An Introduction To Mathematical Optimal Control Theory Epdf Download
An Introduction To Mathematical Optimal Control Theory Epdf Download
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本书是数学规划和优化的入门教材，适合具有数学背景的学生，其中包括一个学期的线性代数和完整的微积分序列。它包括帮助学生培养计算技能的计算示例。这本教科书将控制理论和建模相结合，介绍并建立了模拟和解决各种应用科学中的具体问题的方法。作者强调“边做边学”，重点关注现实问题的示例和应用。先进概念的基本介绍、引入新想法的证明以及精心呈现的 MATLAB® 程序有助于促进对基础知识的理解，同时也为新的独立研究开辟道路。本书每章都有最少的先决条件和练习，可以作为数学、物理、工程、计算机科学以及生物学、生物技术、经济学和金融领域的研究生和高年级本科生、研究人员和从业者的优秀教科书和参考书。这是对经典力学以及控制理论和变分演算相关领域的许多主题的直观演示。本书中的所有主题都对未透露的定义和让读者一无所知的证明采取零容忍态度。一些特别令人感兴趣的领域是：行星轨道椭圆率的极短推导；对“网球拍悖论”的陈述和解释；对陀螺效应的启发式解释（和严格处理）；粒子动力学与弹簧静力学之间的揭示性等价性；庞特里亚金极大原理的简短几何解释，等等。在最后一章中，针对更高级的读者，将哈密顿量和动量与某个静态问题中的力进行了比较。这为一些看似抽象的概念和定理赋予了明显的物理意义。本书具备由基础微积分和基础本科物理组成的最低先决条件，适合从本科生到研究生初级水平的课程，以及数学、物理和工程学学生的混合读者。这门学科的大部分乐趣在于解决本书中的近 200 个问题。本书以简短易读的形式向普通读者介绍了基本的优化原理和基于梯度的算法。它使专业人士能够将优化理论应用于工程、物理、化学或商业经济学。许多例子都强调了使用线性二次高斯方法进行控制系统设计的处理方法。它从工程角度探讨了线性最优控制理论，并举例说明了实际应用。关键主题包括环路恢复技术、频率整形和控制器简化。大量的例子和完整的解决方案。 1990年版。高年级本科教材介绍了最优控制理论的各个方面：动态规划、庞特里亚金最小原理和轨迹优化的数值技术。大量的数字、表格。可根据要求提供解决方案指南。 1970年版。本书重点介绍不完全信息前向-后向随机微分方程（FBSDE）的极大值原理和验证定理及其在线性二次最优控制和数学金融中的应用。数学金融领域出现的许多有趣现象都可以用 FBSDE 来描述。 FBSDE 的最优控制问题具有重要的理论意义和实际意义。文献中的一个标准假设是模型中的随机噪声被完全观察到。然而，在现实世界中这种情况很少发生。完全信息下的最优控制问题得到了广泛的研究。然而，当信息不完整时，人们对这些问题知之甚少。本书的目的就是填补这一空白。本书的写作风格适合具有随机过程、最优控制和数学金融基础知识的数学和工程领域的研究生和研究人员。本文适用于初学者。对于控制理论领域的研究工作者来说，这并不是一篇最先进的论文。其目的是向读者介绍控制理论中的一些问题和结果，说明这些结果的应用，并为读者进一步阅读该主题提供指导。我尝试通过示例来激发结果，尤其是第 3 节中描述的一个规范的简单示例。许多结果，例如极大值原理，都需要漫长而困难的证明。我省略了这些证明。一般来说，我只包含以下证明：（1）不太困难或（2）对于结果的性质相当有启发性。然而，我通常试图从给定的证据中得出最有力的结论。例如，控制理论中关于紧凑目标和解的唯一性的许多现有证明也适用于封闭目标和非唯一性。最后，在每个部分的末尾，我都给出了该部分中讨论的结果的概括和起源的参考文献。然而，我并不声称参考文献是完整的，因为我常常满足于仅仅向读者推荐一篇论述或一篇包含大量参考书目的论文。 IV 这些讲义是我在 1967 年 6 月于意大利瓦伦纳举行的数学系统和经济学国际暑期学校上使用的关于控制理论的九个讲义系列讲义的修订版。本书面向参与研究（有限维空间中）（静态）优化问题的人员（毕业生、研究人员，也包括具有良好数学背景的本科生）。它包含大量材料，从凸分析的基本工具到平滑优化问题、非平滑优化问题和向量优化问题的最优条件。学科的发展是独立的，参考书目通常在不同的书籍中处理（只有少数关于优化理论的书籍也涉及向量问题），因此本书可以作为进一步阅读更专业文献的起点。假设只有良好的（即使不是高级的）数学分析和线性代数知识，本书就介绍了优化问题中数学理论的各个方面。该处理是在有限维空间中进行的，不考虑算法问题。在分别涉及介绍性主题和凸分析的基本工具和概念的两章之后，本书广泛讨论了光滑情况、非光滑情况以及最后的向量优化问题中的数学规划问题。 · 内容自成一体 · 清晰的风格和结果通过充分的参考文献得到证明或精确陈述 · 作者在该领域拥有多年的经验 · 一本书中包含多个主题（其中一些在此类书籍中不常见），包括非光滑优化和向量优化问题 · 每章末尾都有有用的长参考文献列表 这本本科教材向科学和工程专业的学生介绍了迷人的优化领域。这是一本独特的书，汇集了各个子领域
This book serves as an introductory text in mathematical programming and optimization for students having a mathematical background that includes one semester of linear algebra and a complete calculus sequence. It includes computational examples to aid students develop computational skills. Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance. This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book. This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics. Numerous examples highlight this treatment of the use of linear quadratic Gaussian methods for control system design. It explores linear optimal control theory from an engineering viewpoint, with illustrations of practical applications. Key topics include loop-recovery techniques, frequency shaping, and controller reduction. Numerous examples and complete solutions. 1990 edition. Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition. This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. ?Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance. This paper is intended for the beginner. It is not a state of-the-art paper for research workers in the field of control theory. Its purpose is to introduce the reader to some of the problems and results in control theory, to illustrate the application of these re sults, and to provide a guide for his further reading on this subject. I have tried to motivate the results with examples, especial ly with one canonical, simple example described in §3. Many results, such as the maximum principle, have long and difficult proofs. I have omitted these proofs. In general I have included only the proofs which are either (1) not too difficult or (2) fairly enlightening as to the nature of the result. I have, however, usually attempted to draw the strongest conclusion from a given proof. For example, many existing proofs in control theory for compact targets and uniqueness of solutions also hold for closed targets and non-uniqueness. Finally, at the end of each section I have given references to generalizations and origins of the results discussed in that section. I make no claim of completeness in the references, however, as I have often been content merely to refer the reader either to an exposition or to a paper which has an extensive bibliography. IV These 1ecture notes are revisions of notes I used for aseries of nine 1ectures on contro1 theory at the International Summer Schoo1 on Mathematica1 Systems and Economics held in Varenna, Ita1y, June 1967. The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems. The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature. Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems. · Self-contained · Clear style and results are either proved or stated precisely with adequate references · The authors have several years experience in this field · Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems · Useful long references list at the end of each chapter This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of