qualitative structure "as0" with a very small portion of singular arc whereas for k = 16:66;
there is no more optimal trajectory. The "best" solution is T = 0 and is reduced to a point.
The red portion is the corresponding trajectory of the uncontrolled system. The growth will
eventually reach the equilibrium point.
It is possible to obtain a better approximation of  by using the "Bisection Method"
on the interval I = (16:65;16:66): The process is similar to the bisection method used to
approximate a zero of a given function. Each time we divide the interval in two parts, we
only retain the part where we have di¤erent types of optimal control at the boundaries. This
iterative method helped us narrow the interval to (16:65138;16:65139):
x 10
4
2.4
2.2
2
st
l co
a
1.8
fin Mi n i mu m
1.6
1.4
1.2
0 5 10 15 20
t i me
RFigure 6.10: Cost function for p(T) + 16:65 T
0 u(t)dt
48
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