Observer-based adaptive control for HIV infection therapy using the Baskakov operator

This paper presents an adaptive observer-based robust controller design for HIV infection therapy using the Baskakov operators as a Universal approximator. The purpose of the treatment is to reduce, asymptotically, the number of infected CD4+T cells to zero using the assumption of accessibility to the total number of CD4+T cells. The lumped uncertainties including un-modeled dynamics and parameter uncertainties are modeled with the Baskakov operators. All of the aforementioned uncertainties are assumed as a function of time instead a function of several variables. The Baskakov operators' coefficients are then adaptively adjusted. It must be noted that Baskakov operators' have been used for function approximation usually in an offline manner in mathematics. However, the contribution of this paper is using Baskakov operators' in an online manner for an engineering problem. Also, considering the nonlinearities originated from antiretroviral drugs' dosage limitation is another important novelty of this paper which has not been considered in previous related works. Uniformly ultimately boundedness of the observer estimation error and the systems' states are guaranteed through Lyapunov stability concept. The performance is evaluated analytically to confirm that the observer transient response performs satisfactorily. Simulation results and a comparison with observer/controller based on radial basis functions neural network (RBFNN) verify that the proposed Baskakov operator-based observer/controller achieves reasonable performance for reducing the number of infected CD4+ T cells even in the presence of un-modeled dynamics and parametric uncertainties.