Hamiltonian (control Theory)
The Hamiltonian of optimal control theory was developed by L. S. Pontryagin as part of his minimum principle. It was inspired by, but is distinct from, the Hamiltonian of classical mechanics. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to minimize the Hamiltonian. For details see Pontryagin's minimum principle.
Read more about Hamiltonian (control Theory): Notation and Problem Statement, Definition of The Hamiltonian, The Hamiltonian in Discrete Time, The Hamiltonian of Control Compared To The Hamiltonian of Mechanics