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Author: Quan-Fang Wang Publisher: LAP Lambert Academic Publishing ISBN: 9783844303964 Category : Differential equations, Parabolic Languages : en Pages : 108
Book Description
In this work, we have studied the quadratic cost optimal control problems and their numerical analysis of nonlinear parabolic distributed parameter systems. After established the fundamental existence and uniqueness results, we have developed the nonlinear optimal control theory for the equations having uniform Lipschitz continuous nonlinearity. Then we have applied the theoretical results to practical nonlinear parabolic partial differential equations including reaction-diffusion equations, diffusion Hopfield neural network equations. Furthermore, numerical evidences for these issues have also been solved by using variational method and finite element approach.
Author: Quan-Fang Wang Publisher: LAP Lambert Academic Publishing ISBN: 9783844303964 Category : Differential equations, Parabolic Languages : en Pages : 108
Book Description
In this work, we have studied the quadratic cost optimal control problems and their numerical analysis of nonlinear parabolic distributed parameter systems. After established the fundamental existence and uniqueness results, we have developed the nonlinear optimal control theory for the equations having uniform Lipschitz continuous nonlinearity. Then we have applied the theoretical results to practical nonlinear parabolic partial differential equations including reaction-diffusion equations, diffusion Hopfield neural network equations. Furthermore, numerical evidences for these issues have also been solved by using variational method and finite element approach.
Author: Goong Chen Publisher: CRC Press ISBN: 9780203904190 Category : Mathematics Languages : en Pages : 382
Book Description
An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics a
Author: Jean-Pierre Babary Publisher: Elsevier ISBN: 1483153231 Category : Technology & Engineering Languages : en Pages : 661
Book Description
Control of Distributed Parameter Systems 1982 covers the proceeding of the Third International Federation of Automatic Control (IFAC) Symposium on Control of Distributed Parameter Systems. The book reviews papers that tackle issues concerning the control of distributed parameter systems, such as modeling, identification, estimation, stabilization, optimization, and energy system. The topics that the book tackles include notes on optimal and estimation result of nonlinear systems; approximation of the parameter identification problem in distributed parameters systems; and optimal control of a punctually located heat source. This text also encompasses the stabilization of nonlinear parabolic equations and the decoupling approach to the control of large spaceborne antenna systems. Stability of Hilbert space contraction semigroups and the tracking problem in the fractional representation approach are also discussed. This book will be of great interest to researchers and professionals whose work concerns automated control systems.
Author: Pekka Neittaanmaki Publisher: CRC Press ISBN: 9780824790813 Category : Mathematics Languages : en Pages : 432
Book Description
This book discusses theoretical approaches to the study of optimal control problems governed by non-linear evolutions - including semi-linear equations, variational inequalities and systems with phase transitions. It also provides algorithms for solving non-linear parabolic systems and multiphase Stefan-like systems.
Author: W. Desch Publisher: Birkhäuser ISBN: 303488849X Category : Mathematics Languages : en Pages : 308
Book Description
Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.
Author: David A. Wismer Publisher: ISBN: Category : Control theory Languages : en Pages : 130
Book Description
The (approximate) solution of optimal control problems involving partial differential equations is studied by discretizing the space domain and considering the resultant set of ordinary differential equations. This approach is certainly not new. However, earlier efforts along this path have been hampered by the difficulties involved in solving the optimal control problem for the very large sets of interacting ordinary differential equations which arise as the discretization interval is decreased. This dissertation suggests the use of multilevel control techniques to overcome this computational difficulty. The major conclusion stemming from this research is that the multilevel approach does appear feasible in solving the optimal control problem for certain classes of distributed parameter systems; namely, linear and nonlinear parabolic or elliptic equations. The convergence properties of the second-level controller are of paramount importance in accomplishing this task. Of the three types of second-level controllers discussed here (feasible, nonfeasible, and Gauss-Seidel), the only one considered suitable in this application is the Gauss-Seidel controller. It is extremely simple and was found to have good convergence properties for this type of problem. In particular, the systems of semidiscrete equations may become very large and the number of subsystems likewise. By its very nature, the performance of the Gauss-Seidel controller does not seem to be degraded by increasing the number of subsystems as long as the discretization interval is not 'too small.' The reason for the good convergence properties observed for this controller is largely the tridiagonal form of the A sub j matrix.
Author: Dan Tiba Publisher: Springer ISBN: 3540467556 Category : Science Languages : en Pages : 166
Book Description
The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
Author: Alfred C. Robinson Publisher: ISBN: Category : Control theory Languages : en Pages : 54
Book Description
The report is a survey of theoretical and computational methods in the field of optimal control of distributed parameter systems. This includes systems described by integral equations and partial differential equations. The various studies which have been done are grouped according to the method employed. A number of applications and potential applications of these methods are discussed, and certain deficiencies in the current state of knowledge are noted. Difficulties and opportunities in practical applications are discussed, and suggestions are offered for directions of research to render the results more readily usable. A list of references is included numbering more than 250 items: papers, report, and books.
Author: Wolfgang Desch Publisher: Birkhäuser ISBN: 303488530X Category : Mathematics Languages : en Pages : 403
Book Description
22 papers on control of nonlinear partial differential equations highlight the area from a broad variety of viewpoints. They comprise theoretical considerations such as optimality conditions, relaxation, or stabilizability theorems, as well as the development and evaluation of new algorithms. A significant part of the volume is devoted to applications in engineering, continuum mechanics and population biology.
Author: Quan-Fang Wang
Author: Quan-Fang Wang
Author: Goong Chen
Author: Jean-Pierre Babary
Author: Pekka Neittaanmaki
Author: W. Desch
Author: David A. Wismer
Author: Dan Tiba
Author: Alfred C. Robinson
Author: Wolfgang Desch
Author: J. L. Lions