Optimization of Dynamic Systems

Optimization of Dynamic Systems

Author: S. K. Agrawal

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 230

ISBN-13: 9401591490

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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.


Book Synopsis Optimization of Dynamic Systems by : S. K. Agrawal

Download or read book Optimization of Dynamic Systems written by S. K. Agrawal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimization and Dynamical Systems

Optimization and Dynamical Systems

Author: Uwe Helmke

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 409

ISBN-13: 1447134672

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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.


Book Synopsis Optimization and Dynamical Systems by : Uwe Helmke

Download or read book Optimization and Dynamical Systems written by Uwe Helmke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Applied Dynamic Programming for Optimization of Dynamical Systems

Author: Rush D. Robinett III

Publisher: SIAM

Published: 2005-01-01

Total Pages: 278

ISBN-13: 9780898718676

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Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized.


Book Synopsis Applied Dynamic Programming for Optimization of Dynamical Systems by : Rush D. Robinett III

Download or read book Applied Dynamic Programming for Optimization of Dynamical Systems written by Rush D. Robinett III and published by SIAM. This book was released on 2005-01-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized.

Optimization and Control of Dynamic Systems

Optimization and Control of Dynamic Systems

Author: Henryk Górecki

Publisher: Springer

Published: 2017-07-26

Total Pages: 679

ISBN-13: 3319626469

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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.


Book Synopsis Optimization and Control of Dynamic Systems by : Henryk Górecki

Download or read book Optimization and Control of Dynamic Systems written by Henryk Górecki and published by Springer. This book was released on 2017-07-26 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Structural Dynamic Systems Computational Techniques and Optimization

Structural Dynamic Systems Computational Techniques and Optimization

Author: Cornelius T. Leondes

Publisher: CRC Press

Published: 1999-01-27

Total Pages: 338

ISBN-13: 9789056996437

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The finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems. Starting from the system differential equations and its boundary conditions, what is referred to as a weak form of the problem (elaborated in the text) is developed in a variational sense. This variational statement is used to define elemental properties that may be written as matrices and vectors as well as to identify primary and secondary boundaries and all possible boundary conditions. Specific equilibrium problems are also solved. This book clearly reveals the effectiveness and great significance of the finite element method available and the essential role it will play in the future as further development occurs.


Book Synopsis Structural Dynamic Systems Computational Techniques and Optimization by : Cornelius T. Leondes

Download or read book Structural Dynamic Systems Computational Techniques and Optimization written by Cornelius T. Leondes and published by CRC Press. This book was released on 1999-01-27 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems. Starting from the system differential equations and its boundary conditions, what is referred to as a weak form of the problem (elaborated in the text) is developed in a variational sense. This variational statement is used to define elemental properties that may be written as matrices and vectors as well as to identify primary and secondary boundaries and all possible boundary conditions. Specific equilibrium problems are also solved. This book clearly reveals the effectiveness and great significance of the finite element method available and the essential role it will play in the future as further development occurs.

Dynamic Optimization

Dynamic Optimization

Author: Karl Hinderer

Publisher: Springer

Published: 2017-01-12

Total Pages: 530

ISBN-13: 3319488147

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This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.


Book Synopsis Dynamic Optimization by : Karl Hinderer

Download or read book Dynamic Optimization written by Karl Hinderer and published by Springer. This book was released on 2017-01-12 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.

Analysis, Control and Optimization of Complex Dynamic Systems

Analysis, Control and Optimization of Complex Dynamic Systems

Author: El-Kébir Boukas

Publisher: Springer Science & Business Media

Published: 2005-04-20

Total Pages: 280

ISBN-13: 9780387254753

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Analysis, Control and Optimization of Complex Dynamic Systems gathers in a single volume a spectrum of complex dynamic systems related papers written by experts in their fields, and strongly representative of current research trends. Complex systems present important challenges, in great part due to their sheer size which makes it difficult to grasp their dynamic behavior, optimize their operations, or study their reliability. Yet, we live in a world where, due to increasing inter-dependencies and networking of systems, complexity has become the norm. With this in mind, the volume comprises two parts. The first part is dedicated to a spectrum of complex problems of decision and control encountered in the area of production and inventory systems. The second part is dedicated to large scale or multi-agent system problems occurring in other areas of engineering such as telecommunication and electric power networks, as well as more generic context.


Book Synopsis Analysis, Control and Optimization of Complex Dynamic Systems by : El-Kébir Boukas

Download or read book Analysis, Control and Optimization of Complex Dynamic Systems written by El-Kébir Boukas and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, Control and Optimization of Complex Dynamic Systems gathers in a single volume a spectrum of complex dynamic systems related papers written by experts in their fields, and strongly representative of current research trends. Complex systems present important challenges, in great part due to their sheer size which makes it difficult to grasp their dynamic behavior, optimize their operations, or study their reliability. Yet, we live in a world where, due to increasing inter-dependencies and networking of systems, complexity has become the norm. With this in mind, the volume comprises two parts. The first part is dedicated to a spectrum of complex problems of decision and control encountered in the area of production and inventory systems. The second part is dedicated to large scale or multi-agent system problems occurring in other areas of engineering such as telecommunication and electric power networks, as well as more generic context.

Dynamic Systems for Everyone

Dynamic Systems for Everyone

Author: Asish Ghosh

Publisher: Springer

Published: 2015-04-06

Total Pages: 252

ISBN-13: 3319107356

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This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.


Book Synopsis Dynamic Systems for Everyone by : Asish Ghosh

Download or read book Dynamic Systems for Everyone written by Asish Ghosh and published by Springer. This book was released on 2015-04-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.

Optimization of Dynamic Systems

Optimization of Dynamic Systems

Author: Robert Wilson

Publisher:

Published: 1965

Total Pages: 26

ISBN-13:

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Book Synopsis Optimization of Dynamic Systems by : Robert Wilson

Download or read book Optimization of Dynamic Systems written by Robert Wilson and published by . This book was released on 1965 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

LQ Dynamic Optimization and Differential Games

LQ Dynamic Optimization and Differential Games

Author: Jacob Engwerda

Publisher: John Wiley & Sons

Published: 2005-06-17

Total Pages: 514

ISBN-13: 9780470015247

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Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.


Book Synopsis LQ Dynamic Optimization and Differential Games by : Jacob Engwerda

Download or read book LQ Dynamic Optimization and Differential Games written by Jacob Engwerda and published by John Wiley & Sons. This book was released on 2005-06-17 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.