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Mathematics and Its Applications

Operator Approach to Linear Control Systems

Authors: Cheremensky, A., Fomin, V.N.

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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.

Table of contents (8 chapters)

  • Operator Approach to Linear Control Systems

    Cheremensky, A. (et al.)

    Pages 1-10

  • Introduction to systems theory

    Cheremensky, A. (et al.)

    Pages 11-25

  • Resolution spaces

    Cheremensky, A. (et al.)

    Pages 27-92

  • Linear control plants in a resolution space

    Cheremensky, A. (et al.)

    Pages 93-135

  • Linear quadratic optimization in preplanned control class

    Cheremensky, A. (et al.)

    Pages 137-180

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-94-009-0127-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA in USD
  • ISBN 978-0-7923-3765-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-94-010-6544-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Operator Approach to Linear Control Systems
Authors
Series Title
Mathematics and Its Applications
Series Volume
345
Copyright
1996
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-009-0127-8
DOI
10.1007/978-94-009-0127-8
Hardcover ISBN
978-0-7923-3765-2
Softcover ISBN
978-94-010-6544-3
Edition Number
1
Number of Pages
XVI, 398
Number of Illustrations and Tables
1 b/w illustrations
Topics