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Optimal Control

  • Leonid T. Aschepkov
  • Dmitriy V.  Dolgy
  • Taekyun Kim
  • Ravi P.  Agarwal

Table of contents

  1. Front Matter
    Pages i-xv
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 3-6
    3. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 7-13
  3. Control of Linear Systems

    1. Front Matter
      Pages 15-15
    2. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 17-39
    3. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 41-61
    4. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 63-75
    5. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 77-90
    6. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 91-100
    7. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 101-106
  4. Control of Nonlinear Systems

    1. Front Matter
      Pages 107-107
    2. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 109-113
    3. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 115-123
    4. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 125-137
    5. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 139-162
    6. Leonid T. Aschepkov, Dmitriy V. Dolgy, Taekyun Kim, Ravi P. Agarwal
      Pages 163-172
  5. Back Matter
    Pages 173-209

About this book

Introduction

This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes.

In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.

Keywords

Optimal Control Linear Systems Non-Linear Systems Cauchy Formula Kalman Theorem Krasovskii Theorem

Authors and affiliations

  • Leonid T. Aschepkov
    • 1
  • Dmitriy V.  Dolgy
    • 2
  • Taekyun Kim
    • 3
  • Ravi P.  Agarwal
    • 4
  1. 1.Far Eastern Federal UniversityDepartment of Mathematics Far Eastern Federal UniversityVladivostokRussia
  2. 2.Far Eastern Federal UniversityDept. of Mathematical Methods in Economy Far Eastern Federal UniversityVladivostokRussia
  3. 3.Dept of MathematicsKwangwoon University Dept of MathematicsSeoulKorea (Republic of)
  4. 4.Mathematics, Rhode Hall 217BTexas A&M University-Kingsville Mathematics, Rhode Hall 217BKingsvilleUSA

Bibliographic information