Bang-Bang Control Applied on an HIV-1 within host Model

Local controllability analysis of an HIV infection model on which three controls are effective is investigated, the optimal control policy to minimize the number of infected cells, the number of free virus and maximize the number of healthy cells for each control separately, then for all controls applied at once is formulated and solved as an optimal bang-bang control problem (command all or nothing). Numerical examples are given to illustrate the obtained results.