Using shifted Legendre polynomials for solving optimal control problem of an HIV infection treatment control model

In this paper we introduce a numerical technique based on Legendre polynomials for solving of nonlinear optimal control problems, where this approach is used for solving optimal control problem of an HIV infection treatment control model. In this paper, first by using healthy cells CD4+T (T), infected cells CD4+T (I), viral load (V) and also by using a drug inhibitor of reverse polygraph as a control function, a control model is presented for treatment of HIV infection. A cost function to minimize the cost of drug during the treatment is defined as well. To find the pair of trajectory and control of such nonlinear optimal control problem, we used shifted Legendre polynomials to approximate optimal pair of trajectory and control.