Download or read book On Convergence of Discrete Approximations to Constrained Optimal Control Problems written by Lylia Esther Cuesta Sainz de la Torre and published by . This book was released on 1991 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Consistent Approximations of Constrained Optimal Control Problems written by Vadim Azhmyakov and published by Logos Verlag Berlin. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved over a period of years as the author taught classes in numerical analysis, optimization theory and optimal control to graduate students in mathematics and engineering. The material presented in this monograph is the result of author's work at the E.M.A. University of Greifswald and at the Technical University of Berlin. The book has likewise been influenced by my research programs that have relied on the application of the proximal-based numerical schemes and algorithms to constrained optimal control problems. The task of my project was to look closely at the possible consistent techniques of numerical analysis for constrained optimal control problems and the corresponding convergence analysis. The aim of this book is to provide some proximal-type regular computational methods for optimal control processes governed by ordinary differential equations.This book gives a self-contained and systematic exposition of the proximal-regularization methods to optimal control problems with general constraints. It can be used as a textbook for PhD students majoring in mathematical control theory and also serve as a reference for researchers in applied mathematics, control engineering and computational sciences.
Download or read book Constrained Optimization and Optimal Control for Partial Differential Equations written by Günter Leugering and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Download or read book Numerical Methods for Optimal Control Problems with State Constraints written by Radoslaw Pytlak and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This book fills the gap by providing a family of new methods. Among others, a novel convergence analysis of optimal control algorithms is introduced. The analysis refers to the topology of relaxed controls only to a limited degree and makes little use of Lagrange multipliers corresponding to state constraints. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods. Further, the implementation aspects of the methods developed in the book are presented and discussed. The results concerning ordinary differential equations are then extended to control problems described by differential-algebraic equations in a comprehensive way for the first time in the literature.
Download or read book Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control written by Boris S. Mordukhovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.
Download or read book Discrete Approximations to Continuous Optimal Control Problems written by Maurice Eggen and published by . This book was released on 1972 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control of Partial Differential Equations written by Andrea Manzoni and published by Springer Nature. This book was released on 2022-01-01 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.
Download or read book Rates of Convergence for Discrete Approximations to Problems in Control Theory written by William Ward Hager and published by . This book was released on 1974 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Control Part B written by Emmanuel Trélat and published by Elsevier. This book was released on 2023-02-20 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control
Download or read book Perturbations Approximations and Sensitivity Analysis of Optimal Control Systems written by A. L. Dontchev and published by Springer. This book was released on 1983 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to current problems in sensitivity analysis of optimal control. Two topics are considered: well-posedness, i.e. continuation of the solutions; & estimation of variations in solutions of constrained optimal control problems resulting from various changes of the model.
Download or read book On the Numerical Solution of Nonlinear and Hybrid Optimal Control Problems written by Matthias Rungger and published by kassel university press GmbH. This book was released on 2012 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convex Analysis and Minimization Algorithms I written by Jean-Baptiste Hiriart-Urruty and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.
Download or read book Some Successive Approximation Methods in Control and Oscillation Theory by Peter L Falb and Jan L de Jong written by and published by Academic Press. This book was released on 1969 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 1996 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Approximations to Continuous Optimal Control Problems written by J. Cullum and published by . This book was released on 1967 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Approximations in Discrete Time Stochastic Control written by Naci Saldi and published by Birkhäuser. This book was released on 2018-05-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.
Download or read book Optimal Control of Complex Structures written by K.-H. Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the area of control of systems defined by partial differential Equations has increased strongly in recent years. A major reason has been the requirement of these systems for sensible continuum mechanical modelling and optimization or control techniques which account for typical physical phenomena. Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics. This volume contains original articles by world reknowned experts in the fields of optimal control of partial differential equations, shape optimization, numerical methods for partial differential equations and fluid dynamics, all of whom have contributed to the analysis and solution of many of the problems discussed. The collection provides a state-of-the-art overview of the most challenging and exciting recent developments in the field. It is geared towards postgraduate students and researchers dealing with the theoretical and practical aspects of a wide variety of high technology problems in applied mathematics, fluid control, optimal design, and computer modelling.
