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Optimal Control of Dynamic Systems Driven by Vector Measures - Theory and Applications (Hardcover, 1st ed. 2021)
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Optimal Control of Dynamic Systems Driven by Vector Measures - Theory and Applications (Hardcover, 1st ed. 2021)
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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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