Multicriteria Optimization With Uncertainty In The Dynamics
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Multicriteria Optimization with Uncertainty in the Dynamics
Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. It is assumed that nature chooses the uncertainty, subject to bounds, to maximize the performance index which the controller attempts to minimize. Using Pareto optimality as the optimality criterion, sufficient conditions for an optimal solution are presented. The conditions also suggest a technique for determining the optimal control. The results are illustrated with an example. (Author).
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Multicriteria Optimization
Author: Matthias Ehrgott
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
Life is about decisions. Decisions, no matter if made by a group or an indi vidual, involve several conflicting objectives. The observation that real world problems have to be solved optimally according to criteria, which prohibit an "ideal" solution - optimal for each decision-maker under each of the criteria considered - has led to the development of multicriteria optimization. From its first roots, which where laid by Pareto at the end of the 19th century the discipline has prospered and grown, especially during the last three decades. Today, many decision support systems incorporate methods to deal with conflicting objectives. The foundation for such systems is a mathematical theory of optimization under multiple objectives. Fully aware of the fact that there have been excellent textbooks on the topic before, I do not claim that this is better text, but it has a has a consid erably different focus. Some of the available books develop the mathematical background in great depth, such as [SNT85, GN90, Jah86). Others focus on a specific structure of the problems covered as [Zel74, Ste85, Mie99) or on methodology [Yu85, CH83a, HM79). Finally there is the area of multicriteria decision aiding [Roy96, Vin92, KR93), the main goal of which is to help deci sion makers find the final solution (among many "optimal" ones) eventually to be implemented.