An SDRE Based Estimator Approach for HIV Feedback Control

We consider optimal dynamic multidrug therapies for human immunodeficiency virus (HIV) type 1 infection. In this context we describe an optimal tracking problem attempting to drive the states of the system to a stationary state in which the viral load is low and the immune response is strong. We consider optimal feedback control with full state as well as with partial state measurements. In the case of partial state measurement, a state estimator is constructed based on viral load and T-cell count measurements. We demonstrate by numerical simulations that by anticipation of and response to the disease progression, the dynamic multidrug strategy reduces the viral load, increases the CD4+ T-cell count and improves the immune response. ∗Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, NC 27695–8205. †Department of Mathematics, Inha University, Incheon, South Korea. Email: [email protected]. ‡Author for correspondence. E-mail: [email protected]