Closed-loop optimal control stategy for cancer chemotheraphy

Cancer chemotherapy is the treatment of cancer using drugs that kill the cancer cells, when the drugs are administered either orally or through veins. The drugs are delivered according to a schedule so that a particular dosage of drug level is maintained in the body. The disadvantage of these drugs is that they not only kill the cancer cells but also kill the normal healthy cells. The role of optimal control in chemotherapy is to maintain an optimum amount of drug level in the body so that only cancer cells are killed and hence the effect of drug on the healthy cells is minimized. Three different mathematical models for cancer growth are considered: log-kill hypothesis, Norton-simon model, and Emax model. Two different cost functions are considered for constrained and unconstrained optimal control, respectively. An open loop optimal control strategy has been reported in the literature. In this paper, a closed-loop optimal control strategy is addressed using all the three models and for both the cases of constrained and unconstrained drug delivery. For the unconstrained case the original nonlinear model has been linearized and the closed loop design is obtained by using matrix Riccati solutions. On the other hand, for the constrained case the original nonlinear model has been used to obtain closed loop optimal control using bang-bang strategy. Final simulation results show the advantages of closed loop implementation in terms of simpler and elegant controller design and incorporating the effect of current state variations.