1. Consider the system: 
with the output
in 
. It is desired that
tracks 
with an LQ tracking function where
and 
. (
is the unit step in discrete domain). Find the control law
and simulate the system for initial condition:
Some Problems in Optimal Control
By A. H. Haji
1. Consider the system: with the output
in . It is desired that
tracks with an LQ tracking function where
and . ( is the unit step in discrete domain). Find the control law
and simulate the system for initial condition:
2. We want to minimize the cost function
for the system
with initial condition
where 
, 
, and the final time is free. Is there any answer for
?
3. How much would be the optimal cost to drive a second order system:
from 
to the origin while minimizing a quadratic performance:
, when 
and N=10.
4. For the system 
and weighting matrix
find the closed loop poles of the optimal infinite horizon
control law which minimizes
.