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Author: Ugo Boscain
Publisher: Springer Science & Business Media
ISBN: 9783540203063
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This book is devoted to optimal syntheses in control theory and focuses on minimum time on 2-D manifolds. The text outlines examples of applicability, introduces geometric methods in control theory, and analyzes single input systems on 2-D manifolds including classifications of optimal syntheses and feedbacks, their singularities, extremals projection and minimum time singularities. Various extensions and applications are also illustrated.
Author: Ugo Boscain
Publisher: Springer Science & Business Media
ISBN: 9783540203063
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This book is devoted to optimal syntheses in control theory and focuses on minimum time on 2-D manifolds. The text outlines examples of applicability, introduces geometric methods in control theory, and analyzes single input systems on 2-D manifolds including classifications of optimal syntheses and feedbacks, their singularities, extremals projection and minimum time singularities. Various extensions and applications are also illustrated.
Author: Heinz Schättler
Publisher: Springer Science & Business Media
ISBN: 1461438349
Category : Mathematics
Languages : en
Pages : 652
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Book Description
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.
Author: Jérôme Harmand
Publisher: John Wiley & Sons
ISBN: 1119597234
Category : Science
Languages : en
Pages : 241
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Book Description
Optimal control is a branch of applied mathematics that engineers need in order to optimize the operation of systems and production processes. Its application to concrete examples is often considered to be difficult because it requires a large investment to master its subtleties. The purpose of Optimal Control in Bioprocesses is to provide a pedagogical perspective on the foundations of the theory and to support the reader in its application, first by using academic examples and then by using concrete examples in biotechnology. The book is thus divided into two parts, the first of which outlines the essential definitions and concepts necessary for the understanding of Pontryagin’s maximum principle – or PMP – while the second exposes applications specific to the world of bioprocesses. This book is unique in that it focuses on the arguments and geometric interpretations of the trajectories provided by the application of PMP.
Author: Gianna Stefani
Publisher: Springer
ISBN: 331902132X
Category : Mathematics
Languages : en
Pages : 385
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Book Description
Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.
Author: Françoise Lamnabhi-Lagarrigu
Publisher: John Wiley & Sons
ISBN: 1118615131
Category : Technology & Engineering
Languages : en
Pages : 605
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Book Description
This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and experiences and reinforce scientific contacts in the large multidisciplinary area of the control of nonlinear and hybrid systems.
Author: Stuart A. Rice
Publisher: John Wiley & Sons
ISBN: 1118135237
Category : Science
Languages : en
Pages : 391
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Book Description
The Advances in Chemical Physics series—the cutting edge of research in chemical physics The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series offers contributions from internationally renowned chemists and serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics. This volume explores: Hydrogen Bond Topology and Proton Ordering in Ice and Water Clusters (Sherwin J. Singer and Chris Knight) Molecular Inner-Shell Spectroscopy, Arpis Technique and Its Applications (Eiji Shigemasa and Nobuhiro Kosugi) Geometric Optimal Control of Simple Quantum Systems: Geometric Optimal Control Theory (Dominique Sugny) Density Matrix Equation for a Bathed Small System and its Application to Molecular Magnets (D. A. Garanin) A Fractional Langevin Equation Approach to Diffusion Magnetic Resonance Imaging (Jennie Cooke)
Author: Daniel Liberzon
Publisher: Princeton University Press
ISBN: 1400842646
Category : Mathematics
Languages : en
Pages : 254
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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: Erol Sahin
Publisher: Springer
ISBN: 354071541X
Category : Computers
Languages : en
Pages : 232
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Book Description
This book constitutes the thoroughly refereed post-proceedings of the 2nd SAB 2006 International Workshop on Swarm Robotics held in Rome, Italy in September/October 2006 as a satellite event of SAB 2006, the 9th Conference on Simulation of Adaptive Behavior. The 14 revised full papers are organized in topical sections on algorithms, modeling and analysis, hardware, and evolutionary approaches.
Author: René Dáger
Publisher: Springer Science & Business Media
ISBN: 3540377263
Category : Science
Languages : en
Pages : 227
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Book Description
This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.
Author: Lionel Thibault
Publisher: World Scientific
ISBN: 981125818X
Category : Mathematics
Languages : en
Pages : 1629
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Book Description
The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.
