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A Variational Approach To Optimal Control Of Odes
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Book Synopsis A Variational Approach to Optimal Control of ODEs by : Pablo Pedregal
Download or read book A Variational Approach to Optimal Control of ODEs written by Pablo Pedregal and published by SIAM. This book was released on 2022-07-26 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book presents in a unified, systematic way the basic principles of optimal control governed by ODEs. Using a variational perspective, the author incorporates important restrictions like constraints for control and state, as well as the state system itself, into the equivalent variational reformulation of the problem. The fundamental issues of existence of optimal solutions, optimality conditions, and numerical approximation are then examined from this variational viewpoint. Inside, readers will find a unified approach to all the basic issues of optimal control, academic and real-world examples testing the book’s variational approach, and a rigorous treatment stressing ideas and arguments rather than the underlying mathematical formalism. A Variational Approach to Optimal Control of ODEs is mainly for applied analysts, applied mathematicians, and control engineers, but will also be helpful to other scientists and engineers who want to understand the basic principles of optimal control governed by ODEs. It requires no prerequisites in variational problems or expertise in numerical approximation. It can be used for a first course in optimal control.
Book Synopsis A Variational Approach to Problems of Optimal Control by : A. Louis Posthauer
Download or read book A Variational Approach to Problems of Optimal Control written by A. Louis Posthauer and published by . This book was released on 1970 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control by : Arturo Locatelli
Download or read book Optimal Control written by Arturo Locatelli and published by Springer Science & Business Media. This book was released on 2001-03 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control
Book Synopsis Optimal Control Theory by : Zhongjing Ma
Download or read book Optimal Control Theory written by Zhongjing Ma and published by . This book was released on 2021 with total page 0 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.
Book Synopsis Optimal Control of ODEs and DAEs by : Matthias Gerdts
Download or read book Optimal Control of ODEs and DAEs written by Matthias Gerdts and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics and interest in optimal control. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Examples are provided for illustration purposes.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Business Dynamics Models by : Eugenius Kaszkurewicz
Download or read book Business Dynamics Models written by Eugenius Kaszkurewicz and published by SIAM. This book was released on 2022-11-24 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces optimal control methods, formulated as optimization problems, applied to business dynamics problems. Business dynamics refers to a combination of business management and financial objectives embedded in a dynamical system model. The model is subject to a control that optimizes a performance index and takes both management and financial aspects into account. Business Dynamics Models: Optimization-Based One Step Ahead Optimal Control includes solutions that provide a rationale for the use of optimal control and guidelines for further investigation into more complex models, as well as formulations that can also be used in a so-called flight simulator mode to investigate different complex scenarios. The text offers a modern programming environment (Jupyter notebooks in JuMP/Julia) for modeling, simulation, and optimization, and Julia code and notebooks are provided on a website for readers to experiment with their own examples. This book is intended for students majoring in applied mathematics, business, and engineering. The authors use a formulation-algorithm-example approach, rather than the classical definition-theorem-proof, making the material understandable to senior undergraduates and beginning graduates.
Book Synopsis Extremum Seeking Through Delays and PDEs by : Tiago Roux Oliveira
Download or read book Extremum Seeking Through Delays and PDEs written by Tiago Roux Oliveira and published by SIAM. This book was released on 2022-12-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.
Book Synopsis Optimal Periodic Control by : Fritz Colonius
Download or read book Optimal Periodic Control written by Fritz Colonius and published by Springer. This book was released on 2006-11-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.
Download or read book Hill's Equation written by Wilhelm Magnus and published by Courier Corporation. This book was released on 2013-10-29 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part treatment explains basic theory and details, including oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention to stability problems and coexistence of periodic solutions. 1966 edition.
Book Synopsis A Variational Approach to Lyapunov Type Inequalities by : Antonio Cañada
Download or read book A Variational Approach to Lyapunov Type Inequalities written by Antonio Cañada and published by Springer. This book was released on 2015-11-24 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.
Book Synopsis Malware Diffusion Models for Modern Complex Networks by : Vasileios Karyotis
Download or read book Malware Diffusion Models for Modern Complex Networks written by Vasileios Karyotis and published by Morgan Kaufmann. This book was released on 2016-02-02 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Malware Diffusion Models for Wireless Complex Networks: Theory and Applications provides a timely update on malicious software (malware), a serious concern for all types of network users, from laymen to experienced administrators. As the proliferation of portable devices, namely smartphones and tablets, and their increased capabilities, has propelled the intensity of malware spreading and increased its consequences in social life and the global economy, this book provides the theoretical aspect of malware dissemination, also presenting modeling approaches that describe the behavior and dynamics of malware diffusion in various types of wireless complex networks. Sections include a systematic introduction to malware diffusion processes in computer and communications networks, an analysis of the latest state-of-the-art malware diffusion modeling frameworks, such as queuing-based techniques, calculus of variations based techniques, and game theory based techniques, also demonstrating how the methodologies can be used for modeling in more general applications and practical scenarios. Presents a timely update on malicious software (malware), a serious concern for all types of network users, from laymen to experienced administrators Systematically introduces malware diffusion processes, providing the relevant mathematical background Discusses malware modeling frameworks and how to apply them to complex wireless networks Provides guidelines and directions for extending the corresponding theories in other application domains, demonstrating such possibility by using application models in information dissemination scenarios
Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen
Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Book Synopsis Optimal Control of PDEs under Uncertainty by : Jesús Martínez-Frutos
Download or read book Optimal Control of PDEs under Uncertainty written by Jesús Martínez-Frutos and published by Springer. This book was released on 2018-09-13 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control Applied to Biological Models by : Suzanne Lenhart
Download or read book Optimal Control Applied to Biological Models written by Suzanne Lenhart and published by CRC Press. This book was released on 2007-05-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t
Book Synopsis Surveys in Differential-Algebraic Equations II by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations II written by Achim Ilchmann and published by Springer. This book was released on 2014-12-04 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
