Differential Equations Classical To Controlled
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Author | : L Brugnano |
Publisher | : CRC Press |
Total Pages | : 438 |
Release | : 1998-05-22 |
Genre | : Mathematics |
ISBN | : 9789056991074 |
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
Author | : Dahlard L. Lukes |
Publisher | : |
Total Pages | : 346 |
Release | : 1982 |
Genre | : Control theory |
ISBN | : |
Matrix algebra - the natural language of linear systems; Linear constant - coefficient equations: computation; Linear constant - coefficient equations: theory; Linear constant - coefficient equations: qualitative behavior; General linear equations with time - varying coefficients; Commutative linear differential equations; Periodic linear equations; Local existence and uniqueness theory of nonlinear equations; Global solutions; The general solution - dependence of solutions on parameters; Limit properties of solutions; Applications in control theory.
Author | : Isaak Rubinstein |
Publisher | : Cambridge University Press |
Total Pages | : 704 |
Release | : 1998-04-28 |
Genre | : Mathematics |
ISBN | : 9780521558464 |
The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Author | : Steven A. Frank |
Publisher | : Springer |
Total Pages | : 112 |
Release | : 2018-05-29 |
Genre | : Technology & Engineering |
ISBN | : 3319917072 |
This open access Brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon has a view of the whole. Each concept is illustrated by detailed examples and graphics. The full software code for each example is available, providing the basis for experimenting with various assumptions, learning how to write programs for control analysis, and setting the stage for future research projects. The topics focus on robustness, design trade-offs, and optimality. Most of the book develops classical linear theory. The last part of the book considers robustness with respect to nonlinearity and explicitly nonlinear extensions, as well as advanced topics such as adaptive control and model predictive control. New students, as well as scientists from other backgrounds who want a concise and easy-to-grasp coverage of control theory, will benefit from the emphasis on concepts and broad understanding of the various approaches. Electronic codes for this title can be downloaded from https://extras.springer.com/?query=978-3-319-91707-8
Author | : Dahlard L. Lukes |
Publisher | : |
Total Pages | : 0 |
Release | : 1982 |
Genre | : |
ISBN | : 9780124599802 |
Author | : Bill Goodwine |
Publisher | : Springer Science & Business Media |
Total Pages | : 762 |
Release | : 2010-11-11 |
Genre | : Mathematics |
ISBN | : 1441979190 |
This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.
Author | : A. K. Nandakumaran |
Publisher | : Cambridge University Press |
Total Pages | : 377 |
Release | : 2020-10-29 |
Genre | : Mathematics |
ISBN | : 1108839800 |
A valuable guide covering the key principles of partial differential equations and their real world applications.
Author | : V. Dhanya Ram |
Publisher | : Cambridge University Press |
Total Pages | : 417 |
Release | : 2022-10-31 |
Genre | : Technology & Engineering |
ISBN | : 1316517217 |
This book trains engineering students to identify multivariable transfer function models and design classical controllers for such systems.
Author | : Roland Herzog |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 474 |
Release | : 2022-03-07 |
Genre | : Mathematics |
ISBN | : 3110695987 |
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Author | : Philip Hartman |
Publisher | : SIAM |
Total Pages | : 612 |
Release | : 1982-01-01 |
Genre | : Mathematics |
ISBN | : 9780898719222 |
Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustrates techniques involving simple topological arguments, fixed point theorems, and basic facts of functional analysis. Unlike many texts, which supply only the standard simplified theorems, this book presents the basic theory of ODEs in a general way. This SIAM reissue of the 1982 second edition covers invariant manifolds, perturbations, and dichotomies, making the text relevant to current studies of geometrical theory of differential equations and dynamical systems. In particular, Ordinary Differential Equations includes the proof of the Hartman-Grobman theorem on the equivalence of a nonlinear to a linear flow in the neighborhood of a hyperbolic stationary point, as well as theorems on smooth equivalences, the smoothness of invariant manifolds, and the reduction of problems on ODEs to those on "maps" (Poincaré). Audience: readers should have knowledge of matrix theory and the ability to deal with functions of real variables.