Optimal Control of Stochastic Difference Volterra Equations

An Introduction

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Technology, Automation
Cover of the book Optimal Control of Stochastic Difference Volterra Equations by Leonid Shaikhet, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Leonid Shaikhet ISBN: 9783319132396
Publisher: Springer International Publishing Publication: November 27, 2014
Imprint: Springer Language: English
Author: Leonid Shaikhet
ISBN: 9783319132396
Publisher: Springer International Publishing
Publication: November 27, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book A Practical Introduction to Fuzzy Logic using LISP by Leonid Shaikhet
Cover of the book Climate Actions by Leonid Shaikhet
Cover of the book Interactivity, Collaboration, and Authoring in Social Media by Leonid Shaikhet
Cover of the book Adversary Detection For Cognitive Radio Networks by Leonid Shaikhet
Cover of the book Parallel Robots With Unconventional Joints by Leonid Shaikhet
Cover of the book Arabic Science Fiction by Leonid Shaikhet
Cover of the book Early Modern Humanism and Postmodern Antihumanism in Dialogue by Leonid Shaikhet
Cover of the book Human Nature and the Causes of War by Leonid Shaikhet
Cover of the book Current Controversies in Cancer Care for the Surgeon by Leonid Shaikhet
Cover of the book Evaluating Investments in Health Care Systems by Leonid Shaikhet
Cover of the book Introduction to the Theory of Lie Groups by Leonid Shaikhet
Cover of the book Sensing and Control for Autonomous Vehicles by Leonid Shaikhet
Cover of the book Hypervelocity Launchers by Leonid Shaikhet
Cover of the book The Human Body and Weightlessness by Leonid Shaikhet
Cover of the book Sovereign Debt Crises and Negotiations in Brazil and Mexico, 1888-1914 by Leonid Shaikhet
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy