The purpose of the Conference on Optimal Control of Partial Differential Equations was to bring together leading experts in this field and to exchange ideas and information about recent advances in control theory connected with partial differential equations. The papers collected in these Proceedings are mainly research papers in which new results are presented. Out of a broad spectrum of topics the problem of exact controllability played a central role, and also shape control was given some special attention. Nonlinear problems were mainly treated under the aspect of optimality whereas identification problems and also numerical aspects were considered only treated marginally.

The 2-yearly French-German Conferences on Optimization review the state-of-the-art and the trends in the field. The proceedings of the Fifth Conference include papers on projective methods in linear programming (special session at the conference), nonsmooth optimization, two-level optimization, multiobjective optimization, partial inverse method, variational convergence, Newton type algorithms and flows and on practical applications of optimization. A. Ioffe and J.-Ph. Vial have contributed survey papers on, respectively second order optimality conditions and projective methods in linear programming.

This international conference on "Advances in Communications and Control Systems" was held to bring together researchers in communications, control systems, computing and signal processing to explore common themes and present research results of broad interest. The focus of the conference was on presenting research results in a fashion that would make them accessible to groups wider than that of the narrow specialist. Many papers, therefore, are of a type that might be termed survey/research. The topics include control theory, communication detection, high speed computing, distributed parameter systems, nonlinear systems, stochastic optimization, source coding, robust control and applications, and neural networks. Selected papers from the conference are presented both in this book and in its companion volume Advances in Computing and Control.

This monograph considers the integration of knowledge-based soft control with hard control algorithms. As a specific application, the development of a knowledge-based controller for robotic manipulators is addressed. Servo control alone is known to be inadequate for nonlinear and high-speed processes including robots. Furthermore, knowledge-based control such as fuzzy control, when directly included in the servo loop, has produced insatisfactory performance in research robots. These considerations, along with the fact that human experts can very effectively perform tuning functions in process controllers, form the basis for the control structure proposed in this work. The book is suitable for students, researchers and practising professionals in the fields of Automatic Control and Robotics. The material is presented in simple and clear language with sufficient introductory information. Someone with an undergraduate knowledge in dynamics and control should be able to use the book without any difficulty.

This conference on nonlinear control theory was organized within a special "Nonlinear Year" of the French "Centre National de la Recherche Scientifique." This volume is a collection of invited papers giving an overview of new trends in research all over the world. It was the aim of the editors to bring together theoretical contributions by pure mathematicians and more applied communications dedicated to robotics, electrical engines, biology and computer science.

This volume consists of six essays that develop and/or apply "rational expectations equilibrium inventory models" to study the time series behavior of production, sales, prices, and inventories at the industry level. By "rational expectations equilibrium inventory model" I mean the extension of the inventory model of Holt, Modigliani, Muth, and Simon (1960) to account for: (i) discounting, (ii) infinite horizon planning, (iii) observed and unobserved by the "econometrician" stochastic shocks in the production, factor adjustment, storage, and backorders management processes of firms, as well as in the demand they face for their products; and (iv) rational expectations. As is well known according to the Holt et al. model firms hold inventories in order to: (a) smooth production, (b) smooth production changes, and (c) avoid stockouts. Following the work of Zabel (1972), Maccini (1976), Reagan (1982), and Reagan and Weitzman (1982), Blinder (1982) laid the foundations of the rational expectations equilibrium inventory model. To the three reasons for holding inventories in the model of Holt et al. was added (d) optimal pricing. Moreover, the popular "accelerator" or "partial adjustment" inventory behavior equation of Lovell (1961) received its microfoundations and thus overcame the "Lucas critique of econometric modelling.

This monograph is sums up the development of singular system theory and provides the control circle with a systematic theory of the system. It focuses on the analysis and synthesis of singular control systems. Its distinctive features include systematic discussion of controllabilities and observabilities, design of singular or normal observers and compensators with their structural stability, systems analysis via transfer matrix, and studies of discrete-time singular systems. Some acquaintance with linear algebra and linear systems is assumed. Prospective readers are graduate students, scientists, and other researchers in control theory and its applications. Much of the material in the book is new.

Traditional FEM and the more recent BEM underlie many engineering computational methods and corresponding software. Both methods have their merits and also their limitations. The combination of both methods will provide an improved numerical tool in the future. The aim of this book is to present significant basic formulations of FEM and BEM and to show their common practical and mathematical foundations, their differences and possibilities for their combination. These include variational foundations, FEM and BEM for linear and non-linear elasticity and potential problems, the combination of FEM-BEM asymptotic error analysis, modifications due to corner and crack singularities and corresponding improvement of convergence, plastic analysis, numerical algorithms and engineering applications.

