Online Optimization of Large Scale Systems

ISBN-13: 9783642076336 / Angielski / Miękka / 2010 / 804 str.

Martin Grotschel; Sven O. Krumke; Jorg Rambau

Opis

In its thousands of years of history, mathematics has made an extraordinary ca reer. It started from rules for bookkeeping and computation of areas to become the language of science. Its potential for decision support was fully recognized in the twentieth century only, vitally aided by the evolution of computing and communi cation technology. Mathematical optimization, in particular, has developed into a powerful machinery to help planners. Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. Opti mization is particularly strong if precise models of real phenomena and data of high quality are at hand - often yielding reliable automated control and decision proce dures. But what, if the models are soft and not all data are around? Can mathematics help as well? This book addresses such issues, e. g., problems of the following type: - An elevator cannot know all transportation requests in advance. In which order should it serve the passengers? - Wing profiles of aircrafts influence the fuel consumption. Is it possible to con tinuously adapt the shape of a wing during the flight under rapidly changing conditions? - Robots are designed to accomplish specific tasks as efficiently as possible. But what if a robot navigates in an unknown environment? - Energy demand changes quickly and is not easily predictable over time. Some types of power plants can only react slowly."

Spis treści

I Optimal Control for Ordinary Differential Equations.- Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods.- Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints.- Real-Time Control of an Industrial Robot under Control and State Constraints.- Real-Time Optimal Control of Shape Memory Alloy Actuators in Smart Structures.- Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy.- Real-Time Optimization of DAE Systems.- Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems.- Conflict Avoidance During Landing Approach Using Parallel Feedback Control.- II Optimal Control for Partial Differential Equations.- Optimal Control Problems with a First Order PDE System — Necessary and Sufficient Optimality Conditions.- Optimal Control Problems for the Nonlinear Heat Equation.- Fast Optimization Methods in the Selective Cooling of Steel.- Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements.- Instantaneous Control of Vibrating String Networks.- Modelling, Stabilization, and Control of Flow in Networks of Open Channels.- Optimal Control of Distributed Systems with Break Points.- to Model Based Optimization of Chemical Processes on Moving Horizons.- Multiscale Concepts for Moving Horizon Optimization.- Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column.- Towards Nonlinear Model-Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants.- IV Delay Differential Equations in Medical Decision Support Systems.- Differential Equations with State-Dependent Delays.- Biomathematical Models with State-Dependent Delays for Granulocytopoiesis.- Stochastic Optimization for Operating Chemical Processes under Uncertainty.- A Multistage Stochastic Programming Approach in Real-Time Process Control.- Optimal Control of a Continuous Distillation Process under Probabilistic Constraints.- Adaptive Optimal Stochastic Trajectory Planning.- Stochastic Optimization Methods in Robust Adaptive Control of Robots.- Multistage Stochastic Integer Programs: An Introduction.- Decomposition Methods for Two-Stage Stochastic Integer Programs.- Modeling of Uncertainty for the Real-Time Management of Power Systems.- Online Scheduling of Multiproduct Batch Plants under Uncertainty.- VIII Combinatorial Online Planning in Transportation.- Combinatorial Online Optimization in Real Time.- Online Optimization of Complex Transportation Systems.- Stowage and Transport Optimization in Ship Planning.- IX Real-Time Annealing in Image Segmentation.- Basic Principles of Annealing for Large Scale Non-Linear Optimization.- Multiscale Annealing and Robustness: Fast Heuristics for Large Scale Non-linear Optimization.- Author Index.

O autorze

Prof. Dr. Sven O. Krumke lehrt und forscht an der Technischen Universität Kaiserslautern. Prof. Dr. Dr. h.c. mult. Martin Grötschel, Technische Universität Berlin, Zuse-Institut Berlin (ZIB) und MATHEON.

Blurb

Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. In online optimization the main issue is: incomplete data; and the scientific challenge: How well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In real-time optimization there is an additional requirement, decisions have to be computed very fast, fast in relation to the time frame of the instance we consider. Online and real-time optimization problems occur in all branches of optimization: linear, nonlinear, integer, stochastic. These areas have developed their own techniques but they are addressing the same issues: quality, stability, and robustness of the solutions. To fertilize this emerging topic of optimization theory and to foster cooperation between the different branches of optimization, the Deutsche Forschungsgemeinschaft (DFG) has supported a Priority Programme "Online Optimization of Large Systems". This volume contains "background articles" and "research articles". Background articles are intended to give an overview over the basic theory in the respective area and are accessible to graduate math students. Research articles summarize the progress in a project achieved in the Priority Programme.