Operator Approach to Linear Control Systems

  • A. Cheremensky
  • V. Fomin

Part of the Mathematics and Its Applications book series (MAIA, volume 345)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. A. Cheremensky, V. Fomin
    Pages 1-10
  3. A. Cheremensky, V. Fomin
    Pages 11-25
  4. A. Cheremensky, V. Fomin
    Pages 27-92
  5. A. Cheremensky, V. Fomin
    Pages 93-135
  6. A. Cheremensky, V. Fomin
    Pages 137-180
  7. A. Cheremensky, V. Fomin
    Pages 181-269
  8. A. Cheremensky, V. Fomin
    Pages 271-316
  9. A. Cheremensky, V. Fomin
    Pages 317-357
  10. Back Matter
    Pages 359-398

About this book


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.


Operator theory control control system design material operator optimization systems theory

Authors and affiliations

  • A. Cheremensky
    • 1
  • V. Fomin
    • 2
  1. 1.Institute of MechanicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Mathematics and MechanicsSt Petersburg UniversitySt Petersburg-PetrodvoretzRussia

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-6544-3
  • Online ISBN 978-94-009-0127-8
  • Buy this book on publisher's site
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