Based on successive linear time varying (LTV) approximations, the paper suggests an optimal control design method for a general class of nonlinear systems. By using the LTV approximations, optimal state feedback gain matrix is designed such that a given non-quadratic cost function is minimized It is proved that optimal state feedback gain matrix obtained from the LTV approximations converges to the optimal state feedback gain matrix of the nonlinear system. This enables one to use the approximated optimal state feedback gain matrix for the optimal control of the nonlinear dynamical system. The proposed approach is then used to design optimal chemotherapy administration for the cancer treatment. It is shown that once the optimal state feedback gain matrix is designed for the treatment then the drug administration could be carried out with the same gain matrix. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.