Page 43 - Control Theory in Biomedical Engineering

30 Control theory in biomedical engineering

3.4.1 Optimal control
A typical optimal control problem in physiological systems is to apply the
adequate control laws in order to converge the controlled system on its opti-
mal trajectory (Swan, 1981). This type of control is characterized by some
degree of precision. Due to the predictive character of optimal control, these
controllers are the most incorporated control algorithms in endocrine sys-
tems. Three applications are presented in this part especially for endocrine
applications.
• Optimal control problem in psoriasis treatment
The dynamics behaviors of psoriasis treatment is modeled by nonlinear dif-
ferential equations. This system is characterized by T-lymphocytes cells, ker-
atinocytes cells and dendritic cells. In order to minimize the interactions
between these types of cells, two optimal bounded controls are applied to
the psoriasis treatment system (Grigorieva and Khailov, 2018). Finally,
the applied control algorithm suppresses the weighted sum of keratinocytes
concentration so that the total cost of treatment decreases.
• Optimal control problem in tumor-immune interaction system
The dynamics behaviors of tumor-immune interactions system in presence
of immuno-chemotherapy is modeled by delay differential model. In order
to optimize the cost associated with immuno-chemotherapy and to mini-
mize the number of tumor cells, an optimal control is applied to the last sys-
tem (Rihan et al., 2019).
• Optimal control problem in intracellular delayed HIV model
The intracellular delayed HIV model is characterized by a cytotoxic
T lymphocyte (CTL) immune response. In order to reduce the number
of infected cells and the viral load, two optimal controls are applied to
the HIV model (Allali et al., 2018). Thus, the number of uninfected cells
increases, which confirms the efficiency of drug treatment.

3.4.2 Adaptive control
A typical adaptive control problem in physiology can compensate automat-
ically the dynamic variation in physiological systems by adjusting their fea-
tures and characteristics. Thus, the controlled system has the same overall
performances. In the literature, adaptive controllers are the most incorpo-
rated control algorithms in diabetes treatments.
• Adaptive control problem in Artificial Pancreas Systems
Blood glucose regulation is a complex system due to the variability of the
dynamic behaviors of blood glucose concentration. In fact, meals and
time-varying delays of insulin infusion can affect the control of the blood