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.

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.

At present, in order to resolve problems of ecology and to save mineral resources for future population generations, it is quite necessary to know how to maintain nature arrangement in an efficient way. It is possible to achieve a rational nature arrangement when analyzing solutions to problems concerned with optimal control of distributed systems and with optimization of modes in which main ground medium processes are functioning (motion of liquids, generation of temperature fields, mechanical deformation of multicomponent media). Such analysis becomes even more difficult because of heterogeneity of the region that is closest to the Earth surface, and thin inclusions/cracks in it exert their essential influence onto a state and development of the mentioned processes, especially in the cases of mining. Many researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L. Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E. Sanchez-Palencia [94] and others stress that it is necessary to consider how thin inclusions/cracks exert their influences onto development of these processes, while such inclusions differ in characteristics from main media to a considerable extent (moisture permeability, permeability to heat, bulk density or shear strength may be mentioned). Xll An influence exerted from thin interlayers onto examined processes is taken into account sufficiently adequately by means of various constraints, namely, by the conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52, 53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].

The applications of the theory of Optimal Control of distributed parameters is an extremely wide field and, although a large number of questions remain open, the whole subject continues to expand very rapidly. The author does not attempt to cover the field but does discuss a number of the more interesting areas of application.

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.

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.

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.