A HG/LMI-Based Observer for a Tumor Growth Model

Cancer is one of the major causes of death all over the word. Research dedicated to understanding and combating cancer continues to attract the interest of scientists. In this paper, we investigate a system of nonlinear ordinary differential equations describing a tumor growth model accounting for angiogenic stimulation and inhibition. This model has a high Lipschitz constant which renders the implementation of the standard high-gain observer very complicated. To overcome this problem, we propose in this paper to use a HG/LMI-based observer strategy to estimate the tumor volume. By combining the high-gain methodology with linear matrix inequalities based technique, such an observer allows reducing significantly the high-gain tuning parameter which improves highly the performances with respect to measurement noise, and avoids the peaking phenomenon. These two advantages, which are the weaknesses of the standard high-gain observer, play an important role in very sensitive applications like tumor growth control. The numerical simulations show the superiority of the HG/LMI-based observer compared to other observers in the literature.