The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational in equalities theory are the topics of the well-known monograph by G. Du vaut and J. L. Lions, Les iniquations en micanique et en physique (1972)."

This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.

It is already a tradition that conferences on operations research are organized by the Mathematisches Forschungsinstitut in Oberwolfach/Germany. The mean point of the 1987 conference was to discuss recentl.v developed methods in optimization theory derived from various fields of mathematics. On the other hand, the practical use of results in operations research is very important. In the last few years* essenti.al progress in this direction was made at the International Insti- tute for Applied Systems Analysis (IIASA) at Laxenburg/Austria. Therefore a three days workshop on Advanced Computation Techniques, Parallel Processing and Optimi- zation organized by IIASA and the University of Karlsruhe immediately followed the Oberwolfach Conference. This volume contains selected pape~s which have been presented at one of these conferences. It:is divided into five sections based on the above topics: I. Algorithms and Optimization Methods II. Optimization and Parallel Processing III. Graph Theory and Scheduling IV. Differential Equations and Operator Theory V. Applications. We would like to thank the director of the Mathematisches Forschungsinstitut Oberwolfach Prof. Dr. M. Barner and the International Institute for Applied Systems Analysis, particularly Prof. Dr. V. Kaftanov, and also to the director of the Computer Center of the University of Karlsruhe Prof. Dr. A. Schreiner for their support in organizing these conferences. We also appreciate the excellent coopera- tion of Springer Verlag. We also thank Dr. P. Recht, Dr. D. Solte and Dr. K. Wieder as well as*Mrs.

This monograph provides a sample of relevant new results on dynamical nonlinear statistical modeling and estimation which forms a basis for more effective signal processing, decision and control. While the research literature is rich in linear Gaussian methodologies, new contributions to the most relevant area of nonlinear and non-Gaussian processes have been scarce. Among the significant areas of application for which such methodologies are needed are: economics, biology, immunology, underwater acoustics, electric power generation, chemical process control, and variable structure systems in general. The latter include adaptive, intelligent, and decomposing mathematical structures or processes. The volume includes ten research papers on theory, computational methods, and applications. Topics include filtering with application to inertial navigation, structural-change detection, bilinear time-series models, bispectral estimation, threshold models, catastrophic models and a generalized eigenstructure method.

The purpose of this monograph is to present recent results concerning frequency response properties of linear feedback systems. The basic theme is to develop extensions of classical feedback theory from scalar to multivariable systems, and the obstacle is the fact that multivariable systems may possess properties having no scalar analogue. The monograph contains sections reviewing ideas from classical control theory that are extended to multivariable systems, a summary of work we have done on design limitation in scalar systems, and a review of some previous work on extending classical ideas to a multivariable setting. The bulk of the monograph develops analysis methods with which to study properties of multivariable systems having no scalar analogue. Although the monograph does contain expository material, its primary character is that of a research monograph, and its primary audience researchers in the field of linear multivariable control. Its contents should be accessible to a first year graduate student with a good knowledge of classical feedback theory.

This book treats the subject of global optimization with minimal restrictions on the behavior on the objective functions. In particular, optimal conditions were developed for a class of noncontinuous functions characterized by their having level sets that are robust. The integration-based approach contrasts with existing approaches which require some degree of convexity or differentiability of the objective function. Some computational results on a personal computer are presented.

This volume comprises the proceedings of the Working Conference "Boundary variations and boundary control" held in Nice (France), June 10-13, 1986. The aim of this Conference was to stimulate exchange of ideas between the group working on shape optimization (including free boundary problems) and the group working on boundary control of hyperbolic systems (including stabilization). An important remark is that if one considers a dynamical system governed by linear elasticity the choice of Lagrangian coordinates leads to discuss boundary conditions, or boundary control (for example to stabilize), while the choice of Eulerian coordinates lead to a moving boundary and moving domain . This remark challenges us to consider the domain (or its boundary) as a control.

In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods.

This volume comprises the Proceedings of the IFIP 7/2 Conference on Control Problems for Systems Described by Partial Differential Equations and Applications held at the University of Florida, Gainesville, Florida in February 1987. The papers presented in this volume encompass several main directions of current research in the area including optimal control for variational inequalities, free boundary value problems, shape optimization, pareto-control, stabilization and controllability of hyperbolic equations, control problems for large space flexible structures, identification and estimation of distributed parameter systems, and numerical methods for control problems.

The volume contains new research papers (some of which are of a tutorial nature) on theory and computational methods, oscillatory control, deterministic control of uncertain systems, nonlinear perturbed optimal control, and on control of systems with distributed parameters.

This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. However, an additional chapter on elementary topology makes the book more complete as an advanced calculus text, and sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.