Robust positive control of tumour growth using angiogenic inhibition

Abstract

In practice, many physical systems, including physiological ones, can be considered whose input can take only positive quantities. However, most of the conventional control methods do not support the positivity of the main input data to the system. Furthermore, the parameters of these systems, similar to other non-linear systems, are either not accurately identified or may change over time. Therefore, it is reasonable to design a controller that is robust against system uncertainties. A robust positive-input control method is proposed for the automatic treatment of targeted anti-angiogenic therapy implementing a recently published tumour growth model based on experiments conducted on mouse models. The backstepping (BS) approach is applied to design the positive input controller using sensory data of tumour volume as feedback. Unlike previous studies, the proposed controller only requires the measurement of tumour volume and does not require the measurement of inhibitor level. The exponential stability of the controlled system is proved mathematically using the Lyapunov theorem. As a result, the convergence rate of the tumour volume can be controlled, which is an important issue in cancer treatment. Moreover, the robustness of the system against parametric uncertainties is verified mathematically using the Lyapunov theorem. The real-time simulation results-based (OPAL-RT) and comparisons with previous studies confirm the theoretical findings and effectiveness of the proposed method.