A pointwise projected gradient method applied to an optimal control problem

The aim of this work is to present a method for finding pointwise control approximations of an optimal control problem with control constraints. The method is oriented to practical applications of the gradient projection method. By applying Euler scheme to the state and costate equations we find a sequence of approximate values of the gradient. Approximate values of the control in the grid points are obtained by projecting on the set of control values. We define a sequence having an accumulation point that is at a distance C h 1 / 2 (in L 2 r metric) from the optimal control. Finally, numerical examples are given.