Overview
- Expands upon the study of hereditary systems
- Defines and describes a class of equations popular in modelling systems from many academic disciplines
- Emphasises and explains the uses of optimal estimation, stabilization and control in treating stochastic systems
- Includes supplementary material: sn.pub/extras
Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 17)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (6 chapters)
-
Front Matter
-
Back Matter
Keywords
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 tospecialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering.
Authors and Affiliations
Bibliographic Information
Book Title: Optimal Control of Stochastic Difference Volterra Equations
Book Subtitle: An Introduction
Authors: Leonid Shaikhet
Series Title: Studies in Systems, Decision and Control
DOI: https://doi.org/10.1007/978-3-319-13239-6
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-13238-9Published: 09 December 2014
Softcover ISBN: 978-3-319-38606-5Published: 23 August 2016
eBook ISBN: 978-3-319-13239-6Published: 27 November 2014
Series ISSN: 2198-4182
Series E-ISSN: 2198-4190
Edition Number: 1
Number of Pages: X, 220
Number of Illustrations: 8 illustrations in colour
Topics: Control and Systems Theory, Systems Theory, Control, Calculus of Variations and Optimal Control; Optimization