Optimization And Dynamical Systems
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Optimization And Dynamical Systems
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Author : Uwe Helmke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimization And Dynamical Systems written by Uwe Helmke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather deep existence and uniqueness results for the solution of certain matrix least squares optimization problems in geomet ric invariant theory. These problems, as well as many other optimization problems arising in linear algebra and systems theory, do not always admit solutions which can be found by algebraic methods.
Applied Dynamic Programming For Optimization Of Dynamical Systems
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Author : Rush D. Robinett III
language : en
Publisher: SIAM
Release Date : 2005-07-01
Applied Dynamic Programming For Optimization Of Dynamical Systems written by Rush D. Robinett III and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-01 with Mathematics categories.
This book presents a range of dynamic programming (DP) techniques applied to the optimization of dynamical systems.
Optimization And Control Of Dynamic Systems
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Author : Henryk Górecki
language : en
Publisher: Springer
Release Date : 2017-07-26
Optimization And Control Of Dynamic Systems written by Henryk Górecki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Technology & Engineering categories.
This book offers a comprehensive presentation of optimization and polyoptimization methods. The examples included are taken from various domains: mechanics, electrical engineering, economy, informatics, and automatic control, making the book especially attractive. With the motto “from general abstraction to practical examples,” it presents the theory and applications of optimization step by step, from the function of one variable and functions of many variables with constraints, to infinite dimensional problems (calculus of variations), a continuation of which are optimization methods of dynamical systems, that is, dynamic programming and the maximum principle, and finishing with polyoptimization methods. It includes numerous practical examples, e.g., optimization of hierarchical systems, optimization of time-delay systems, rocket stabilization modeled by balancing a stick on a finger, a simplified version of the journey to the moon, optimization of hybrid systems and of the electrical long transmission line, analytical determination of extremal errors in dynamical systems of the rth order, multicriteria optimization with safety margins (the skeleton method), and ending with a dynamic model of bicycle. The book is aimed at readers who wish to study modern optimization methods, from problem formulation and proofs to practical applications illustrated by inspiring concrete examples.
Optimization Of Dynamical Systems With Impulse Controls And Shocks
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Author : Boris Miller
language : en
Publisher: Birkhäuser
Release Date : 2024-09-01
Optimization Of Dynamical Systems With Impulse Controls And Shocks written by Boris Miller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-01 with Science categories.
This text explores the state-of-the-art in the rapidly developing theory of impulse control and introduces the theory of singular space-time transformations, a new method for studying shock mechanical systems. Two approaches in the theory of impulse control are presented: The first, more traditional approach defines the impulsive action as a discontinuity of phase coordinates depending on the current time, the state preceding the action, and its magnitude. The second requires the use of modern methods for describing dynamical systems - differential equations with measures. The impulse is treated as an idealization of a very short action of high magnitude, which produces an almost abrupt change of phase coordinates. The relation between these two approaches is also discussed, and several applications, both traditional and emerging, are considered. This text is intended for graduate students and researchers in control engineering and optimal control theory for dynamical systems. Readers are assumed to be familiar with the theory of ODEs, optimal control, and functional analysis, though an appendix is included that covers many of the necessary mathematical concepts.
Optimization Algorithms
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Author : Mykhaylo Andriychuk
language : en
Publisher: BoD – Books on Demand
Release Date : 2024-07-10
Optimization Algorithms written by Mykhaylo Andriychuk and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-10 with Mathematics categories.
Optimization Algorithms - Classics and Last Advances is devoted to developing algorithm theory and exploring the use of different optimization algorithms for solving various problems in pure science, applied physics, and information technology. The book consists of two sections. The first focuses on developing abstract algorithms with subsequent applications to real-world optimization problems. It discusses optimization problems based on partial differential equations, canonical polyadic decomposition, variational approach, and ant colony optimization, which are discussed here. The second section presents problems related to optimization in information technologies. Chapters in this section address the utilization of optimization algorithms to solve problems of reducing computation time and computer memory, reducing kernel mechanism processing time in multimedia authoring tools, arranging access optimization for special applications, and minimizing resources for solving vehicle routing problems.
