Hamiltonian (control theory)

In control theory, the Hamiltonian is a function that is central to optimal control problems. It is used in the formulation of the Hamiltonian control methods, particularly in dynamic programming and optimal control strategies, such as the Pontryagin's Maximum Principle. ### Definition of the Hamiltonian The Hamiltonian \( H \) is typically defined for a control system described by: - A set of state variables \( x(t) \) that represent the system's configuration at time \( t \).