Numerical Methods for Optimal Control Problems with State Constraints

  • Authors
  • Radosław Pytlak
Book
Part of the Lecture Notes in Mathematics book series (LNM, volume 1707)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Radosław Pytlak
    Pages 1-12
  3. Radosław Pytlak
    Pages 27-53
  4. Radosław Pytlak
    Pages 55-79
  5. Radosław Pytlak
    Pages 81-128
  6. Back Matter
    Pages 169-216

About this book

Introduction

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.

Keywords

Necessary Optimality Conditions Nonlinear Programming Numerical Algorithms Optimal control Optimality Conditions State Constrained Problems algorithms ordinary differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0097244
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66214-3
  • Online ISBN 978-3-540-48662-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book