Runge-Kutta Schemes in Control Constrained Optimal Control

Abstract

We consider an optimal control problem with control constraints satisfying conditions of smoothness and coercivity. By applying two Runge-Kutta schemes: one to the differential equation and a different one to the adjoint differential equation that is related to the maximum principle for optimal control, we show that the error of approximation taken with respect to the mesh spacing is of second order. This extends previous results where the same scheme was applied to the prime and to the adjoint equation. This extends previously known results where the same discretization scheme is applied to the primal and to the adjoint equation.