Optimal Control of Stochastic Difference Volterra Equations

An Introduction

  • Leonid Shaikhet

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 17)

Table of contents

  1. Front Matter
    Pages i-x
  2. Leonid Shaikhet
    Pages 13-55
  3. Leonid Shaikhet
    Pages 79-125
  4. Leonid Shaikhet
    Pages 127-158
  5. Back Matter
    Pages 207-220

About this book


This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools.

The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations.

Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed.

Integrating the author’s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.


Difference Volterra Equations Optimal Control Optimal Estimation Optimal Stabilization Stochastic Hereditary Systems

Authors and affiliations

  • Leonid Shaikhet
    • 1
  1. 1.Department of Higher MathematicsDonetsk State University of ManagementDonetskUkraine

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-13238-9
  • Online ISBN 978-3-319-13239-6
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • Buy this book on publisher's site
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