Lyapunov based control design for cancer Gompertz-Logistic generalized model therapy

摘要

This article explores the structure of the Gompertz-Logistic generalized model, that describes several cancer types, to design drug administration profiles. The aim is to handle the nonlinear behaviour of the generalized model such that the tumor size follows a decreasing reference target. Since the Gompertz model can be transformed in a linear dynamical model by applying the ln(.) transformation, this transformation is applied to the Gompertz-Logistic generalized model to simplify the controller design formed by the ln(.) function and a PI controller (LnPI). The Lyapunov stability analysis is employed to evaluate the LnPI controller. The main conclusion is this appraoch provides a globally asymptotically stable closed-loop for the Gompertz-Logistic model family in the presence of model parameter uncertainty.