Analysis of tracking control designs for a delay differential equation model used in the study of nanoparticle dosing strategies

In earlier work [1], an LQR tracking control of a delay differential equation model was used in the analysis of nanoparticle dosing strategies for cancer therapy. In this work, comparisons are made between the LQR-controlled system, but with modified dose, and two other controlled systems. One system investigated uses Dirac delta functions to achieve a discrete dosing strategy. The other system under consideration uses a PID tracking control because it is a common controller employed in the engineering, industrial, and lab settings. These different methods of tracking to a specific therapeutic target, though all effective, produce different results with different control efforts required. In this work, all of these methods with their respective results are analyzed and discussed.