ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Method of Inverse Movements for Control of the Angular Coordinates of State-linear Systems


Sergey Mikhailovich Khryashchev

Saint-Petersburg State Polytechnic University,
Doctor of Physics and Mathematics, professor,
29 Politechnicheskaya,
195251, Saint-Petersburg, Russia


For dynamical polysystem we give a characterization of the controllability property which is a fundamental property for control theory. This characterization establishes a link between the controllability and recurrence. Basing on this connection we propose a control method called the method of inverse movements. This method is not directly associated with any special properties of control systems, and it can be applied to arbitrary control systems having the structural stability property. Existence of the sequence of inverse movements can be established for some special systems. In particular, by this method the angular controllability of state-linear control systems can be investigated. For such systems new controllability conditions in the terms of the spectral characteristic of the matrix function of the state-linear control system have been given. These conditions for specific systems can be tested by using computer graphics.


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