A sequential quadratic Hamiltonian scheme to compute optimal relaxed controls

A new sequential quadratic Hamiltonian method for computing optimal relaxed controls a class of control problems governed by ordinary differential equations is presented. This iterative approach based on the characterisation means Pontryagin maximum principle in framework Young measures, and it belongs to family successive approximations schemes. The ability proposed optimisation solve with regular controls, including cases oscillations concentration effects, demonstrated results numerical experiments. In all cases, scheme appears robust efficient, agreement convergence theoretical investigation presented this paper.