Some Extensions to Optimal Control Problems

Optimal control problems often arise in system engineering. The objective of optimal control is to find, in open loop control, optimal manipulated variable time profiles for a dynamic system that optimize a given performance index. In this paper, the geometrical extensions for solving optimal control problems are summarized in a way that is a good reflection of the Pontryagin minimum principle.

Keywords:

Hamiltonian system , Optimal control problem , Pontryagin minimum principle , Reduced system , Symmetry