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An Introduction to Optimal Control Theory - The Dynamic Programming Approach (Hardcover, 1st ed. 2023)
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An Introduction to Optimal Control Theory - The Dynamic Programming Approach (Hardcover, 1st ed. 2023)
Series: Texts in Applied Mathematics, 76
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This book introduces optimal control problems for large families of
deterministic and stochastic systems with discrete or continuous
time parameter. These families include most of the systems studied
in many disciplines, including Economics, Engineering, Operations
Research, and Management Science, among many others. The main
objective is to give a concise, systematic, and reasonably self
contained presentation of some key topics in optimal control
theory. To this end, most of the analyses are based on the dynamic
programming (DP) technique. This technique is applicable to almost
all control problems that appear in theory and applications. They
include, for instance, finite and infinite horizon control problems
in which the underlying dynamic system follows either a
deterministic or stochastic difference or differential equation. In
the infinite horizon case, it also uses DP to study undiscounted
problems, such as the ergodic or long-run average cost. After a
general introduction to control problems, the book covers the topic
dividing into four parts with different dynamical systems: control
of discrete-time deterministic systems, discrete-time stochastic
systems, ordinary differential equations, and finally a general
continuous-time MCP with applications for stochastic differential
equations. The first and second part should be accessible to
undergraduate students with some knowledge of elementary calculus,
linear algebra, and some concepts from probability theory (random
variables, expectations, and so forth). Whereas the third and
fourth part would be appropriate for advanced undergraduates or
graduate students who have a working knowledge of mathematical
analysis (derivatives, integrals, ...) and stochastic processes.
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