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.

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.