Optimization Of Dynamic Systems
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Author : S. K. Agrawal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Optimization Of Dynamic Systems written by S. K. Agrawal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.
This textbook deals with optimization of dynamic systems. The motivation for undertaking this task is as follows: There is an ever increasing need to produce more efficient, accurate, and lightweight mechanical and electromechanical de vices. Thus, the typical graduating B.S. and M.S. candidate is required to have some familiarity with techniques for improving the performance of dynamic systems. Unfortunately, existing texts dealing with system improvement via optimization remain inaccessible to many of these students and practicing en gineers. It is our goal to alleviate this difficulty by presenting to seniors and beginning graduate students practical efficient techniques for solving engineer ing system optimization problems. The text has been used in optimal control and dynamic system optimization courses at the University of Deleware, the University of Washington and Ohio University over the past four years. The text covers the following material in a straightforward detailed manner: • Static Optimization: The problem of optimizing a function that depends on static variables (i.e., parameters) is considered. Problems with equality and inequality constraints are addressed. • Numerical Methods: Static Optimization: Numerical algorithms for the solution of static optimization problems are presented here. The methods presented can accommodate both the unconstrained and constrained static optimization problems. • Calculus of Variation: The necessary and sufficient conditions for the ex tremum of functionals are presented. Both the fixed final time and free final time problems are considered.
Springer Handbook Of Computational Intelligence
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Author : Janusz Kacprzyk
language : en
Publisher: Springer
Release Date : 2015-05-28
Springer Handbook Of Computational Intelligence written by Janusz Kacprzyk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-28 with Technology & Engineering categories.
The Springer Handbook for Computational Intelligence is the first book covering the basics, the state-of-the-art and important applications of the dynamic and rapidly expanding discipline of computational intelligence. This comprehensive handbook makes readers familiar with a broad spectrum of approaches to solve various problems in science and technology. Possible approaches include, for example, those being inspired by biology, living organisms and animate systems. Content is organized in seven parts: foundations; fuzzy logic; rough sets; evolutionary computation; neural networks; swarm intelligence and hybrid computational intelligence systems. Each Part is supervised by its own Part Editor(s) so that high-quality content as well as completeness are assured.
Dynamical Search Applications Of Dynamical Systems In Search And Optimization
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Author : Luc Pronzato
language : en
Publisher:
Release Date : 2000
Dynamical Search Applications Of Dynamical Systems In Search And Optimization written by Luc Pronzato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Differentiable dynamical systems categories.
Dynamical Search
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Author : Luc Pronzato
language : en
Publisher: CRC Press
Release Date : 1999-08-27
Dynamical Search written by Luc Pronzato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-27 with Mathematics categories.
Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies. This all feeds back to suggest new algorithms with faster rates of convergence. For example, in line-search, we can improve upon the Golden Section algorithm with new classes of algorithms that have their own special-and sometimes chaotic-dynamical systems. The ellipsoidal algorithms of linear and convex programming have fast, "deep cut" versions whose dynamical systems contain cyclic attractors. And ordinary steepest descent has, buried within, a beautiful fractal that controls the gateway to a special two-point attractor. Faster "relaxed" versions exhibit classical period doubling. Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization. It will prove fascinating and open doors to new areas of investigation for researchers in both fields, plus those in statistics and computer science.
Structural Dynamic Systems Com
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Author : Cornelius T. Leondes
language : en
Publisher: CRC Press
Release Date : 1999-01-27
Structural Dynamic Systems Com written by Cornelius T. Leondes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-27 with Computers categories.
The availability of powerful computers along with highly effective computational techniques have allowed computer-aided design and engineering of structural dynamics systems to achieve a high level of capability and importance. This volume clearly reveals the great significance of these techniques and the essential role they will play in the future as further development occurs. This will be a significant and unique reference for students, research workers, practitioners, computer scientists and others for years to come.