State Dependent Riccati Equation controlled drug delivery for mixed therapy of cancer treatment*

The paper presents a drug delivery solution to the mixed therapy of cancer treatment using the State Dependent Riccati Equations (SDRE) control method. A sixth-order nonlinear ordinary differential equation describes the cancer dynamics considering the number of cells of tumor, natural killers, circulating lymphocytes and cytotoxic T-cells, together with chemotherapy drug concentration and immunotherapy drug concentration. The control problem is posed as the suboptimal solution for minimizing a quadratic objective function, which is constructed using the states and mixed therapy inputs of “chemotherapy” and “immunotherapy” drug injections. The SDRE approach provides an attractive solution to the highly nonlinear multi-input (mixed therapy) cancer dynamics problem, which is compared with the results presented in the literature.