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Generalized Adjoint Systems

  • Demetrios Serakos

Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Demetrios Serakos
    Pages 1-3
  3. Demetrios Serakos
    Pages 5-11
  4. Demetrios Serakos
    Pages 17-19
  5. Demetrios Serakos
    Pages 21-26
  6. Demetrios Serakos
    Pages 45-46
  7. Demetrios Serakos
    Pages 47-53
  8. Demetrios Serakos
    Pages 55-56
  9. Back Matter
    Pages 57-66

About this book

Introduction

This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Then properties of the generalized adjoint map are derived. Afterward the author demonstrates that the inverse of an input-output system may be represented in terms of the generalized adjoint. The use of generalized adjoints to determine bounds for undesired inputs such as noise and disturbance to an input-output system is presented and methods which parallel adjoints in linear systems theory are utilized. Finally, an illustrative example is presented which utilizes an integral operator representation for the system mapping.

Keywords

Systems theory Theorems of Hahn-Banach type adjoint methods disturbances and noise input-output systems nonlinear analysis

Authors and affiliations

  • Demetrios Serakos
    • 1
  1. 1.DahlgrenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16652-0
  • Copyright Information Demetrios Serakos 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16651-3
  • Online ISBN 978-3-319-16652-0
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • Buy this book on publisher's site