Nonlinear Robust Control and Regulation Problems for Biomedical Dynamical Systems

Aziz Belmiloudi (1, 2)

1 INSA Rennes - Institut National des Sciences Appliquées - Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes

Motivated by topics and issues critical to human health, and safety and efficacy of medical treatment practices, this communication investigates a nonlinear robust control approach of some uncertain biomedical nonlinear complex systems. The concept consists in setting the problem in the worst-case disturbances, which leads to the game theory in which controls and disturbances (which destabilize the dynamical behavior of the system) play antagonistic roles. The proposed strategy consists in controlling these instabilities by acting on certain parameters and data to maintain the system in a desired state (see Stabilization, Optimal and Robust Control, Springer, London (2008)). This approach is applied to two problems: first, controlling and regulating the blood glucose level in subjects with type 1 diabetes and predicting the dosages of insulin administered, and second, controlling and stabilizing the thermal distribution and damage during the treatment of cancer, in order to eradicate tumor while preserving the surrounding health tissues.

Mots clés: mathematical-models

Domaines: Analyse numérique [math.NA]

Aziz Belmiloudi. Nonlinear Robust Control and Regulation Problems for Biomedical Dynamical Systems. Cojocaru, MG; Kotsireas, IS; Makarov, RN; Melnik, RVN; Shodiev, H. Interdisciplinary Topics in Applied Mathematics, Modeling, and Computational Science, 117, Springer, pp.49-55, 2015, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-319-12307-3_8⟩. ⟨hal-01340550⟩