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This book offers the first comprehensive presentation of
measure-valued solutions for nonlinear deterministic and stochastic
evolution equations on infinite dimensional Banach spaces. Unlike
traditional solutions, measure-valued solutions allow for a much
broader class of abstract evolution equations to be addressed,
providing a broader approach. The book presents extensive results
on the existence of measure-valued solutions for differential
equations that have no solutions in the usual sense. It covers a
range of topics, including evolution equations with
continuous/discontinuous vector fields, neutral evolution equations
subject to vector measures as impulsive forces, stochastic
evolution equations, and optimal control of evolution equations.
The optimal control problems considered cover the existence of
solutions, necessary conditions of optimality, and more,
significantly complementing the existing literature. This book will
be of great interest to researchers in functional analysis, partial
differential equations, dynamic systems and their optimal control,
and their applications, advancing previous research and providing a
foundation for further exploration of the field.
This book is devoted to the development of optimal control theory
for finite dimensional systems governed by deterministic and
stochastic differential equations driven by vector measures. The
book deals with a broad class of controls, including regular
controls (vector-valued measurable functions), relaxed controls
(measure-valued functions) and controls determined by vector
measures, where both fully and partially observed control problems
are considered. In the past few decades, there have been remarkable
advances in the field of systems and control theory thanks to the
unprecedented interaction between mathematics and the physical and
engineering sciences. Recently, optimal control theory for dynamic
systems driven by vector measures has attracted increasing
interest. This book presents this theory for dynamic systems
governed by both ordinary and stochastic differential equations,
including extensive results on the existence of optimal controls
and necessary conditions for optimality. Computational algorithms
are developed based on the optimality conditions, with numerical
results presented to demonstrate the applicability of the
theoretical results developed in the book. This book will be of
interest to researchers in optimal control or applied functional
analysis interested in applications of vector measures to control
theory, stochastic systems driven by vector measures, and related
topics. In particular, this self-contained account can be a
starting point for further advances in the theory and applications
of dynamic systems driven and controlled by vector measures.
This book is devoted to the development of optimal control theory
for finite dimensional systems governed by deterministic and
stochastic differential equations driven by vector measures. The
book deals with a broad class of controls, including regular
controls (vector-valued measurable functions), relaxed controls
(measure-valued functions) and controls determined by vector
measures, where both fully and partially observed control problems
are considered. In the past few decades, there have been remarkable
advances in the field of systems and control theory thanks to the
unprecedented interaction between mathematics and the physical and
engineering sciences. Recently, optimal control theory for dynamic
systems driven by vector measures has attracted increasing
interest. This book presents this theory for dynamic systems
governed by both ordinary and stochastic differential equations,
including extensive results on the existence of optimal controls
and necessary conditions for optimality. Computational algorithms
are developed based on the optimality conditions, with numerical
results presented to demonstrate the applicability of the
theoretical results developed in the book. This book will be of
interest to researchers in optimal control or applied functional
analysis interested in applications of vector measures to control
theory, stochastic systems driven by vector measures, and related
topics. In particular, this self-contained account can be a
starting point for further advances in the theory and applications
of dynamic systems driven and controlled by vector measures.
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