1 80 00
*
1 60 00
1 40 00
1 20 00
1 00 00
80 00
60 00
40 00
20 00
0
0 20 00 40 00 60 00 80 00 1 00 00 1 20 00 1 40 00 1 60 00 1 80 00
Figure 3.2: Phase portraits for u = 0
tumor. Thus we will assume that:
Ga > b: (3.37)
Figure 3.3 shows the the phase portraits for the controlled system under constant control
u = a with a value of a = 15. Note the convergence of the trajectories to the origin.
This clearly shows that the treatment is e�ective. Now, we will look for an optimal way to
administer the drug using the tools of optimal control theory.
15
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