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Books > Professional & Technical > Electronics & communications engineering > Electronics engineering > Automatic control engineering
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Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems (Paperback, 1st ed. 2020)
Loot Price: R4,376
Discovery Miles 43 760
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Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems (Paperback, 1st ed. 2020)
Series: Communications and Control Engineering
Expected to ship within 10 - 15 working days
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This monograph applies the relative optimization approach to time
nonhomogeneous continuous-time and continuous-state dynamic
systems. The approach is intuitively clear and does not require
deep knowledge of the mathematics of partial differential
equations. The topics covered have the following distinguishing
features: long-run average with no under-selectivity, non-smooth
value functions with no viscosity solutions, diffusion processes
with degenerate points, multi-class optimization with state
classification, and optimization with no dynamic programming. The
book begins with an introduction to relative optimization,
including a comparison with the traditional approach of dynamic
programming. The text then studies the Markov process, focusing on
infinite-horizon optimization problems, and moves on to discuss
optimal control of diffusion processes with semi-smooth value
functions and degenerate points, and optimization of
multi-dimensional diffusion processes. The book concludes with a
brief overview of performance derivative-based optimization. Among
the more important novel considerations presented are: the
extension of the Hamilton-Jacobi-Bellman optimality condition from
smooth to semi-smooth value functions by derivation of explicit
optimality conditions at semi-smooth points and application of this
result to degenerate and reflected processes; proof of
semi-smoothness of the value function at degenerate points;
attention to the under-selectivity issue for the long-run average
and bias optimality; discussion of state classification for time
nonhomogeneous continuous processes and multi-class optimization;
and development of the multi-dimensional Tanaka formula for
semi-smooth functions and application of this formula to stochastic
control of multi-dimensional systems with degenerate points. The
book will be of interest to researchers and students in the field
of stochastic control and performance optimization alike.
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