A gradient projection method for solving nonlinear optimal control problems with time-varying delays

An effective numerical method using gradient projection is proposed for solving an optimal control problems that involve time-varying delays in control and state variables. First, a variational inequality is established as necessary conditions. The main idea in variational inequality is to compute the gradient of the objective functional, taking into account time-dependent delays in control and state variables. Then, an iterative scheme utilizing a projection operator is presented, followed by a convergence analysis of the method for a coercive objective functional. At the end, several examples are provided to illustrate that the theoretical finding is efficient.

کلیدواژه ها:

Nonlinear optimal control problems ، Time delay systems ، variational inequality ، Time-varying delay ، Gradient projection method