On the design of human immunodeficiency virus treatment based on a non‐linear time‐delay model

Abstract

Mathematical modelling and methods from control theory can be employed to find appropriate drug regimens in human immunodeficiency virus (HIV) treatment. In this study, using a non-linear time-delay model, the authors design some suboptimal highly active antiretroviral therapy (HAART) [http://www.en.wikipedia.org/wiki/Protease_inhibitor_%28pharmacology%29] regimens for patients with HIV. The non-linear delayed model is used to describe the dynamical interactions between HIV and human immune system in the presence of HAART. Based on the model, a set point tracking problem is defined in order to set the number of susceptible CD4+T cells to a desired value. To solve this set point tracking problem in a suboptimal way, the authors introduce a new method which is able to consider constraints on the amount of drug dosage. It is proved that the proposed method is able to set the number of susceptible CD4+T cells to the desired value. Simulation results confirm that the method is efficient even in the presence of parametric uncertainties.

Design of state‐dependent impulsive observer for non‐linear time‐delay systems

“…Moreover, in [30], The state‐dependent Riccati equation based on pseudo‐linearisation factorisation is proposed to control autonomous underwater vehicles. The pseudo‐linearisation technique is extended for non‐linear time‐delay systems [31–33]. In [31], suboptimal sliding mode controller is designed for non‐linear time‐delay systems based on extended pseudo‐linearisation.…”

“…In [31], suboptimal sliding mode controller is designed for non‐linear time‐delay systems based on extended pseudo‐linearisation. Also, based on this approach, suboptimal observer [32] and controller [33] are presented for non‐linear time‐delay systems. Applying the extended pseudo‐linearisation approach, the presented observer can be utilised for several kinds of non‐linear time‐delay systems such as systems with multiple discrete delays, time‐varying delay and distributed delay.…”

“…Therefore, the proposed SDIO based on extended pseudo‐linearisation can be applied for a wider class of non‐linear time‐delay systems. Another advantage of the extended pseudo‐linearisation approach is that, irrespective of the delay value, the proposed observer is asymptotically stable [31–33]. Thus, in this paper, unlike the previous methods, the upper bound of the time‐delays is not required.…”

State‐dependent Riccati equation–based MRAC and fuzzy sliding mode control for maximum power point tracking in partially shaded conditions in PV systems

“…In addition, this algorithm is useless under the rapid variation of environmental conditions. [13][14][15] Several papers have suggested a combination of the RCC [16][17][18][19] and MRAC 20,21 to better the underdamped response of PV systems after fast changes of the duty cycle. 7,8 It is shown that the INC technique works well in fast varying environmental conditions, but the main drawback is that this algorithm needs complex hardware and software resulting increase of cost.…”

“…9 Therefore, the ideal MPPT algorithm is straightforward and low-cost and reaches the MPP with least oscillations. [13][14][15] Several papers have suggested a combination of the RCC [16][17][18][19] and MRAC 20,21 to better the underdamped response of PV systems after fast changes of the duty cycle. The RCC unit accepts the array voltage and power as inputs and generates the duty cycle.…”