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.
