About this book
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.
- Book Title Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems
- Series Title Communications and Control Engineering
- Series Abbreviated Title Communicat., Control Engineering
- DOI https://doi.org/10.1007/978-3-030-41846-5
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Springer, Cham
- eBook Packages Intelligent Technologies and Robotics Intelligent Technologies and Robotics (R0)
- Hardcover ISBN 978-3-030-41845-8
- Softcover ISBN 978-3-030-41848-9
- eBook ISBN 978-3-030-41846-5
- Series ISSN 0178-5354
- Series E-ISSN 2197-7119
- Edition Number 1
- Number of Pages XIX, 365
- Number of Illustrations 9 b/w illustrations, 12 illustrations in colour
Control and Systems Theory
Calculus of Variations and Optimal Control; Optimization
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