; 11. WillcoxMOR; 12. Feedback control of flow separation; Part IV. Applications: 13. Shape and topological sensitivity; 14. COFIR: Coarse and fine image registration; 15. Real-time, large scale optimization of water network systems using a subdomain approach; Index.
