{"product_id":"9783030418458","title":"Communications and Control Engineering","description":"\u003ch1\u003eCommunications and Control Engineering\u003c\/h1\u003e \u003ch2\u003eCao, Xi-Ren\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cp\u003eAmong the more important novel considerations presented are:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ethe 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;\u003c\/li\u003e\n\u003cli\u003eproof of semi-smoothness of the value function at degenerate points;\u003c\/li\u003e\n\u003cli\u003eattention to the under-selectivity issue for the long-run average and bias optimality; \u003c\/li\u003e\n\u003cli\u003ediscussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and\u003c\/li\u003e\n\u003cli\u003edevelopment 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.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe book will be of interest to researchers and students in the field of stochastic control andperformance optimization alike.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2020-05-14\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030418458\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-41846-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 365\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":50090667769996,"sku":"9783030418458","price":152.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030418458.jpg?v=1779505722","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030418458","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}