Abstract:
The present Ph.D thesis deals with feedforward (open-loop) control methods, in clas-
sical and quasi-classical physical systems like nonlinear oscillators, quantum particles
in external electromagnetic field etc. We investigate the special case of fast oscillating
control when the time of control period is sufficiently less to compare with the typical
time of controlled system behavior ( for instance its period of oscillation). We apply
mathematical technique specially developed for feedforward control systems such as
Lyapunov method and Kapitza averaging.
First we demonstrate that the Lyapunov spectrum of Kapitza averaged systems are
sufficiently different from the original spectra of non-controlled plants. That means
the description of averaged system in the neighborhood of their fixed points does
not describe appropriately the original system behavior. Secondly we apply Kapitza
averaging procedure to the original systems to derive the correcting terms in their
dynamical equations.
As a result we demonstrate re-design of original dynamical systems by fast changing
control periodical force.
