東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Relative optimization of continuous-...

Cao, Xi-Ren.

Linked to FindBook

Google Book

Amazon

博客來

Relative optimization of continuous-time and continuous-state stochastic systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Relative optimization of continuous-time and continuous-state stochastic systems/ by Xi-Ren Cao.
Author:	Cao, Xi-Ren.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xix, 365 p. :ill., digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: Inﬁnite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index.
Contained By:	Springer eBooks
Subject:	Dynamic programming. -
Online resource:	https://doi.org/10.1007/978-3-030-41846-5
ISBN:	9783030418465

Relative optimization of continuous-time and continuous-state stochastic systems
Cao, Xi-Ren.

Relative optimization of continuous-time and continuous-state stochastic systems[electronic resource] /by Xi-Ren Cao. - Cham :Springer International Publishing :2020. - xix, 365 p. :ill., digital ;24 cm. - Communications and control engineering,0178-5354. - Communications and control engineering..

Chapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: Inﬁnite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index.

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.

ISBN: 9783030418465

Standard No.: 10.1007/978-3-030-41846-5doiSubjects--Topical Terms:

641303
Dynamic programming.

LC Class. No.: T57.83 / .C369 2020

Dewey Class. No.: 519.703

Relative optimization of continuous-time and continuous-state stochastic systems
LDR:03350nmm a2200337 a 4500 001 2255248
003 DE-He213
005 20200928170101.0
006 m d
007 cr nn 008maaau
008 220419s2020 sz s 0 eng d
020 $a 9783030418465 $q (electronic bk.)
020 $a 9783030418458 $q (paper)
024 7 $a 10.1007/978-3-030-41846-5 $2 doi
035 $a 978-3-030-41846-5
040 $a GP $c GP
041 0 $a eng
050 4 $a T57.83 $b .C369 2020
072 7 $a TJFM $2 bicssc
072 7 $a TEC004000 $2 bisacsh
072 7 $a TJFM $2 thema
082 0 4 $a 519.703 $2 23
090 $a T57.83 $b .C235 2020
100 1 $a Cao, Xi-Ren. $3 3393597
245 1 0 $a Relative optimization of continuous-time and continuous-state stochastic systems $h [electronic resource] / $c by Xi-Ren Cao.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xix, 365 p. : $b ill., digital ; $c 24 cm.
490 1 $a Communications and control engineering, $x 0178-5354
505 0 $a Chapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: Inﬁnite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index.
520 $a 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.
650 0 $a Dynamic programming. $3 641303
650 0 $a Mathematical optimization. $3 517763
650 1 4 $a Control and Systems Theory. $3 3381515
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Markov model. $3 3411069
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Communications and control engineering. $3 1566566
856 4 0 $u https://doi.org/10.1007/978-3-030-41846-5
950 $a Intelligent Technologies and Robotics (Springer-42732)