Properties of Hamiltonian in free final multitime problems

Abstract

"In single-time autonomous optimal control problems, the Hamiltonian is constant on optimal evolution. In addition, if the final time is free, the optimal Hamiltonian vanishes on the hole interval of evolution. The purpose of this paper is to extend some of these results to the case of multitime optimal control. The original results include: anti-trace problem, weak and strong multitime maximum principles, multitime-invariant systems and change rate of Hamiltonian, the variational derivative of volume integral, necessary conditions for a free final multitime expressed with the Hamiltonian tensor that replaces the energy-momentum tensor, change of variables in multitime optimal control, conversion of free final multitime problems to problems over fixed interval."