Relative Optimization of Continuous-Time and Continuous-State Stochastic Systems
€ 172,90
Informação do Produto
| ISBN | 9783030418458 |
|---|---|
| Autores | Xi-Ren Cao |
| Editora | Springer Nature Switzerland AG |
| Formato | Capa dura |
| Número de páginas | 365 |
| Peso (kg) | 0,796 |
| Data de Publicação | 14/05/2020 |
| Preço (iva excl.) | € 163,11 |
| Imposto | € 9,79 |
| Preço (iva inc.) | € 172,90 |
| Disponibilidade | 1 unidade em armazém externo |
Descrição do Produto
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; anddevelopment 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 andperformance optimization alike.