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Nazari, Mostafa; Ghaffari, Ali; Arab, Farhad

Finite duration treatment of cancer by using vaccine therapy and optimal chemotherapy: state-dependent Riccati equation control and extended Kalman filter. (English) Zbl 1343.92239

J. Biol. Syst. 23, No. 1, 1-29 (2015).
Summary: The main purpose of this paper is to propose an optimal finite duration treatment method for preventing tumor growth. The obtained results show that changing the dynamics of the cancer model is essential for a finite duration treatment. Therefore, vaccine therapy is used for changing the parameters of the system and chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. The state-dependent Riccati equation (SDRE)-based optimal control method is used for optimal chemotherapy. In this method, the special conditions of the patients could be considered by choosing suitable weighting matrices in the cost function and restricting the drug dosage. Also, there are infinite ways to choose these state-dependent matrices. In this paper, these interesting features of this method are used for each patient. Since measuring the states of the system is impossible at each time for states feedback; an extended Kalman filter (EKF) is designed as an observer in the nonlinear system. So, the SDRE method is employed just by measuring the population of normal cells. Numerical simulations show the flexibility and effectiveness of this treatment method.

Cited in 2 Documents

MSC:

92C50 Medical applications (general)
49N90 Applications of optimal control and differential games

Keywords:

SDRE optimal control; extended Kalman filter; chemotherapy; vaccine therapy; tumor growth
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References:

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