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Titlebook: Geometric Optimal Control; Theory, Methods and Heinz Sch?ttler,Urszula Ledzewicz Textbook 2012 Springer Science+Business Media, LLC 2012 L

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發(fā)表于 2025-3-21 17:31:50 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Geometric Optimal Control
副標(biāo)題Theory, Methods and
編輯Heinz Sch?ttler,Urszula Ledzewicz
視頻videohttp://file.papertrans.cn/384/383583/383583.mp4
概述Comprehensive presentation of an up-to-date geometric approach to optimal control, both necessary and sufficient conditions, which has not been done in a book form before.Rigorous presentation, writte
叢書(shū)名稱(chēng)Interdisciplinary Applied Mathematics
圖書(shū)封面Titlebook: Geometric Optimal Control; Theory, Methods and  Heinz Sch?ttler,Urszula Ledzewicz Textbook 2012 Springer Science+Business Media, LLC 2012 L
描述This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a mo
出版日期Textbook 2012
關(guān)鍵詞Lie bracket computations; Pontryagin Maximum Principle; calculus of variations; geometric optimal contr
版次1
doihttps://doi.org/10.1007/978-1-4614-3834-2
isbn_softcover978-1-4899-8680-1
isbn_ebook978-1-4614-3834-2Series ISSN 0939-6047 Series E-ISSN 2196-9973
issn_series 0939-6047
copyrightSpringer Science+Business Media, LLC 2012
The information of publication is updating

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發(fā)表于 2025-3-21 22:23:22 | 只看該作者
The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solut= .(.), is linked in time to the application of a control function, . = .(.), by means of the solution to an ordinary differential equation whose right-hand side is shaped by the control. We now consider multidimensional systems in which both the state and the control variables no longer need to be
板凳
發(fā)表于 2025-3-22 00:38:30 | 只看該作者
The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Con setting. It is somewhat technical, but provides a uniform treatment of .. As a result, we not only prove Theorem 2.2.1, but obtain a general high-order version of the maximum principle (e.g., see [140]) from which we then derive the high-order necessary conditions for optimality that were introduce
地板
發(fā)表于 2025-3-22 08:14:53 | 只看該作者
The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum,m the first-order necessary conditions for optimality of a controlled trajectory (aside from the much stronger minimum condition on the Hamiltonian that generalizes the Weierstrass condition of the calculus of variations). Clearly, as in ordinary calculus, first-order conditions by themselves are no
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發(fā)表于 2025-3-22 21:39:57 | 只看該作者
,Ideenintensivierung und -fortführung,sfies the Hamilton–Jacobi–Bellman equation in regions where this flow covers an open set of the state injectively (.-space in the time-invariant case, respectively (., .)-space in the time-dependent case).
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發(fā)表于 2025-3-23 03:52:22 | 只看該作者
Stephan Güsken,Gero Ritzenh?fer a point. If the reachable sets are known exactly, not only necessary conditions, but complete solutions can be obtained for related optimal control problems (e.g., the time-optimal control problem). In general, determining these sets is as difficult a problem as solving an optimal control problem.
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發(fā)表于 2025-3-23 09:32:54 | 只看該作者
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