This project was carried out as part of my semester long internship at the Indian Institute of Science. During this internship, I simulated an optimal controller for effective radiotherapy using Model Predictive Static Programming (MPSP). This technique aims to solve the originial nonlinear optimal control problem in a computationally efficient manner. It derives it’s ideas from Model Predictive Control (MPC) and Approximate Dynamic Programming (ADP). The initial phase of my project was to use a modified MPSP technique called Impulsive-MPSP or I-MPSP to determine the distribution of radiation dosages to drive the number of cancer cells to zero using external beam radiotherapy. To model the tumor dynamics, a two-compartment oxygen model was utilized. This was a re-implementation of a prior work in this area.

The second phase of the project involved extending this technique to account for the uncertainites in the model parameters and initial conditions. To do so, I designed a new techique known as Unscented MPSP for Impulsive Systems. This uses the technique of unscented optimal control with MPSP for impulsive systems. I formulated the mathematics for this controller to achieve the final time constraints as well as mimimize the final time variance for impulsive systems. An example prey-predator problem containing parametric uncertainties was discussed to verify the algorithm.

The above two projects are explained in greater details in the following two reports: