

Title of Thesis
Open Loop Control Methods in NonLinear Dynamical Equations 
Author(s)
Babar Ahmad 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences / GC
University, Lahore 
Session 2009 
Subject Mathematics 
Number of Pages 72 
Keywords (Extracted from title, table of contents and
abstract of thesis) Open Loop, Control, Methods, NonLinear, Dynamical, Equations,
investigate, stabilization, quantum, beamsplitter 
Abstract In this thesis we
concentrate on openloop control scheme to investigate the behavior
of dynamical system described by nonlinear 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 openloop 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 cosperiodical force.
In Chapter 3 an effective quantum particle beamsplitter in the
momentum space is realized in the frame of openloop 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.

