An Introduction to Optimal Control Theory: The Dynamic Programming Approach
Hernández-Lerma, Onésimo, Laura-Guarachi, Leonardo R., Mendoza-Palacios, Saul
- 出版商: Springer
- 出版日期: 2024-02-24
- 售價: $2,510
- 貴賓價: 9.5 折 $2,385
- 語言: 英文
- 頁數: 273
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031211413
- ISBN-13: 9783031211416
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商品描述
This book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others.
The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost.After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations.
The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.
商品描述(中文翻譯)
本書介紹了針對大型確定性和隨機系統的最佳控制問題，這些系統具有離散或連續時間參數。這些系統涵蓋了許多學科中研究的大多數系統，包括經濟學、工程學、運籌學和管理科學等。
主要目的是提供一個簡明、系統且相對自足的最佳控制理論關鍵主題的介紹。為此，大多數分析基於動態規劃（Dynamic Programming, DP）技術。這種技術幾乎適用於所有理論和應用中的控制問題。例如，它包括有限和無限時間範圍的控制問題，其中基礎動態系統遵循確定性或隨機的差分或微分方程。在無限時間範圍的情況下，它還使用DP來研究不折現的問題，例如遍歷性或長期平均成本。
在對控制問題進行一般介紹後，本書將主題分為四個部分，涵蓋不同的動態系統：離散時間確定性系統的控制、離散時間隨機系統、常微分方程，最後是針對隨機微分方程的通用連續時間MCP及其應用。
第一部分和第二部分應該對具備一些基礎微積分、線性代數和概率論（隨機變數、期望值等）知識的本科生是可接觸的。而第三部分和第四部分則適合具備數學分析（導數、積分等）和隨機過程工作知識的高年級本科生或研究生。
作者簡介
Onésimo Henández-Lerma is a researcher in topics related to discrete- and continuous-time stochastic control problems and dynamic games. He is a member of the Inaugural Class of Fellows of the American Mathematical Society.
Leonardo Laura-Guarachi received the Ph. D. degree in Mathematical Sciences from the Universidad Nacional Autónoma de México. Currently he is an associate professor at the SEPI-ESE-IPN. His research interests include optimal control problems, dynamic games, and their applications. Saul Mendoza-Palacios is a researcher at the Center for Economic Studies of El Colegio de México. He concluded his doctoral studies at the Mathematics Department of CINVESTAV-IPN. His research interest are in evolutionary games, optimal transport theory in market matching models, optimal control, and applications in economics.
作者簡介(中文翻譯)
大衛·岡薩雷斯-桑切斯（David Gonzalez-Sanchez）是墨西哥索諾拉大學數學系的副教授及CONACYT的成員。他在墨西哥的CINVESTAV-IPN獲得數學博士學位，並在CIDE獲得經濟學碩士學位。他的主要研究興趣為最優控制與博弈論及其應用。
奧內西莫·亨南德斯-萊爾馬（Onésimo Henández-Lerma）是一位研究離散與連續時間隨機控制問題及動態博弈的研究員。他是美國數學學會首屆研究員班的成員。
萊昂納多·勞拉-瓜拉奇（Leonardo Laura-Guarachi）在墨西哥國立自治大學獲得數學科學博士學位。目前，他是SEPI-ESE-IPN的副教授。他的研究興趣包括最優控制問題、動態博弈及其應用。
薩烏爾·門多薩-帕拉西奧斯（Saul Mendoza-Palacios）是墨西哥學院經濟研究中心的研究員。他在CINVESTAV-IPN的數學系完成博士學位。他的研究興趣包括進化博弈、市場匹配模型中的最優運輸理論、最優控制及其在經濟學中的應用。
