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Author: R. Saeks Publisher: Springer Science & Business Media ISBN: 3642807356 Category : Computers Languages : en Pages : 279
Book Description
If one takes the intuitive point of view that a system is a black box whose inputs and outputs are time functions or time series it is natural to adopt an operator theoretic approach to the stUdy of such systems. Here the black box is modeled by an operator which maps an input time function into an output time function. Such an approach yields a unification of the continuous (time function) and discrete (time series) theories and simultaneously allows one to formulate a single theory which is valid for time-variable distributed and nonlinear systems. Surprisingly, however, the great potential for such an approach has only recently been realized. Early attempts to apply classical operator theory typically having failed when optimal controllers proved to be non-causal, feedback systems unstable or coupling networks non-lossless. Moreover, attempts to circumvent these difficulties by adding causality or stability constraints to the problems failed when it was realized that these time based concepts were undefined and; in fact, undefinable; in the Hilbert and Banach spaces of classical operator theory.
Author: A. Cheremensky Publisher: Springer Science & Business Media ISBN: 9400901275 Category : Science Languages : en Pages : 411
Book Description
The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form.
Author: Don H. Tucker Publisher: Academic Press ISBN: 1483261026 Category : Mathematics Languages : en Pages : 475
Book Description
Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.
Author: H. Thiriez Publisher: Springer Science & Business Media ISBN: 3642875637 Category : Business & Economics Languages : en Pages : 419
Book Description
The conference was organized in order to assemble a group of researchers and practitioners in the area of Multiple Criteria Decision Making. The purpose was to discuss the current state of the art with respect to both theory and practice. This conference considered such points as recent t_heoretical developments in terms of models, the behavioral aspects of multiple criteria decision making, as well as practical applications already realized and 1n progress. In addition, there was interest in the problems of implementation of multiple-criteria methods, and the interface between theory and practice, Approximately 78 participants from 15 different countries attended the conference - both theorists and practitioners. A list of participants and their addresses is found on page 411 • Because of the relatively large number of papers presented, large morning sessions followed by smaller parallel afternoon sessions were employed'. In general a discussant commented on each paper. In addition, considerable time was reserved for small-group discussion and interaction. In addition to expressing our gratitude to the participants for their enthusiastic reception and participation in the conference, we want. to thank particularly the speakers, session chairmen and discussants. We also wish to thank the C.E.S.A. and the European Institute for their support, as well as Mrs. Randee Pomerantz and Miss Dina Nagler.~oth of the E.I.A.S.M.,for their active role in the organization and arrangements for the conference, and Mrs. Jessie Goveas, E.I.A.S.M. for typing the conference proceedings.
Author: G. Hasenkamp Publisher: Springer Science & Business Media ISBN: 364245481X Category : Business & Economics Languages : en Pages : 163
Book Description
This monograph is intended as a contribution to applied work in production theory by treating: a) The measurement problems involved whenever several outputs are jointly produced, and b) The (possible) econometric framework for estimating production function parameters whenever (relative) prices vary sufficiently over the observations. Thus, the "pure" theory of production, and the theory of non-linear regression is not treated in sufficient detail: for these topics we refer to the available literature~ for a comprehensive list of references we refer to Uebe (1975). Some years ago, papers by L. J. Lau and W. E. Diewert initiated my interest in duality within production theory, and then I started to appreciate R. W. Shephard's fundamental contribution to this topic. This monograph is a (minor) revision of a Ph. D. dissertation submitted to the Department of Economics, The University of Wisconsin, Madison, in August 1973. The Graduate School and the Social Systems Research Institute provided funds for the reported computer work, Lawrence R. Klein and Laurits R. Christensen provided data, and as a Graduate Student I received financial support in form of an University Fellowship~ all this is very much appreciated. With some nostalgia I think back to the enjoyable period of learning during the preparation of my diFosertation~ I appreciate the spirit within the department, and the guidance of my committee Arthur S. Goldberger, Dennis J. Aigner, and Laurits R. Christensen.
Author: M.A. Florian Publisher: Springer Science & Business Media ISBN: 364248123X Category : Business & Economics Languages : en Pages : 457
Book Description
The interest in the mathematical modeling of transportation systems stems from the need to predict how people might make use of new or improved transport infrastruc ture in order to evaluate the benefit of the required investments. To this end it is necessary to build models of the demand for transportation and models that de termine the way in which people who travel use the transportation network. If such models may be constructed and their validity reasonably assured, then the predic tion of the traffic flows on future and present transportation links may be carried out by simulating future situations and then evaluating the potential benefits of alternative improvement projects. In the attempts that were made to construct mathematical models of transportation networks, the notion of equilibrium plays a central role. Suppose that the demand for transportation, that is, the number of trips that occur between the - rious origins and destinations is known. Then it is necessary to determine how these trips are attracted to the alternative routes available between origins and destinations. Knight (1924), gave a simple and intuitively clear description of the behaviour of road traffic under conditions of congestion.
