Operator Approach to Linear Control Systems

Operator Approach to Linear Control Systems

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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 (qthe better is the enemy of the goodq) 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 qsmallq 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.For control systems on the infinite time interval aside from causality of transfer operators it is to require that they have to be ... the obtained closed-loop system is an open loop system with the system operator - A B B s-[: aquot; : admitting the obvious anbsp;...

Title:Operator Approach to Linear Control Systems
Author:A. Cheremensky, V.N. Fomin
Publisher:Springer Science & Business Media - 2013-11-11


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