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Optimization And Dynamical Systems
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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.
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.
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 666 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.
Author :Maria Tomas-Rodriguez Publisher :Springer Science & Business Media ISBN 13 :184996100X Total Pages :303 pages Book Rating :4.8/5 (499 download)
Book Synopsis Linear, Time-varying Approximations to Nonlinear Dynamical Systems by : Maria Tomas-Rodriguez
Download or read book Linear, Time-varying Approximations to Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez and published by Springer Science & Business Media. This book was released on 2010-02-04 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.
Book Synopsis Introduction to Discrete Dynamical Systems and Chaos by : Mario Martelli
Download or read book Introduction to Discrete Dynamical Systems and Chaos written by Mario Martelli and published by John Wiley & Sons. This book was released on 2011-11-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.
Book Synopsis Optimal Reference Shaping for Dynamical Systems by : Tarunraj Singh
Download or read book Optimal Reference Shaping for Dynamical Systems written by Tarunraj Singh and published by CRC Press. This book was released on 2009-10-28 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrating feedforward control with feedback control can significantly improve the performance of control systems compared to using feedback control alone. Focusing on feedforward control techniques, Optimal Reference Shaping for Dynamical Systems: Theory and Applications lucidly covers the various algorithms for attenuating residual oscillations that are excited by reference inputs to dynamical systems. The reference shaping techniques presented in the book require the system to be stable or marginally stable, including systems where feedback control has been used to stabilize the system. Illustrates Techniques through Benchmark Problems After developing models for applications in which the dynamics are dominated by lightly damped poles, the book describes the time-delay filter (input shaper) design technique and reviews the calculus of variations. It then focuses on four control problems: time-optimal, fuel/time-optimal, fuel limited time-optimal, and jerk limited time-optimal control. The author explains how the minimax optimization problem can help in the design of robust time-delay filters and explores the input-constrained design of open-loop control profiles that account for friction in the design of point-to-point control profiles. The final chapter presents numerical techniques for solving the problem of designing shaped inputs. Supplying MATLAB® code and a suite of real-world problems, this book provides a rigorous yet accessible presentation of the theory and numerical techniques used to shape control system inputs for achieving precise control when modeling uncertainties exist. It includes up-to-date techniques for the design of command-shaped profiles for precise, robust, and rapid point-to-point control of underdamped systems.
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.
Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss
Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.
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.
Book Synopsis Optimal Control and Forecasting of Complex Dynamical Systems by :
Download or read book Optimal Control and Forecasting of Complex Dynamical Systems written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2005-07-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a range of dynamic programming (DP) techniques applied to the optimization of dynamical systems.
Book Synopsis Numerical Data Fitting in Dynamical Systems by : Klaus Schittkowski
Download or read book Numerical Data Fitting in Dynamical Systems written by Klaus Schittkowski and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Book Synopsis Algorithmic Foundations of Robotics X by : Emilio Frazzoli
Download or read book Algorithmic Foundations of Robotics X written by Emilio Frazzoli and published by Springer. This book was released on 2013-02-14 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms are a fundamental component of robotic systems. Robot algorithms process inputs from sensors that provide noisy and partial data, build geometric and physical models of the world, plan high-and low-level actions at different time horizons, and execute these actions on actuators with limited precision. The design and analysis of robot algorithms raise a unique combination of questions from many elds, including control theory, computational geometry and topology, geometrical and physical modeling, reasoning under uncertainty, probabilistic algorithms, game theory, and theoretical computer science. The Workshop on Algorithmic Foundations of Robotics (WAFR) is a single-track meeting of leading researchers in the eld of robot algorithms. Since its inception in 1994, WAFR has been held every other year, and has provided one of the premiere venues for the publication of some of the eld's most important and lasting contributions. This books contains the proceedings of the tenth WAFR, held on June 13{15 2012 at the Massachusetts Institute of Technology. The 37 papers included in this book cover a broad range of topics, from fundamental theoretical issues in robot motion planning, control, and perception, to novel applications.
Book Synopsis Mathematical Methods in Optimization of Differential Systems by : Viorel Barbu
Download or read book Mathematical Methods in Optimization of Differential Systems written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.
Download or read book Dynamical Search written by Luc Pronzato and published by CRC Press. This book was released on 1999-08-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Estimation and Control of Dynamical Systems by : Alain Bensoussan
Download or read book Estimation and Control of Dynamical Systems written by Alain Bensoussan and published by Springer. This book was released on 2018-05-23 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games. The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general. Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.
Book Synopsis Optimal Estimation of Dynamic Systems by : John L. Crassidis
Download or read book Optimal Estimation of Dynamic Systems written by John L. Crassidis and published by CRC Press. This book was released on 2004-04-27 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most newcomers to the field of linear stochastic estimation go through a difficult process in understanding and applying the theory.This book minimizes the process while introducing the fundamentals of optimal estimation. Optimal Estimation of Dynamic Systems explores topics that are important in the field of control where the signals receiv
