摘要：This paper addresses the problem of drug injection schedules design for cancer treatment, in the presence of model parametric uncertainties. It is commonly known that achieving optimal recovery performances under uncertainties is a complex task. Therefore, we propose to use a recent optimal control approach, based on the moment optimization framework. This method allows to formulate and solve robust optimal control problems by taking into account uncertain parameters and initial states, modeled as probability distributions. We analyse a two dimensional model that describes the interaction dynamics between tumor and immune cells. Furthermore, we derive statistically optimal combined strategies of chemo-and immunotherapy treatments, assuming the knowledge of probability distributions of some uncertain model parameters, namely, the tumor growth rate and the rate of immune cells influx. Numerical simulations are carried out in order to illustrate the effects of parametric uncertainties on dynamics, when using a nominal injection profile. Finally, we compare the recovery performance of nominal and robust schedules.
关键词：KeywordsBiomedical controlrobust optimal controluncertain dynamic systemsgeneralized moment problemcancer treatment schedulingchemotherapyimmunotherapy
