Download or read book Approximate Minimization of Functionals by Discretization Numerical Methods in Optimal Control written by James W. Daniel and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximate Minimization of Functionals by Discretization Numerical Methods in Optimal Control written by James W. Daniel and published by . This book was released on 1970 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamilton Jacobi Bellman Equations written by Dante Kalise and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
Download or read book On the Approximate Minimization of Functionals written by James W. Daniel and published by . This book was released on 1968 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers in general the problem of finding the minimum of a given functional f(u) over a set B by approximately minimizing a sequence of functionals f sub n(u sub n) over a 'discretized' set B sub n; theorems are given proving the convergence of the approximating points u sub n in B sub n to the desired point u in B. Applications are given to the Rayleigh-Ritz method, regularization, Chebyshev solution of differential equations, and the calculus of variations. (Author).
Download or read book The Approximate Minimization of Functionals written by James W. Daniel and published by Prentice Hall. This book was released on 1971 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control of ODEs and DAEs written by Matthias Gerdts and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics and interest in optimal control. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Examples are provided for illustration purposes.
Download or read book Numerical Methods for Optimal Control Problems written by Maurizio Falcone and published by Springer. This book was released on 2019-01-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.
Download or read book Some Aspects of the Optimal Control of Distributed Parameter Systems written by J. L. Lions and published by SIAM. This book was released on 1972-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses a number of the more interesting areas in the application of the theory of Optimal Control of distributed parameters.
Download or read book On the Convergence of a Numerical Method for Optimal Control Problems written by James W. Daniel and published by . This book was released on 1968 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: A recent method for the numerical solution of certain types of optimal control problems consists in discretizing the problem, that is, in replacing differential equations by difference equations and integral functionals of continuous functions by functions of finitely many variables; the solution of the resulting mathematical programming problem is taken as an approximate solution for the control problem. In this paper we prove, under intuitively reasonable assumptions, the convergence of this process as the discretization size tends to zero. (Author).
Download or read book The Approximate Minimization of Functionals written by James W. Daniel and published by Prentice Hall. This book was released on 1971 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fast Solution of Discretized Optimization Problems written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Download or read book Optimization with PDE Constraints written by Ronald Hoppe and published by Springer. This book was released on 2014-09-11 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).
Download or read book A Variational Approach to Optimal Control of ODEs written by Pablo Pedregal and published by SIAM. This book was released on 2022-07-26 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book presents in a unified, systematic way the basic principles of optimal control governed by ODEs. Using a variational perspective, the author incorporates important restrictions like constraints for control and state, as well as the state system itself, into the equivalent variational reformulation of the problem. The fundamental issues of existence of optimal solutions, optimality conditions, and numerical approximation are then examined from this variational viewpoint. Inside, readers will find a unified approach to all the basic issues of optimal control, academic and real-world examples testing the book’s variational approach, and a rigorous treatment stressing ideas and arguments rather than the underlying mathematical formalism. A Variational Approach to Optimal Control of ODEs is mainly for applied analysts, applied mathematicians, and control engineers, but will also be helpful to other scientists and engineers who want to understand the basic principles of optimal control governed by ODEs. It requires no prerequisites in variational problems or expertise in numerical approximation. It can be used for a first course in optimal control.
Download or read book The University of Texas Publication written by and published by . This book was released on 1970 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods and Applications written by Ivan Lirkov and published by Springer Science & Business Media. This book was released on 2003 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control from Theory to Computer Programs written by Viorel Arnăutu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present the mathematical theory and the know-how to make computer programs for the numerical approximation of Optimal Control of PDE's. The computer programs are presented in a straightforward generic language. As a consequence they are well structured, clearly explained and can be translated easily into any high level programming language. Applications and corresponding numerical tests are also given and discussed. To our knowledge, this is the first book to put together mathematics and computer programs for Optimal Control in order to bridge the gap between mathematical abstract algorithms and concrete numerical ones. The text is addressed to students and graduates in Mathematics, Mechanics, Applied Mathematics, Numerical Software, Information Technology and Engineering. It can also be used for Master and Ph.D. programs.
Download or read book The Construction of Algorithms for the Approximation of Certain Optimal Control Problems written by S. Ulm and published by . This book was released on 1968 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution to certain optimum control problems can be reduced to problems of finding the absolute minima of certain functionals in function spaces. For an approximate solution to the latter problems use can be made of algorithms developed for the solution of nonlinear equations. In previous works by other authors Newton's method and a particular variant of the method of gradients were generalized for the solution of optimum control problems. On the basis of methods of functional analysis the present article gives a more general scheme for the construction of methods of this type for the solution of certain optimum control problems.
