Operator Approach to Linear Control Systems

1. Front Matter

   Pages i-xvi

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2. Operator Approach to Linear Control Systems

   • A. Cheremensky, V. Fomin

   Pages 1-10

3. Introduction to systems theory

   • A. Cheremensky, V. Fomin

   Pages 11-25

4. Resolution spaces

   • A. Cheremensky, V. Fomin

   Pages 27-92

5. Linear control plants in a resolution space

   • A. Cheremensky, V. Fomin

   Pages 93-135

6. Linear quadratic optimization in preplanned control class

   • A. Cheremensky, V. Fomin

   Pages 137-180

7. Linear quadratic optimization in feedback control class

   • A. Cheremensky, V. Fomin

   Pages 181-269

8. Finite-dimensional LQP

   • A. Cheremensky, V. Fomin

   Pages 271-316

9. Some computing methods in stationary finite-dimensional SLQPs

   • A. Cheremensky, V. Fomin

   Pages 317-357

10. Back Matter

    Pages 359-398

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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 ("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

• Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

  A. Cheremensky

• Department of Mathematics and Mechanics, St Petersburg University, St Petersburg-Petrodvoretz, Russia

  V. Fomin

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