The Hamiltonian of Control Compared To The Hamiltonian of Mechanics
William Rowan Hamilton defined the Hamiltonian as a function of three variables:
where is defined implicitly by
Hamilton then formulated his equations as
In contrast the Hamiltonian of control theory (as defined by Pontryagin) is a function of 4 variables
and the associated conditions for a maximum are
This difference is somewhat confusing, nevertheless a specific problem, such as the Brachystochrone problem, can be solved by either method. For details, see the article by Sussmann and Willems.
Read more about this topic: Hamiltonian (control Theory)
Famous quotes containing the words control, compared and/or mechanics:
“If the technology cannot shoulder the entire burden of strategic change, it nevertheless can set into motion a series of dynamics that present an important challenge to imperative control and the industrial division of labor. The more blurred the distinction between what workers know and what managers know, the more fragile and pointless any traditional relationships of domination and subordination between them will become.”
—Shoshana Zuboff (b. 1951)
“What’s breaking into a bank compared with founding a bank?”
—Bertolt Brecht (1898–1956)
“the moderate Aristotelian city
Of darning and the Eight-Fifteen, where Euclid’s geometry
And Newton’s mechanics would account for our experience,
And the kitchen table exists because I scrub it.”
—W.H. (Wystan Hugh)