Title of Thesis
Open Loop Control Methods in Non-Linear Dynamical Equations
Abdus Salam School of Mathematical Sciences / GC
|Number of Pages|
|Keywords (Extracted from title, table of contents and
abstract of thesis)|
Open Loop, Control, Methods, Non-Linear, Dynamical, Equations,
investigate, stabilization, quantum, beam-splitter
In this thesis we
concentrate on open-loop control scheme to investigate the behavior
of dynamical system described by non-linear differential equation.
We will discuss different types of the system: classical and
quantum, and apply control methods to change the dynamical behavior
of the system in coordinate or momentum space.
In Chapter 1 we give some basic definitions and describe Kapitza
procedure of averaging for open-loop control, then we give examples
of stabilization by this method.
In Chapter 2 we propose the generalization of Kapitza procedure of
averaging to stabilize the oscillator driven by periodical external
field. We do this with the help of periodical external rectangular
pulses, by applying Generalized Kapitza procedure of averaging, then
we stabilize the oscillator by minimizing the effective potential
energy function. We demonstrate the effect of stabilization with
relatively low frequency for special shape of the external
periodical field to compare with sin- or cos-periodical force.
In Chapter 3 an effective quantum particle beam-splitter in the
momentum space is realized in the frame of open-loop control scheme.
We demonstrate for small interaction time that the splitting effect
§40~k with summarized relative intensity in both main components is
about 50 per cent from initial intensity of the atomic beam.