Implications of change management in public administration

Economic Theories – International Economic Relations
F
m
i1
2
u i
( t).
If the cost is not quadratic, then we cannot guarantee that the Hamiltonian can be
calculated without dependence on the control. However, there exist several situations
when the Hamiltonian still be found.
3. Application
Let us consider in the three dimensional space
system
with
and minimizing the cost
.
1 2 3
( t)
u X1
u X
2
u X
3
X
(6)
1
X
1
0
,
0
I
0
X
2
x
,
0
3
R the drift less control affine
0
X
3
0
x
min F ( u(
t))
dt , (7)
u(.)
1 2 2 2 3 2 1
where F ( u ) ( u ) ( u ) u
, 0 1
is the positive homogeneous cost
(Randers metric).
The distribution D is generated by the vectors X
1
, X
2,
X
3
and we can write
D={ X
1
, X
2,
X
3
}. We observe that
3
if x 0
rankD
1
if x 0
3
In the canonical base of R we have X
1
, X
2
x , X
3
x and the Lie
x
y
z
brackets are given by
X
,
1
X
2 X
4
D
y
,
X1, X
z
X
D
3
5
, X 2, X
3 0 .
It results that the distribution is nonholonomic, but is bracket generating, because the
vector fields { X X , X , X [ X , X ], X [ X , ] } generate the entire space
3
R .
1, 2 3 4 1 2 5 1
X
3
From (6) we obtain
109