Hamiltonian (Control Theory)

In optimal control theory, the Hamiltonian is a function used to solve problems that ask for the best way to steer a dynamical system over a period of time, built as an instantaneous version of the Lagrangian expression that the overall problem is trying to optimize. It was developed by the mathematician Lev Pontryagin as part of his maximum principle, which established that a necessary condition for a control to be optimal is that it must optimize this Hamiltonian at every instant. Although it takes its name and some of its form from the Hamiltonian of classical mechanics, the control-theory Hamiltonian is a distinct construction: it combines an objective function with the system's state equations, playing a role similar to a Lagrange multiplier in ordinary optimization, except that its multipliers, called costate variables, are allowed to vary over time, which is what makes it suited to dynamic optimization problems in economics, engineering, and control systems. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/