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 Control Theory in Engineering written by Constantin Volosencu and published by BoD – Books on Demand. This book was released on 2020-05-27 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation.
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 The Conjugate Gradient Method for Optimal Control Problems written by and published by . This book was released on 1967 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugate Gradient Type Methods for Ill Posed Problems written by Martin Hanke and published by CRC Press. This book was released on 2017-11-22 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Download or read book Experimental Evaluation and Comparison of Conjugate Gradient Methods in Unconstrained Optimal Control written by Patrick A. O'Kane and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Adaptations of the Conjugate Gradient Method to Optimal Control Problems with Terminal State Constraints written by John Kendall Willoughby and published by . This book was released on 1969 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of conjugate gradients (CG) has been shown to be a rapidly converging and efficient means of solving unconstrained optimal control problems. This dissertation presents some theoretical and computational characteristics of three modifications to the CG algorithm which make it applicable to control problems with terminal state variable constraints. The penalty function method and the projection method have been used to adapt ordinary gradient methods to constrained problems. It is concluded here that the penalty function technique is no more or less advantageous with the CG method than with other gradient techniques. The projection method is shown to be theoretically less compatible with the CG algorithm than with other gradient methods. However, a stepsize adjustment policy is suggested that preserves the rapid convergence that is characteristic of the CG method. It is also shown that nonlinear instead of linear terminal constraints cause no additional theoretical of computational difficulty. A third adaptation of the CG method is given which is original to this study. The method, called the modified conjugate gradient method (MCG), is applied to constrained problems by using constant Lagrange multipliers which converge to their optimal values as the iteration proceeds. A unique feature of the MCG method is that each control iterate produced by the method causes the constraints to be satisfied exactly. Furthermore, the technique is equally applicable to nonlinear and linear terminal state constraints. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 994 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugate Gradient Optimal Control Methods written by B. L. Pierson and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems written by J. C. Heideman and published by . This book was released on 1974 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Robust Conjugate gradient Algorithm for Optimal Control Problems written by H. N. Koivo and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems with Nondifferental Constraints Part 1 Theory written by and published by . This book was released on 1977 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies in Smoothing and in Conjugate Gradient Methods Applied to Optimal Control Problems written by Raman Kumar Mehra and published by . This book was released on 1967 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Conjugate Gradient Methods for Discretized Elliptic Optimal Control Problems written by Robert Leitner and published by . This book was released on 2015 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
