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Author: Olaosebikan Temitayo Emmanuel
Publisher: GRIN Verlag
ISBN: 3346060489
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Doctoral Thesis / Dissertation from the year 2019 in the subject Mathematics - Applied Mathematics, grade: 96.50, , course: Mathematics, language: English, abstract: In this research, Euler-Lagrange Method approach, for solving optimal control problems of both one dimensional and generalized form was considered. In years past, calculus of variation, has been used to solve functional optimization problems. However, with some special features in Calculus of Variation technique, making it unique in solving functional unconstrained optimization problems, these features will be advantageous to solving optimal control problems if it can be amended and modified in one way or the other. This call for the Euler-Lagrange Method which is a modification of the Calculus of Variation Method for solving optimal control problems. It is desired that, with the construction of the new algorithm, it will circumvent the difficulties undergone in constructing control operators which are embedded in Conjugate Gradient Method (CGM) for solving optimal control problems. Its application on some test problems have shown improvement in the results compared with existing results of solving this class of problems. The objective function values for problems 3, 4, 6, 7, 8, 9 and 10 which are: 1.359141, -5.000, 0.36950416, 0.51699120, 0.27576806, 1.5934159×[10]^(-2) and -3.880763×[10]^(-2) appreciate to the existing results 1.359141, -5.000, 0.4146562, 0.613969, 0.2739811, 1.5935×[10]^(-3) and -3.9992×[10]^(-2) respectively while the objective function values for problems 1, 2 and 5 do not fully appreciate to the existing results with slight differences. These results is an indication that the method has some advantages over some existing computational techniques built to take care of the said problems.
Author: Olaosebikan Temitayo Emmanuel
Publisher:
ISBN: 9783346060495
Category :
Languages : en
Pages : 192
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Book Description
Doctoral Thesis / Dissertation from the year 2019 in the subject Mathematics - Applied Mathematics, grade: 96.50, course: Mathematics, language: English, abstract: In this research, Euler-Lagrange Method approach, for solving optimal control problems of both one dimensional and generalized form was considered. In years past, calculus of variation, has been used to solve functional optimization problems. However, with some special features in Calculus of Variation technique, making it unique in solving functional unconstrained optimization problems, these features will be advantageous to solving optimal control problems if it can be amended and modified in one way or the other. This call for the Euler-Lagrange Method which is a modification of the Calculus of Variation Method for solving optimal control problems. It is desired that, with the construction of the new algorithm, it will circumvent the difficulties undergone in constructing control operators which are embedded in Conjugate Gradient Method (CGM) for solving optimal control problems. Its application on some test problems have shown improvement in the results compared with existing results of solving this class of problems. The objective function values for problems 3, 4, 6, 7, 8, 9 and 10 which are: 1.359141, -5.000, 0.36950416, 0.51699120, 0.27576806, 1.5934159×[10]^(-2) and -3.880763×[10]^(-2) appreciate to the existing results 1.359141, -5.000, 0.4146562, 0.613969, 0.2739811, 1.5935×[10]^(-3) and -3.9992×[10]^(-2) respectively while the objective function values for problems 1, 2 and 5 do not fully appreciate to the existing results with slight differences. These results is an indication that the method has some advantages over some existing computational techniques built to take care of the said problems.
Author: Daniel Liberzon
Publisher: Princeton University Press
ISBN: 0691151873
Category : Mathematics
Languages : en
Pages : 255
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Book Description
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Author: Daniela Tonon
Publisher: Springer
ISBN: 3319607715
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
Author: James M Longuski
Publisher: Springer Science & Business Media
ISBN: 1461489458
Category : Technology & Engineering
Languages : en
Pages : 286
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Book Description
Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!
Author: Thomas A. Weber
Publisher: MIT Press
ISBN: 0262015730
Category : Business & Economics
Languages : en
Pages : 387
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Book Description
A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Author: Morton I. Kamien
Publisher: Courier Corporation
ISBN: 0486310280
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Author: A. E. Bryson
Publisher: CRC Press
ISBN: 9780891162285
Category : Technology & Engineering
Languages : en
Pages : 500
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Book Description
This best-selling text focuses on the analysis and design of complicated dynamics systems. CHOICE called it “a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates. The format is good, the presentation clear, the diagrams instructive, the examples and problems helpful...References and a multiple-choice examination are included.”
Author: Gerasimos Rigatos
Publisher: Cambridge Scholars Publishing
ISBN: 1527562468
Category : Technology & Engineering
Languages : en
Pages : 741
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Book Description
This volume discusses advances in applied nonlinear optimal control, comprising both theoretical analysis of the developed control methods and case studies about their use in robotics, mechatronics, electric power generation, power electronics, micro-electronics, biological systems, biomedical systems, financial systems and industrial production processes. The advantages of the nonlinear optimal control approaches which are developed here are that, by applying approximate linearization of the controlled systems’ state-space description, one can avoid the elaborated state variables transformations (diffeomorphisms) which are required by global linearization-based control methods. The book also applies the control input directly to the power unit of the controlled systems and not on an equivalent linearized description, thus avoiding the inverse transformations met in global linearization-based control methods and the potential appearance of singularity problems. The method adopted here also retains the known advantages of optimal control, that is, the best trade-off between accurate tracking of reference setpoints and moderate variations of the control inputs. The book’s findings on nonlinear optimal control are a substantial contribution to the areas of nonlinear control and complex dynamical systems, and will find use in several research and engineering disciplines and in practical applications.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1104
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Book Description
Author: Olaosebikan Temitayo Emmanuel
Publisher: GRIN Verlag
ISBN: 3346060489
Category : Mathematics
Languages : en
Pages : 190
Get Book Here
Book Description
Doctoral Thesis / Dissertation from the year 2019 in the subject Mathematics - Applied Mathematics, grade: 96.50, , course: Mathematics, language: English, abstract: In this research, Euler-Lagrange Method approach, for solving optimal control problems of both one dimensional and generalized form was considered. In years past, calculus of variation, has been used to solve functional optimization problems. However, with some special features in Calculus of Variation technique, making it unique in solving functional unconstrained optimization problems, these features will be advantageous to solving optimal control problems if it can be amended and modified in one way or the other. This call for the Euler-Lagrange Method which is a modification of the Calculus of Variation Method for solving optimal control problems. It is desired that, with the construction of the new algorithm, it will circumvent the difficulties undergone in constructing control operators which are embedded in Conjugate Gradient Method (CGM) for solving optimal control problems. Its application on some test problems have shown improvement in the results compared with existing results of solving this class of problems. The objective function values for problems 3, 4, 6, 7, 8, 9 and 10 which are: 1.359141, -5.000, 0.36950416, 0.51699120, 0.27576806, 1.5934159×[10]^(-2) and -3.880763×[10]^(-2) appreciate to the existing results 1.359141, -5.000, 0.4146562, 0.613969, 0.2739811, 1.5935×[10]^(-3) and -3.9992×[10]^(-2) respectively while the objective function values for problems 1, 2 and 5 do not fully appreciate to the existing results with slight differences. These results is an indication that the method has some advantages over some existing computational techniques built to take care of the said problems.
