Hamiltonian-Based Algorithm for Optimal Control

Abstract: This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed controls and projects the final result into the space of ordinary controls. It is based on the descent direction from a given relaxed control towards a pointwise minimizer of the Hamiltonian. This direction comprises a form of gradient projection and for some systems, is argued to have computational advantages over direct gradient directions. The algorithm is shown to be applicable to a class of hybrid optimal control problems. The theoretical results, concerning convergence of the algorithm, are corroborated by simulation examples on switched-mode hybrid systems as well as on a problem of balancing transmission- and motion energy in a mobile robotic system.