Numerical Methods for Optimal Control Problems with State Constraints

1999
ISBN: 978-3-540-66214-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1707, 218 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 367 g

Reihe: Lecture Notes in Mathematics

While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.

Zielgruppe

Research

Autoren/Hrsg.

Pytlak, Radoslaw

Fachgebiete

• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Operations Research Spieltheorie

Inhaltsverzeichnis

Estimates on solutions to differential equations and their approximations.- First order method.- Implementation.- Second order method.- Runge-Kutta based procedure for optimal control of differential— Algebraic Equations.