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

Maximum principle and dynamic progra...

Sun, Bing.

Linked to FindBook

Google Book

Amazon

博客來

Maximum principle and dynamic programming viscosity solution approach = from open-loop to closed-loop /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Maximum principle and dynamic programming viscosity solution approach/ by Bing Sun, Bao-Zhu Guo, Zhen-Zhen Tao.
Reminder of title:	from open-loop to closed-loop /
Author:	Sun, Bing.
other author:	Guo, Bao-Zhu.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xiii, 444 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	- 1. Mathematical Preliminary -- Part I: Open-Loop Control -- 2. Dubovitskii-Milyutin Approach -- 3. Spectral Method -- Part II: Closed-Loop Control -- 4. Dynamic Programming Viscosity Solution Approach -- 5. Multiple Algorithms for DPVS Approach.
Contained By:	Springer Nature eBook
Subject:	Control theory. -
Online resource:	https://doi.org/10.1007/978-981-96-5739-1
ISBN:	9789819657391

Maximum principle and dynamic programming viscosity solution approach = from open-loop to closed-loop /
Sun, Bing.

Maximum principle and dynamic programming viscosity solution approachfrom open-loop to closed-loop /[electronic resource] :by Bing Sun, Bao-Zhu Guo, Zhen-Zhen Tao. - Singapore :Springer Nature Singapore :2025. - xiii, 444 p. :ill. (some col.), digital ;24 cm. - Systems & control: foundations & applications,2324-9757. - Systems & control: foundations & applications..

- 1. Mathematical Preliminary -- Part I: Open-Loop Control -- 2. Dubovitskii-Milyutin Approach -- 3. Spectral Method -- Part II: Closed-Loop Control -- 4. Dynamic Programming Viscosity Solution Approach -- 5. Multiple Algorithms for DPVS Approach.

This book is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs). The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin's maximum principle and the Bellman dynamic programming principle based on the notion of viscosity solution. The Bellman dynamic programming method can produce the optimal control in feedback form, making it more appealing for online implementations and robustness. The determination of the optimal feedback control law is of fundamental importance in optimal control and can be argued as the Holy Grail of control theory. The book is organized into five chapters. Chapter 1 presents necessary mathematical knowledge. Chapters 2 and 3 (Part 1) focus on the open-loop control while Chapter 4 and 5 (Part 2) focus on the closed-loop control. In this monograph, we incorporate the notion of viscosity solution of PDE with dynamic programming approach. The dynamic programming viscosity solution (DPVS) approach is then used to investigate optimal control problems. In each problem, the optimal feedback law is synthesized and numerically demonstrated. The last chapter presents multiple algorithms for the DPVS approach, including an upwind finite-difference scheme with the convergence proof. It is worth noting that the dynamic systems considered are primarily of technical or biologic origin, which is a highlight of the book. This book is systematic and self-contained. It can serve the expert as a ready reference for control theory of infinite-dimensional systems. These chapters taken together would also make a one-semester course for graduate with first courses in PDE-constrained optimal control.

ISBN: 9789819657391

Standard No.: 10.1007/978-981-96-5739-1doiSubjects--Topical Terms:

535880
Control theory.

LC Class. No.: QA402.3

Dewey Class. No.: 515.642

Maximum principle and dynamic programming viscosity solution approach = from open-loop to closed-loop /
LDR:03209nmm a2200349 a 4500 001 2413623
003 DE-He213
005 20250702130324.0
006 m d
007 cr nn 008maaau
008 260205s2025 si s 0 eng d
020 $a 9789819657391 $q (electronic bk.)
020 $a 9789819657384 $q (paper)
024 7 $a 10.1007/978-981-96-5739-1 $2 doi
035 $a 978-981-96-5739-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.3
072 7 $a GPFC $2 bicssc
072 7 $a SCI064000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 515.642 $2 23
090 $a QA402.3 $b .S957 2025
100 1 $a Sun, Bing. $3 1265614
245 1 0 $a Maximum principle and dynamic programming viscosity solution approach $h [electronic resource] : $b from open-loop to closed-loop / $c by Bing Sun, Bao-Zhu Guo, Zhen-Zhen Tao.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Birkhäuser, $c 2025.
300 $a xiii, 444 p. : $b ill. (some col.), digital ; $c 24 cm.
338 $a online resource $b cr $2 rdacarrier
490 1 $a Systems & control: foundations & applications, $x 2324-9757
505 0 $a - 1. Mathematical Preliminary -- Part I: Open-Loop Control -- 2. Dubovitskii-Milyutin Approach -- 3. Spectral Method -- Part II: Closed-Loop Control -- 4. Dynamic Programming Viscosity Solution Approach -- 5. Multiple Algorithms for DPVS Approach.
520 $a This book is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs). The content covers the theory and numerical algorithms, starting with open-loop control and ending with closed-loop control. It includes Pontryagin's maximum principle and the Bellman dynamic programming principle based on the notion of viscosity solution. The Bellman dynamic programming method can produce the optimal control in feedback form, making it more appealing for online implementations and robustness. The determination of the optimal feedback control law is of fundamental importance in optimal control and can be argued as the Holy Grail of control theory. The book is organized into five chapters. Chapter 1 presents necessary mathematical knowledge. Chapters 2 and 3 (Part 1) focus on the open-loop control while Chapter 4 and 5 (Part 2) focus on the closed-loop control. In this monograph, we incorporate the notion of viscosity solution of PDE with dynamic programming approach. The dynamic programming viscosity solution (DPVS) approach is then used to investigate optimal control problems. In each problem, the optimal feedback law is synthesized and numerically demonstrated. The last chapter presents multiple algorithms for the DPVS approach, including an upwind finite-difference scheme with the convergence proof. It is worth noting that the dynamic systems considered are primarily of technical or biologic origin, which is a highlight of the book. This book is systematic and self-contained. It can serve the expert as a ready reference for control theory of infinite-dimensional systems. These chapters taken together would also make a one-semester course for graduate with first courses in PDE-constrained optimal control.
650 0 $a Control theory. $3 535880
650 0 $a Differential equations, Partial. $3 518115
650 1 4 $a Systems Theory, Control. $3 893834
650 2 4 $a Calculus of Variations and Optimization. $3 3538813
650 2 4 $a Optimization. $3 891104
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
700 1 $a Guo, Bao-Zhu. $3 3386818
700 1 $a Tao, Zhen-Zhen. $3 3789838
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Systems & control: foundations & applications. $3 1620349
856 4 0 $u https://doi.org/10.1007/978-981-96-5739-1
950 $a Mathematics and Statistics (SpringerNature-11649)