Hamiltonian (control theory)

The Hamiltonian in the theory of optimal control developed by LS Pontryagin maximum principle as part of his. It is similar to the Hamiltonian mechanics, but differs from it. Pontrjagin showed that a necessary condition for the release of an optimal control problem is that the selected control must minimize the Hamiltonian.

Notation and problem definition

A controller should be chosen so that the following objective function is minimized

Where the state of the system describes which, according to the differential equations

Developed, and must satisfy the following restrictions control

Furthermore, is an arbitrary function of the target state after time, as well as the Lagrangian.

Definition of the Hamiltonian

Where the Lagrange multipliers whose components describe the adjoint states.