After modifying the dynamics of cancer, chemotherapy is exerted to
reduce the population of the cancer cells. Due to side effects of the
chemo-drugs, chemotherapy should be implemented in an optimal manner.
Chemotherapy using the pseudo-spectral method
To impose optimal chemo-drug dose the pseudo-spectral method can be used
[18]. In this method, the original nonlinear control system is
formulated to an infinite-horizon optimal control (IHOC). Then, the
optimal controller, which solves the IHOC problem is used to stabilize
the original nonlinear system. The IHOC problem is solved by the
Legendre pseudo-spectral (LPS) method.
The first three ODE equations (3)-(5) are related to chemotherapy. So,
these equations are used to design an optimal controller to impose
optimal chemo-drug dose.