Robust Optimal Control-based Design of Combined Chemo- and Immunotherapy Delivery Profiles

Robust domain of attraction estimation for a tumor growth model

“…Table 1 summarizes the definitions of the model parameters and their nominal values. We slightly changed the values of some parameters since with the previous set of parameters values (used in [21] and [22] and taken from [8]), the domain of attraction for the uncontrolled system (1) (for u 1 = 0 and u 2 = 0) was unrealistically big. This allows us to solve a problem which is more reasonable and realistic from a practical point of view.…”

“…Moreover, there are other methods based on the moment optimization framework, allowing to estimate the RoAs of polynomial dynamical systems and providing a hierarchy of semi-algebraic outer (or inner) approximations of the ROA, by solving a sequence of linear matrix inequalities (LMIs) problems, see [16] and [15]. However, as mentioned in [21] and [22], the moment optimization based methods are limited to low dimensional systems and require a relatively high computational time. Therefore, extending these approaches to uncertain systems might be challenging.…”

Robust Optimal Scheduling of Combined Chemo- and Immunotherapy: Considerations on Chemotherapy Detrimental Effects

“…As an extension of our work in [19], where we derived robust optimal control strategies for combined chemoand immunotherapy treatments, considering uncertainties description on the tumor growth rate and the rate of immune cells influx, in this paper, we investigate the consequences, in the drug scheduling, of adding a new term standing for the effect of chemotherapy on immune cells. Furthermore, we consider that this parameter is uncertain and described by a probability distribution.…”

“…Similarly to the model that we investigated in [19], we consider in this paper a modified version of Stepanova's model [23], where we replace the exponential growth term by a logistic one f…”

“…since the logistic term allows to consider a limited tumor volume which is more realistic than the exponential growth. Unlike the model considered in [19], we added in model (1) the term −ηu 1 x 2 in the dynamicsẋ 2 , which stands for the direct detrimental effects that chemotherapy has on the immune system. Table I summarizes the definitions of the other model parameters and their numerical values.…”