Download or read book A Gradient Computational Technique for a Class of Optimal Control Problems Subject to Inequality Constraints written by Shyh Jong Wang and published by . This book was released on 1969 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied and Computational Optimal Control written by Kok Lay Teo and published by Springer Nature. This book was released on 2021-05-24 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to furnish the reader with a rigorous and detailed exposition of the concept of control parametrization and time scaling transformation. It presents computational solution techniques for a special class of constrained optimal control problems as well as applications to some practical examples. The book may be considered an extension of the 1991 monograph A Unified Computational Approach Optimal Control Problems, by K.L. Teo, C.J. Goh, and K.H. Wong. This publication discusses the development of new theory and computational methods for solving various optimal control problems numerically and in a unified fashion. To keep the book accessible and uniform, it includes those results developed by the authors, their students, and their past and present collaborators. A brief review of methods that are not covered in this exposition, is also included. Knowledge gained from this book may inspire advancement of new techniques to solve complex problems that arise in the future. This book is intended as reference for researchers in mathematics, engineering, and other sciences, graduate students and practitioners who apply optimal control methods in their work. It may be appropriate reading material for a graduate level seminar or as a text for a course in optimal control.
Download or read book Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraint written by Thomas Shu Fong and published by . This book was released on 1970 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the intersections of the linear spaces spanned by the search directions and the set of admissible controls. The computational aspect of this class of control problems is discussed in detail. This computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (Author).
Download or read book Conjugate gradient method for the solution of optimal control problems governed by weakly singular Volterra integral equations with the use of the collocation method written by Henry Ekah-Kunde and published by GRIN Verlag. This book was released on 2017-07-28 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
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 Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraints written by T. S. Fong and published by . This book was released on 1978 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the itersection of the linear spaces spanned by the search directions and the set of admissible controls. The computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (author).
Download or read book Computational Optimal Control written by Roland Bulirsch and published by Birkhäuser. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resources should be used sparingly both from a point of view of economy and eco logy. Thus in controlling industrial, economical and social processes, optimization is the tool of choice. In this area of applied numerical analysis, the INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL (IFAC) acts as a link between research groups in universities, national research laboratories and industry. For this pur pose, the technical committee Mathematics of Control of IFAC organizes biennial conferences with the objective of bringing together experts to exchange ideas, ex periences and future developments in control applications of optimization. There should be a genuine feedback loop between mathematicians, computer scientists, engineers and software developers. This loop should include the design, application and implementation of algorithms. The contributions of industrial practitioners are especially important. These proceedings contain selected papers from a workshop on CONTROL Ap PLICATIONS OF OPTIMIZATION, which took place at the Fachhochschule Miinchen in September 1992. The workshop was the ninth in a series of very successful bien nial meetings, starting with the Joint Automatic Control Conference in Denver in 1978 and followed by conferences in London, Oberpfaffenhofen, San Francisco, Ca pri, Tbilisi and Paris. The workshop was attended by ninety researchers from four continents. This volume represents the state of the art in the field, with emphasis on progress made since the publication of the proceedings of the Capri meeting, edited by G. di Pillo under the title 'Control Applications of Optimization and Nonlinear Programming'.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1987 with total page 1390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book A Computational Method for a General Class of Optimal Control Problems Involving Integro differential Equations written by M. A. Lukas and published by . This book was released on 1990 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Gradient restoration Algorithm for Optimal Control Problems with Bounded State Variables written by G. R. Hennig and published by . This book was released on 1972 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the numerical solution of optimal control problems involving a functional I subject to differential constraints, a state variable inequality constraint, and terminal constraints. The problem is to find the state x(t), the control u(t), and the parameter pi so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. The approach taken is a sequence of two-phase processes or cycles, composed of a gradient phase and a restoration phase. (Modified author abstract).
Download or read book Engineering Science and Mechanics written by Richard W. Longman and published by . This book was released on 1983 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings written by and published by . This book was released on 1971 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summaries of Projects Completed written by National Science Foundation (U.S.) and published by . This book was released on with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computation of Optimal Controls Within a Class of Piecewise Continuous Functions written by Hans Jurg Rutishauser and published by . This book was released on 1971 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Gradient restoration Algorithm for Optimal Control Problems with Bounded State Variables written by G. R. Hennig and published by . This book was released on 1972 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hennig and Miele developed the sequential gradient-restoration algorithm for minimizing a function subject to differential constraints, a state variable inequality constraint, and terminal constraints. In the report, six numerical examples are presented, four pertaining to the fixed-final-time case and two pertaining to the free-final-time case. The numerical results show the rapid convergence characteristics of the sequential gradient-restoration algorithm. (Author).
Download or read book A Gradient Method of Solving One Class of Optimal Control Problems written by O. V. Vasilev and published by . This book was released on 1969 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The article deals with the problem of minimizing the mean-square value of a part of the components of the final state of an object whose motion is described by a linear system of ordinary differential equations with initial conditions. The problem is solved under the condition that the remaining components of the final state of the object go through a specified point manifold. By making use several premises of functional analysis, and extending a method first described by R. Gabasov and F.M. Kirillova, the problem is reduced to that of determining the maximum of a certain convex function of a finite number of variables, which play the role of the initial values of the vector of a conjugate system. The search is carried out by a gradient method which is analogous in a certain sense with the method of steepest ascent. (Author).
