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).
Download or read book Application of the Euler Lagrange Method for solving optimal control problems written by Olaosebikan Temitayo Emmanuel and published by GRIN Verlag. This book was released on 2019-11-13 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2019 in the subject Mathematics - Applied Mathematics, grade: 96.50, , course: Mathematics, language: English, abstract: In this research, Euler-Lagrange Method approach, for solving optimal control problems of both one dimensional and generalized form was considered. In years past, calculus of variation, has been used to solve functional optimization problems. However, with some special features in Calculus of Variation technique, making it unique in solving functional unconstrained optimization problems, these features will be advantageous to solving optimal control problems if it can be amended and modified in one way or the other. This call for the Euler-Lagrange Method which is a modification of the Calculus of Variation Method for solving optimal control problems. It is desired that, with the construction of the new algorithm, it will circumvent the difficulties undergone in constructing control operators which are embedded in Conjugate Gradient Method (CGM) for solving optimal control problems. Its application on some test problems have shown improvement in the results compared with existing results of solving this class of problems. The objective function values for problems 3, 4, 6, 7, 8, 9 and 10 which are: 1.359141, -5.000, 0.36950416, 0.51699120, 0.27576806, 1.5934159×[10]^(-2) and -3.880763×[10]^(-2) appreciate to the existing results 1.359141, -5.000, 0.4146562, 0.613969, 0.2739811, 1.5935×[10]^(-3) and -3.9992×[10]^(-2) respectively while the objective function values for problems 1, 2 and 5 do not fully appreciate to the existing results with slight differences. These results is an indication that the method has some advantages over some existing computational techniques built to take care of the said problems.
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 Computational Methods in Optimal Control Problems written by I.H. Mufti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows: In the first two sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given. The method of steepest descent and a conjugate gradient-method are dis cussed in Section 3. In the remaining sections, the successive sweep method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of Newton Raphson approximation to the necessary conditions of optimality. The second-variation method and other shooting methods based on minimizing an error function are also considered. TABLE OF CONTENTS 1. 0 INTRODUCTION 1 2. 0 NECESSARY CONDITIONS FOR OPTIMALITY •••••••• 2 3. 0 THE GRADIENT METHOD 4 3. 1 Min H Method and Conjugate Gradient Method •. •••••••••. . . . ••••••. ••••••••. • 8 3. 2 Boundary Constraints •••••••••••. ••••. • 9 3. 3 Problems with Control Constraints ••. •• 15 4. 0 SUCCESSIVE SWEEP METHOD •••••••••••••••••••• 18 4. 1 Final Time Given Implicitly ••••. •••••• 22 5. 0 SECOND-VARIATION METHOD •••••••••••••••••••• 23 6. 0 SHOOTING METHODS ••••••••••••••••••••••••••• 27 6. 1 Newton-Raphson Method ••••••••••••••••• 27 6.
Download or read book Convergence Analysis of a Projected Gradient Method for a Class of Optimal Control Problems written by Tiehong Tian and published by . This book was released on 1992 with total page 146 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 A Generalized Gradient in Optimal Control written by David Davis Barnett and published by . This book was released on 1973 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gradient methods or methods of steepest descent in control-space have been found to be quite useful for the numerical solution of a large class of problems in optimal control. However, there is a large class of problems for which these methods have not been successful. To deal with this larger class of problems, a generalized gradient method is proposed. The convergence rate of this method is analyzed for a certain class of problems and the analysis is verified numerically. The analysis is then used to suggest improvements in the basic algorithm. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The Solution of Optimal Control Problems by a First order Gradient Method written by B.A.M. Piggott and published by . This book was released on 1972 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Techniques IFIP Technical Conference written by Conference on Optimization Techniques and published by Springer. This book was released on 2013-12-01 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Methods in Optimal Control Theory written by Vadim Krotov and published by CRC Press. This book was released on 1995-10-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.
Download or read book Optimal Control written by Bulirsch and published by Birkhäuser. This book was released on 2013-03-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Practical Methods for Optimal Control and Estimation Using Nonlinear Programming written by John T. Betts and published by SIAM. This book was released on 2010-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.
Download or read book Conjugate Gradient Approach for Discrete Time Optimal Control Problems with Model Reality Differences written by Sie Long Kek and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, an efficient computation approach is proposed for solving a general class of discrete-time optimal control problems. In our approach, a simplified optimal control model, which is adding the adjusted parameters into the model used, is solved iteratively. In this way, the differences between the real plant and the model used are calculated, in turn, to update the optimal solution of the model used. During the computation procedure, the equivalent optimization problem is formulated, where the conjugate gradient algorithm is applied in solving the optimization problem. On this basis, the optimal solution of the modified model-based optimal control problem is obtained repeatedly. Once the convergence is achieved, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, both linear and nonlinear examples are demonstrated to show the performance of the approach proposed. In conclusion, the efficiency of the approach proposed is highly presented.
Download or read book An Algorithm for Solving Optimal Control Problems Via the Sequential Conjugate Gradient restoration Method written by A. V. Levy and published by . This book was released on 1976 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
