An Output Feedback Control with State Estimation for the Containment of the HIV / AIDS Diffusion

An optimal control problem formulated to reduce the infection diffusion of an epidemic disease is solved in a locally linearised context. The approach has been driven by the necessity of using a state observer, since the state variable to be controlled is not directly measurable. The solution is computed making reference to a recently introduced model for HIV / AIDS diffusion and control, in which five classes of individuals are considered: two classes of susceptible subjects, the wise and the incautious individuals, and three classes of infectious subjects, the ones not aware of their condition and the subjects in the pre-aids or in the aids status. The control inputs are represented by information campaigns and medication actions. The initial formulation as an optimal control problem, aiming also at minimising the non measurable number of infected subjects, is enriched with an asymptotic state observer for which a local linear approximation has been chosen for simplicity purpose. The structure of the cost index for the reformulated control problem after the observer introduction, suggests to compute the solution in an approximated way referring to a classical LQR control design. The effectiveness of the control, as well as the effects of the linear approximations, are evidenced by some numerical simulation results.