Design of a Hybrid automata model and robust control for tumors, using the three compartments approach

This work is about using a space-time evolution mathematical model for tumors, for the aim of controlling them. The mathematical model used is based on the three compartments approach [1]. The model is a Hybrid automata mainly built according to the treatment strategy itself, which consists of checking the cells in one compartment, and to free them once the eliminating agent is at its optimum potential of elimination. After that, robust control laws are developed for each control mode. These control laws are mainly inspired from the differential geometry methodology, and the sliding modes approach with some improvements. Finally, simulations are done and results discussed.