title: Local controllability and optimal control for a model of combined anticancer therapy with control delays.
abstract: We study some control properties of a class of two-compartmental models of response to anticancer treatment which combines anti-angiogenic and cytotoxic drugs and take into account multiple control delays. We formulate sufficient local controllability conditions for semilinear systems resulting from these models. The control delays are related to PK/PD effects and some clinical recommendations, e.g., normalization of the vascular network. The optimized protocols of the combined therapy for the model, considered as solutions to an optimal control problem with delays in control, are found using necessary conditions of optimality and numerical computations. Our numerical approach uses dicretization and nonlinear programming methods as well as the direct optimization of switching times. The structural sensitivity of the considered control properties and optimal solutions is also discussed.
authors.affiliation: Silesian University of Technology, Department of Automatic Control, Akademicka 16, 44101 Gliwice, Poland. email: jerzy.klamka@polsl.pl.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Klamka
authors.forename: Helmut
authors.initials: H
authors.lastname: Maurer
authors.forename: Andrzej
authors.initials: A
authors.lastname: Swierniak
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use*; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy*; D013997:Time Factors
chemical_list: D000970:Antineoplastic Agents