Duality System In Applied Mechanics And Optimal Control

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Duality System in Applied Mechanics and Optimal Control

Author : Wan-Xie Zhong
Publisher : Springer Science & Business Media
ISBN 13 : 1402078811
Total Pages : 467 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Duality System in Applied Mechanics and Optimal Control by : Wan-Xie Zhong

Download or read book Duality System in Applied Mechanics and Optimal Control written by Wan-Xie Zhong and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: -Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems. -Canonical transformation applied to non-linear systems. -Pseudo-excitation method for structural random vibrations. -Precise integration of two-point boundary value problems. -Wave propagation along wave-guides, scattering. -Precise solution of Riccati differential equations. -Kalman filtering. -HINFINITY theory of control and filter.

Duality System in Applied Mechanics and Optimal Control

Author : Wan-Xie Zhong
Publisher : Springer
ISBN 13 : 9781475779172
Total Pages : 456 pages
Book Rating : 4.7/5 (791 download)

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Book Synopsis Duality System in Applied Mechanics and Optimal Control by : Wan-Xie Zhong

Download or read book Duality System in Applied Mechanics and Optimal Control written by Wan-Xie Zhong and published by Springer. This book was released on 2013-10-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: -Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems. -Canonical transformation applied to non-linear systems. -Pseudo-excitation method for structural random vibrations. -Precise integration of two-point boundary value problems. -Wave propagation along wave-guides, scattering. -Precise solution of Riccati differential equations. -Kalman filtering. -HINFINITY theory of control and filter.

Computational Mechanics

Author : M. W. Yuan
Publisher : 清华大学出版社有限公司
ISBN 13 : 9787302093435
Total Pages : 902 pages
Book Rating : 4.0/5 (934 download)

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Book Synopsis Computational Mechanics by : M. W. Yuan

Download or read book Computational Mechanics written by M. W. Yuan and published by 清华大学出版社有限公司. This book was released on 2004 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symplectic Pseudospectral Methods for Optimal Control

Author : Xinwei Wang
Publisher : Springer Nature
ISBN 13 : 9811534381
Total Pages : 178 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Symplectic Pseudospectral Methods for Optimal Control by : Xinwei Wang

Download or read book Symplectic Pseudospectral Methods for Optimal Control written by Xinwei Wang and published by Springer Nature. This book was released on 2020-10-16 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on symplectic pseudospectral methods for nonlinear optimal control problems and their applications. Both the fundamental principles and engineering practice are addressed. Symplectic pseudospectral methods for nonlinear optimal control problems with complicated factors (i.e., inequality constraints, state-delay, unspecific terminal time, etc.) are solved under the framework of indirect methods. The methods developed here offer a high degree of computational efficiency and accuracy when compared with popular direct pseudospectral methods. The methods are applied to solve optimal control problems arising in various engineering fields, particularly in path planning problems for autonomous vehicles. Given its scope, the book will benefit researchers, engineers and graduate students in the fields of automatic control, path planning, ordinary differential equations, etc.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation and Optimization of Discrete and Differential Inclusions

Author : Elimhan N Mahmudov
Publisher : Elsevier
ISBN 13 : 0123884284
Total Pages : 396 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Approximation and Optimization of Discrete and Differential Inclusions by : Elimhan N Mahmudov

Download or read book Approximation and Optimization of Discrete and Differential Inclusions written by Elimhan N Mahmudov and published by Elsevier. This book was released on 2011-08-25 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Control Of Nonlinear Distributed Parameter Systems

Author : Goong Chen
Publisher : CRC Press
ISBN 13 : 9780203904190
Total Pages : 382 pages
Book Rating : 4.9/5 (41 download)

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Book Synopsis Control Of Nonlinear Distributed Parameter Systems by : Goong Chen

Download or read book Control Of Nonlinear Distributed Parameter Systems written by Goong Chen and published by CRC Press. This book was released on 2001-03-14 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics a

Duality Principles in Nonconvex Systems

Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 9780792361459
Total Pages : 476 pages
Book Rating : 4.3/5 (614 download)

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Book Synopsis Duality Principles in Nonconvex Systems by : David Yang Gao

Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Optimal Control of Mechanical Oscillations

Author : Agnessa Kovaleva
Publisher : Springer Science & Business Media
ISBN 13 : 3540492585
Total Pages : 269 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Optimal Control of Mechanical Oscillations by : Agnessa Kovaleva

Download or read book Optimal Control of Mechanical Oscillations written by Agnessa Kovaleva and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites.

Duality Principles in Nonconvex Systems

Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 1475731760
Total Pages : 463 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Duality Principles in Nonconvex Systems by : David Yang Gao

Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Optimization and Control with Applications

Author : Liqun Qi
Publisher : Springer Science & Business Media
ISBN 13 : 9780387242545
Total Pages : 618 pages
Book Rating : 4.2/5 (425 download)

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Book Synopsis Optimization and Control with Applications by : Liqun Qi

Download or read book Optimization and Control with Applications written by Liqun Qi and published by Springer Science & Business Media. This book was released on 2005-03-04 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.

Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing

Author : B. H. V. Topping
Publisher :
ISBN 13 :
Total Pages : 730 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing by : B. H. V. Topping

Download or read book Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing written by B. H. V. Topping and published by . This book was released on 2005 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the abstracts of the contributed papers presented at the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, held in Rome, Italy, 30 August - 2 September 2005. The length papers are available in electronic format on the accompanying CD-ROM.

American Book Publishing Record

Author :
Publisher :
ISBN 13 :
Total Pages : 864 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis American Book Publishing Record by :

Download or read book American Book Publishing Record written by and published by . This book was released on 2004 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conjugate Duality and Optimization

Author : R. Tyrrell Rockafellar
Publisher : SIAM
ISBN 13 : 9781611970524
Total Pages : 80 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Conjugate Duality and Optimization by : R. Tyrrell Rockafellar

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Optimal Control Theory for Applications

Author : David G. Hull
Publisher : Springer Science & Business Media
ISBN 13 : 1475741804
Total Pages : 402 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Optimal Control Theory for Applications by : David G. Hull

Download or read book Optimal Control Theory for Applications written by David G. Hull and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It is also a book about the mathematical aspects of optimal control theory. It was developed in an engineering environment from material learned by the author while applying it to the solution of engineering problems. One goal of the book is to help engineering graduate students learn the fundamentals which are needed to apply the methods to engineering problems. The examples are from geometry and elementary dynamical systems so that they can be understood by all engineering students. Another goal of this text is to unify optimization by using the differential of calculus to create the Taylor series expansions needed to derive the optimality conditions of optimal control theory.

Canadian Journal of Physics

Author :
Publisher :
ISBN 13 :
Total Pages : 666 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Physics by :

Download or read book Canadian Journal of Physics written by and published by . This book was released on 2008 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Control Theory

Author : Zhongjing Ma
Publisher : Springer Nature
ISBN 13 : 9813362928
Total Pages : 355 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Optimal Control Theory by : Zhongjing Ma

Download or read book Optimal Control Theory written by Zhongjing Ma and published by Springer Nature. This book was released on 2021-01-30 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.