Geometric And Numerical Optimal Control

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Geometric And Numerical Optimal Control

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Author : Bernard Bonnard
language : en
Publisher: Springer
Release Date : 2018-07-27

Geometric And Numerical Optimal Control written by Bernard Bonnard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-27 with Mathematics categories.

This book introduces readers to techniques of geometric optimal control as well as the exposure and applicability of adapted numerical schemes. It is based on two real-world applications, which have been the subject of two current academic research programs and motivated by industrial use – the design of micro-swimmers and the contrast problem in medical resonance imaging. The recently developed numerical software has been applied to the cases studies presented here. The book is intended for use at the graduate and Ph.D. level to introduce students from applied mathematics and control engineering to geometric and computational techniques in optimal control.

Geometric Optimal Control

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Author : Heinz Schättler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26

Geometric Optimal Control written by Heinz Schättler 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 2012-06-26 with Mathematics categories.

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Geometric And Numerical Foundations Of Movements

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Author : Jean-Paul Laumond
language : en
Publisher: Springer
Release Date : 2017-05-02

Geometric And Numerical Foundations Of Movements written by Jean-Paul Laumond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-02 with Technology & Engineering categories.

This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.

Variational Methods

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Author : Maïtine Bergounioux
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-01-11

Variational Methods written by Maïtine Bergounioux and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-11 with Mathematics categories.

With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index

Control Theory From The Geometric Viewpoint

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Author : Andrei A. Agrachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Control Theory From The Geometric Viewpoint written by Andrei A. Agrachev 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 2013-03-14 with Science categories.

This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters.

Optimal Control And Geometry Integrable Systems

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Author : Velimir Jurdjevic
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-04

Optimal Control And Geometry Integrable Systems written by Velimir Jurdjevic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-04 with Mathematics categories.

Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.

Geometric Partial Differential Equations Part 2

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Author : Andrea Bonito
language : en
Publisher: Elsevier
Release Date : 2021-01-26

Geometric Partial Differential Equations Part 2 written by Andrea Bonito and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Mathematics categories.

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Geometry Of Feedback And Optimal Control

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Author : B. Jakubczyk
language : en
Publisher: CRC Press
Release Date : 1997-11-19

Geometry Of Feedback And Optimal Control written by B. Jakubczyk and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-19 with Mathematics categories.

This work gathers important and promising information results in subfields of nonlinear control theory, previously available in journals. It presents the state of the art of geometric methods, their applications optimal control, and feedback transformations. It aims to show how geometric control theory draws from other mathematical fields to create its own powerful tools.

Optimal Control

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Author : Bulirsch
language : en
Publisher: Birkhäuser
Release Date : 2013-03-08

Optimal Control written by Bulirsch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Science categories.

"Optimal Control" reports on new theoretical and practical advances essential for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are discussed. These have been achieved through new techniques for solving large-sized nonlinear programs with sparse Hessians, and through a combination of direct and indirect methods for solving the multipoint boundary value problem. The book also focuses on the construction of feedback controls for nonlinear systems and highlights advances in the theory of problems with uncertainty. Decomposition methods of nonlinear systems and new techniques for constructing feedback controls for state- and control constrained linear quadratic systems are presented. The book offers solutions to many complex practical optimal control problems.

Contemporary Trends In Nonlinear Geometric Control Theory And Its Applications

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Author : A. Anzaldo-Meneses
language : en
Publisher: World Scientific
Release Date : 2002

Contemporary Trends In Nonlinear Geometric Control Theory And Its Applications written by A. Anzaldo-Meneses and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Concerns contemporary trends in nonlinear geometric control theory and its applications.