Nonlinear Lyapunov-based control for HIV-1 dynamics

Nonlinear control theory plays an important role in stabilizing nonlinear dynamic systems such as the Human Immunodeficiency Virus type-1 (HIV-1) infectious disease. This disease targets immune system defenses and may eventually cause Acquired Immune Deficiency Syndrome (AIDS). In this paper, a nonlinear Lyapunov-based control for HIV-1 dynamic reduced models with real data is proposed. A Lyapunov function for a reduced model is constructed, and proof of its global stability is also provided. The feedback control laws using Jurdjevic-Quinn and Sontag designs are compared. The reduced HIV-1 model is stabilized implicitly through infected cells by using two different control laws. Feedback control law using Sontag´s formula showed a slightly smoother performance and less of control effort. On the other hand, the Sontag formula needed more computation than the Jurdjevic-Quinn formula.