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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: 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: 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: 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: S. P. Banks Publisher: Elsevier ISBN: 1483151123 Category : Computers Languages : en Pages : 554
Book Description
Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.
Author: K.A. Lurie Publisher: Springer Science & Business Media ISBN: 147579262X Category : Science Languages : en Pages : 503
Book Description
This book represents an extended and substantially revised version of my earlierbook, Optimal Control in Problems ofMathematical Physics,originally published in Russian in 1975. About 60% of the text has been completely revised and major additions have been included which have produced a practically new text. My aim was to modernize the presentation but also to preserve the original results, some of which are little known to a Western reader. The idea of composites, which is the core of the modern theory of optimization, was initiated in the early seventies. The reader will find here its implementation in the problem of optimal conductivity distribution in an MHD-generatorchannel flow.Sincethen it has emergedinto an extensive theory which is undergoing a continuous development. The book does not pretend to be a textbook, neither does it offer a systematic presentation of the theory. Rather, it reflects a concept which I consider as fundamental in the modern approach to optimization of dis tributed systems. Bibliographical notes,though extensive, do not pretend to be exhaustive as well. My thanks are due to ProfessorJean-Louis Armand and ProfessorWolf Stadler whose friendly assistance in translating and polishing the text was so valuable. I am indebted to Mrs. Kathleen Durand and Mrs. Colleen Lewis for the hard job of typing large portions of the manuscript.
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: Charles Teo Publisher: Academic Press ISBN: 0080956785 Category : Computers Languages : en Pages : 331
Book Description
Optimal control theory of distributed parameter systems has been a very active field in recent years; however, very few books have been devoted to the studiy of computational algorithms for solving optimal control problems. For this rason the authors decided to write this book. Because the area is so broad, they confined themselves to optimal control problems involving first and second boundary-value problems of a linear second-order parabolic partial differential equation. However the techniques used are by no means restricted to these problems. They can be and in some cases already have been applied to problems involving other types of distributed parameter system. The authors aim is to devise computational algorithms for solving optimal control problems with particular emphasis on the mathematical theory underlying the algorithms. These algorithms are obtained by using a first-order strong variational method or gradient-type methods.
Author: David A. Wismer
Author: David A. Wismer
Author: Alfred C. Robinson
Author: Dan Tiba
Author: J. L. Lions
Author: Philip Kunlun Chiu
Author: S. P. Banks
Author: K.A. Lurie
Author: Jean-Pierre Babary
Author: O. R. Benz
Author: Charles Teo