The Robust Maximum Principle

Theory and Applications

  • Vladimir G. Boltyanski
  • Alexander S. Poznyak
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Vladimir G. Boltyanski, Alexander S. Poznyak
    Pages 1-6
  3. Topics of Classical Optimal Control

    1. Front Matter
      Pages 7-7
    2. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 9-43
    3. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 45-69
    4. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 71-118
    5. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 119-128
  4. The Tent Method

    1. Front Matter
      Pages 129-129
  5. Tent Method

    1. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 131-147
    2. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 149-188
  6. Robust Maximum Principle for Deterministic Systems

    1. Front Matter
      Pages 189-189
  7. Robust Maximum Principle for Deterministic Systems

    1. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 191-211
    2. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 213-228
    3. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 229-251
    4. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 253-267
    5. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 269-283
    6. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 285-306
    7. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 307-339
  8. Robust Maximum Principle for Stochastic Systems

    1. Front Matter
      Pages 341-341
  9. Robust Maximum Principle for Stochastic Systems

    1. Vladimir G. Boltyanski, Alexander S. Poznyak
      Pages 343-376

About this book

Introduction

Both refining and extending previous publications by the authors, the material in this monograph has been class-tested in mathematical institutions throughout the world. Covering some of the key areas of optimal control theory (OCT)—a rapidly expanding field that has developed to analyze the optimal behavior of a constrained process over time—the authors use new methods to set out a version of OCT’s more refined ‘maximum principle’ designed to solve the problem of constructing optimal control strategies for uncertain systems where some parameters are unknown. Referred to as a ‘min-max’ problem, this type of difficulty occurs frequently when dealing with finite uncertain sets.

The text begins with a standalone section that reviews classical optimal control theory, covering the principal topics of the maximum principle and dynamic programming and considering the important sub-problems of linear quadratic optimal control and time optimization. Moving on to examine the tent method in detail, the book then presents its core material, which is a more robust maximum principle for both deterministic and stochastic systems. The results obtained have applications in production planning, reinsurance-dividend management, multi-model sliding mode control, and multi-model differential games.

Key features and topics include:

* A version of the tent method in Banach spaces

* How to apply the tent method to a generalization of the Kuhn-Tucker Theorem as well as the Lagrange Principle for infinite-dimensional spaces

* A detailed consideration of the min-max linear quadratic (LQ) control problem

* The application of obtained results from dynamic programming derivations to multi-model sliding mode control and multi-model differential games

* Two examples, dealing with production planning and reinsurance-dividend management, that illustrate the use of the robust maximum principle in stochastic systems

Using powerful new tools in optimal control theory, The Robust Maximum Principle explores material that will be of great interest to post-graduate students, researchers, and practitioners in applied mathematics and engineering, particularly in the area of systems and control.

Keywords

Banach spaces Feynman–Kac formula Kuhn–Tucker Theorem Lagrange principle Riccati differential equation deterministic systems dynamic programming methods linear quadratic control maximum robust principle min-max problem optimal control theory robust maximum principle stochastic systems tent method viscosity solutions

Authors and affiliations

  • Vladimir G. Boltyanski
    • 1
  • Alexander S. Poznyak
    • 2
  1. 1.CIMATGuanajuatoMexico
  2. 2., Automatic Control DepartmentCINVESTAV-IPN, AP-14-740MéxicoMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8152-4
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8151-7
  • Online ISBN 978-0-8176-8152-4