  Current research suggests the use of a liner quadratic performance index for
optimal control of regulators in various applications. Some examples include
correcting the trajectory of rocket and air vehicles, vibration suppression of
flexible structures, and airplane stability. In all these cases, the focus is
in suppressing/decreasing system deviations rapidly. However, if one compares
the Linear Quadratic Regulator (LQR) solution with optimal solutions (minimum
time), it is seen that the LQR solution is less than optimal in some cases
indeed (3-6) times that obtained using a minimum time solution. Moreover, the
LQR solution is sometimes unacceptable in practice due to the fact that values
of control extend beyond admissible limits and thus the designer must choose
coefficients in the linear quadratic form, which are unknown.
  The authors suggest methods which allow finding a quasi-optimal LQR solution
with bounded control which is closed to the minimum time solution. They also
remand the process of the minimum time decision. Keywords: Optimal regulator,
minimum time controller, Linear Quadratic Regulator (LQR). -- This paper is
declared a work of the U.S. Government and not subject to copyright protection
in the USA. The manuscript is accepted as paper AIAA-2003-6638 by 2nd AIAA
Unmanned Unlimited Systems, Technologies, and Operations-Aerospace, Land, and
See Conference and Workshop - Exhibit, San Diego, California, USA, 15-18 Sep.
2003.
