Positive control of a minimal model of tumor growth with bevacizumab treatment

Application of model-based control strategies for physiological control problems, like tumor therapy, may greatly improve the efficiency of clinical treatments. Our aim is to design a positive path tracking controller for a minimal model of tumor growth under angiogenic inhibition with bevacizumab treatment. We extend the dynamics of the system to ensure the positivity of the input, and design path tracking controller after exact linearization is carried out for the extended system. We carry out simulations for different reference signals for the path tracking controllers, and confirm that the tumor can be eliminated using bevacizumab therapy with physiologically feasible input signals. The resulting inputs are positive, and their maximal values are in physiologically feasible regions, thus the results may be applicable in clinical practice.