V.N. Fomin's Books

Optimal Filtering

Volume I: Filtering of Stochastic Processes

By: V.N. Fomin

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Optimal Filtering

Volume I: Filtering of Stochastic Processes

By: V.N. Fomin

This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems.

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387

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Springer Science & Business Media

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ISBN 10

9401153264

ISBN 13

9789401153263

Operator Approach to Linear Control Systems

By: A. Cheremensky,V.N. Fomin

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Operator Approach to Linear Control Systems

By: A. Cheremensky,V.N. Fomin

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.

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411

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Springer Science & Business Media

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ISBN 10

9400901275

ISBN 13

9789400901278

Discrete Linear Control Systems

By: V.N. Fomin

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Discrete Linear Control Systems

By: V.N. Fomin

One service mathematics has rendered the 'Bt mm ... - si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alIe.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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316

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Springer Science & Business Media

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ISBN 10

9401132488

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9789401132480

Mathematical Theory of Control Systems Design

By: V.N. Afanasiev,V. Kolmanovskii,V.R. Nosov

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Mathematical Theory of Control Systems Design

By: V.N. Afanasiev,V. Kolmanovskii,V.R. Nosov

Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is based on several courses of lectures on control theory and appli cations which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University. The book, originally written in Rus sian, was first published by Vysshaya Shkola (Higher School) Publishing House in Moscow in 1989. In preparing a new edition of the book we planned to make only minor changes in the text. However, we soon realized that we like many scholars working in control theory had learned many new things and had had many new insights into control theory and its applications since the book was first published. Therefore, we rewrote the book especially for the English edition. So, this is substantially a new book with many new topics. The book consists of an introduction and four parts. Part One deals with the fundamentals of modern stability theory: general results concerning stability and instability, sufficient conditions for the stability of linear systems, methods for determining the stability or instability of systems of various type, theorems on stability under random disturbances.

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676

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Springer Science & Business Media

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ISBN 10

940172203X

ISBN 13

9789401722032

Environmental Chemistry: Asian Lessons

By: V.N. Bashkin

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Environmental Chemistry: Asian Lessons

By: V.N. Bashkin

At present environmental chemistry is becoming an increasingly popular subject in both under graduate and graduated education in the whole World and especially in all Asian countries. Different courses in ecology, chemistry, environmental science, public health, geography, biology, and environmental engineering all include this subject in their curriculum. Many textbooks have appeared in recent years aiming to fulfill these requirements; however, most of these books operate mainly with examples from developed countries of Europe, USA and Canada. Taking into account the geographic boundaries of environmental pollution that is especially pronounced in Asia and the specific peculiarities of pollution in developing countries, this textbook is supposed to close the gap by providing regionally oriented knowledge in basic and applied environmental chemistry.

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472

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Springer Science & Business Media

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ISBN 10

0306480204

ISBN 13

9780306480201

Plastics for Corrosion Inhibition

By: V.A. Goldade,L.S. Pinchuk,A.V. Makarevich,V.N. Kestelman

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Plastics for Corrosion Inhibition

By: V.A. Goldade,L.S. Pinchuk,A.V. Makarevich,V.N. Kestelman

One of the key problems of failure-free operation of machinery is prevention of corrosion. The global scale of modern production makes this problem even more critical. At the beginning of the 21st century industrial contami- tion and the corrosion-active nature of the environment reached a level such that corrosive damage of materials became commensurate with their prod- tion volume and expenditure on anticorrosion protection of machines became comparable with investments in basic production. Anticorrosion techniques changed from being an auxiliary service to industrial enterprises into a dev- oping, scienti?cally intensive and generously ?nanced branch of production. Polymers occupy a very speci?c place amongst anticorrosion techniques. Polymers combine good chemical resistance with impermeability to di?- ent media and unusual deformation characteristics. The main principle of their application as anticorrosion means is the creation of a tight barrier that insulates metal machine parts or constructions from corrosion agents. The advantages of polymers allow the creation of such a barrier at minimal cost,providingprotectionoftheworkingmachinesfromcorrosion,combining their manufacture with preservation and decreasing the cost of anticorrosion. This is one of the main reasons why world production of polymer materials increased by almost 50% in the past decade.

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394

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Springer Science & Business Media

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ISBN 10

3540270949

ISBN 13

9783540270942

Nonradiative Recombination in Semiconductors

By: V.N. Abakumov,V.I. Perel,I.N. Yassievich

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Nonradiative Recombination in Semiconductors

By: V.N. Abakumov,V.I. Perel,I.N. Yassievich

In recent years, great progress has been made in the understandingof recombination processes controlling the number of excessfree carriers in semiconductors under nonequilibrium conditions. As a result, it is now possible to give a comprehensivetheoretical description of these processes. The authors haveselected a number of experimental results which elucidate theunderlying physical problems and enable a test of theoreticalmodels.The following topics are dealt with: phenomenological theory ofrecombination, theoretical models of shallow and deep localizedstates, cascade model of carrier capture by impurity centers,capture restricted by diffusion, multiphonon processes, Augerprocesses, effect of electric field on capture and thermalemission of carriers.

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337

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Elsevier

Published Date

ISBN 10

0444600825

ISBN 13

9780444600820

Optimal Filtering

Volume II: Spatio-Temporal Fields

By: V.N. Fomin

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Optimal Filtering

Volume II: Spatio-Temporal Fields

By: V.N. Fomin

In this volume the investigations of filtering problems, a start on which has been made in [55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the 'past-future' in the case of fields, which plays a fundamental role in constructing stochastic processes theory. So attempts to introduce naturally the notion of the causality (non-anticipativity) when synthesising stable filters designed for processing fields have not met with success. Mathematically, principal distinctions between multi-dimensional and one-dimensional cases imply that the set of roots of a multi-variable polyno mial does not necessary consist of a finite number of isolated points. From the main theorem of algebra it follows that in the one-dimensional case every poly nomial of degree n has just n roots (considering their multiplicity) in the com plex plane. As a consequence, in particular, an arbitrary rational function ¢(.

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368

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Springer Science & Business Media

Published Date

ISBN 10

9401146918

ISBN 13

9789401146913

Discrete Linear Control Systems

By: V.N. Fomin

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Discrete Linear Control Systems

By: V.N. Fomin

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316

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Springer Science & Business Media

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ISBN 10

9401132488

ISBN 13

9789401132480

Operator Approach to Linear Control Systems

By: A. Cheremensky,V.N. Fomin

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Operator Approach to Linear Control Systems

By: A. Cheremensky,V.N. Fomin

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Page Count

411

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Springer Science & Business Media

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ISBN 10

9400901275

ISBN 13

9789400901278

Book's by V.N. Fomin

Optimal Filtering

Optimal Filtering

Operator Approach to Linear Control Systems

Operator Approach to Linear Control Systems

Discrete Linear Control Systems

Discrete Linear Control Systems

Mathematical Theory of Control Systems Design

Mathematical Theory of Control Systems Design

Environmental Chemistry: Asian Lessons

Environmental Chemistry: Asian Lessons

Plastics for Corrosion Inhibition

Plastics for Corrosion Inhibition

Nonradiative Recombination in Semiconductors

Nonradiative Recombination in Semiconductors

Optimal Filtering

Optimal Filtering

Discrete Linear Control Systems

Discrete Linear Control Systems

Operator Approach to Linear Control Systems

Operator Approach to Linear Control Systems

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