Feedback linearization and optimal design for the control of an HIV pathogenesis model

In this paper, a mathematical model is established and studied. The model, in the form of a system of ordinary differential equations, describes HIV infection dynamics transmission and considers nonlinear proliferation of CD4 T cells. Based on this model, feedback linearization method and optimal control scheme are applied to the control of HIV dynamics. First, we design a state feedback control and a change of variables which can transform nonlinear system of the input-state into an equivalent linear system. To derive the stability of the system, we use linear state feedback to deal with the obtained linear system. Using the Pontryagin Maximum Principle, we set one objective function to maximize the benefit of the T cells and minimize the chemotherapy cost. A charaterization of the optimal control which includes adjoint variables was established.