Suboptimal periodical control for the infinite dimensional systems application to biomedical modelling

摘要

This paper presents analysis of certain class of bilinear models with infinite dimensional, tridiagonal system matrix. For such systems, an optimal control problem is defined. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential one. After giving the necessary conditions for optimal control a gradient method based approach for finding the solution of the stated problem is presented. Analysis of obtained computational results leads to development of another method that allows finding suboptimal, periodical solutions. Finally, the meaning of obtained results for real-life applications is discussed. The solution to the optimization problem is shown for one of model applications, i.e. evolution of drug resistance in cancer cells. However, the approach to the problem can be also applied to other cases in which dynamical models have similar form.