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Optimal Impulsive Control

The Extension Approach

  • Aram Arutyunov
  • Dmitry Karamzin
  • Fernando Lobo Pereira

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 477)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 1-18
  3. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 19-38
  4. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 39-74
  5. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 75-97
  6. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 99-119
  7. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 121-152
  8. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages 153-172
  9. Aram Arutyunov, Dmitry Karamzin, Fernando Lobo Pereira
    Pages C1-C1
  10. Back Matter
    Pages 173-174

About this book

Introduction

Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. 

The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints.

The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.

Keywords

Optimal Impulsive Control Necessary Conditions of Optimality Maximum Principle Existence Theorems Nonlinear Control Systems State Constraints Mixed Constraints Discontinuous Arcs Generalized Control Second-order Conditions of Optimality Extension of Classical Theory

Authors and affiliations

  • Aram Arutyunov
    • 1
  • Dmitry Karamzin
    • 2
  • Fernando Lobo Pereira
    • 3
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia
  3. 3.FEUP/DEECPorto UniversityPortoPortugal

Bibliographic information

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