Operator Approach to Linear Control Systems

1996
ISBN: 978-0-7923-3765-2
Verlag: Springer Netherlands

Buch, Englisch, Band 345, 398 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 793 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Fomin, V. N.

Cheremensky, A.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Mikroprozessoren
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

Inhaltsverzeichnis

Operator Approach to Linear Control Systems.- to systems theory.- Resolution spaces.- Linear control plants in a resolution space.- Linear quadratic optimization in preplanned control class.- Linear quadratic optimization in feedback control class.- Finite-dimensional LQP.- Some computing methods in stationary finite-dimensional SLQPs.