Author: K. Neumann Publisher: Springer Science & Business Media ISBN: 3642953638 Category : Business & Economics Languages : en Pages : 275
Book Description
Towards the end of the fifties methods for planning, scheduling,and control of proj ects were developed on the basis that the evolution of a project can be associated with a special weighted directed graph, called activity network. In this association, the individual activities of the project correspond to the arcs, the so-called proj ect events (beginning or termination of activities) correspond to the nodes, and the durations of the activities correspond to the weights of the respective arcs of the directed graph. 1) Contiguous arcs are assigned to activities which succeed one another immediately. The event corresponding to a node occurs exactly at the time at which all activities which are associated with the arcs leading into the node are terminated. After the occurrence of an event all those activities are be gun which correspond to the arcs emanating from the respective node. This implies especially that the evolution of the project has to be uniquely determined before hand, that every activity and every event are realized exactly once during the exe cution of the project, and that "feedback" (corresponding to cycles in the asso ciated network) is not permitted. Many projects, for example most R&D projects and projects in the area of production p 1 anni ng, do not sa ti sfy the foregoi ng res tri cti ons.
Author: B. Näslund Publisher: Springer Science & Business Media ISBN: 3642463738 Category : Business & Economics Languages : en Pages : 169
Book Description
During the last fifteen years certain very fundamental aspects of economic theory have been very actively debated. The debate has often been called the Cambridge controversy, since the main parti cipants in the debate come from Cambridge, USA and Cambridge, Eng land. In this debate certain important foundations of economic theory have been criticized which are specifically important for understand ing price formation and income distribution. An important starting point has been Sraffa's extensions of Ricardo's theory and one has therefore sometimes called those neo-Ricardians, who have based themselves on Sraffa's work. We shall deal with some important issues that have been debated, and we shall try to describe a rather complete theoretical construction which will be an alternative to neo-classical theory. A special problem relates to the title of the book and classification of authocs to whom we refer. Perhaps post-Keynesian would sometimes be a better label than neo-Ricardian. We have used the latter name for the book due to its large emphasis on Sraffa's work. To understand the main parts of the book only basic algebra and calculus are necessary.
Author: S. Zionts Publisher: Springer Science & Business Media ISBN: 3642463681 Category : Business & Economics Languages : en Pages : 580
Book Description
The objective of this conference was to foster a healthy exchange of ideas and experience in the domain of multiple criteria problem solving. This conference was an outgrowth of an earlier conference I organized with Herve Thiriez at CESA, Jouy-en-Josas, France in 1975 during my stay at the European Institute in Brussels. When I re joined the State University of New York at Buffalo that year, I be gan to search for potential sponsors for this conference. Approxi mately one year later when the prospects began to look promising, I contacted several individuals to act as an informal coordinating committee for the conference. I wanted to avoid biasing the con ference completely to my way of thinking! The members of this committee were Jim Dyer, Peter Fishburn, Ralph Kee. ney, Bernard Roy (Universite de Paris IX Dauphine who was unable to participate in the conference), and Milan Zeleny. Though the committee did not meet, per se, their inputs regarding format, possible participants, number of participants, length of the conference, and so on were of great value to me in planning and organizing the conference. I wish to acknowledge the contributions of this group. We were most fortunate in obtaining the financial support of the European Institute for Advanced Studies in Management, Brussels ·(one of the sponsors of the Jouy-en-Josas conference), the Office of Naval Research, and the State University of New York at Buffalo.
Author: C.-L. Hwang Publisher: Springer Science & Business Media ISBN: 3642455115 Category : Business & Economics Languages : en Pages : 366
Book Description
Decision making is the process of selecting a possible course of action from all the available alternatives. In almost all such problems the multiplicity of criteria for judging the alternatives is pervasive. That is, for many such problems, the decision maker (OM) wants to attain more than one objective or goal in selecting the course of action while satisfying the constraints dictated by environment, processes, and resources. Another characteristic of these problems is that the objectives are apparently non commensurable. Mathematically, these problems can be represented as: (1. 1 ) subject to: gi(~) ~ 0, ,', . . . ,. ! where ~ is an n dimensional decision variable vector. The problem consists of n decision variables, m constraints and k objectives. Any or all of the functions may be nonlinear. In literature this problem is often referred to as a vector maximum problem (VMP). Traditionally there are two approaches for solving the VMP. One of them is to optimize one of the objectives while appending the other objectives to a constraint set so that the optimal solution would satisfy these objectives at least up to a predetermined level. The problem is given as: Max f. ~) 1 (1. 2) subject to: where at is any acceptable predetermined level for objective t. The other approach is to optimize a super-objective function created by multiplying each 2 objective function with a suitable weight and then by adding them together.
Author: R. Saeks
Author: A. Cheremensky
Author: Don H. Tucker
Author: H. Thiriez
Author: G. Hasenkamp
Author: M.A. Florian
Author: K. Neumann
Author: B. Näslund
Author: H. Frisch
Author: S. Zionts
Author: C.-L. Hwang