This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic function
Operator Approach to Linear Control Systems
β Scribed by A. Cheremensky, V. Fomin (auth.)
- Publisher
- Springer Netherlands
- Year
- 1996
- Tongue
- English
- Leaves
- 411
- Series
- Mathematics and Its Applications 345
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
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 opΒ 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 (includΒ 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 interΒ 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.
β¦ Table of Contents
Front Matter....Pages i-xvi
Operator Approach to Linear Control Systems....Pages 1-10
Introduction to systems theory....Pages 11-25
Resolution spaces....Pages 27-92
Linear control plants in a resolution space....Pages 93-135
Linear quadratic optimization in preplanned control class....Pages 137-180
Linear quadratic optimization in feedback control class....Pages 181-269
Finite-dimensional LQP....Pages 271-316
Some computing methods in stationary finite-dimensional SLQPs....Pages 317-357
Back Matter....Pages 359-398
β¦ Subjects
Systems Theory, Control; Operator Theory; Electrical Engineering; Mechanical Engineering
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