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:
“The preservation of life seems to be rather a slogan than a genuine goal of the anti-abortion forces; what they want is control. Control over behavior: power over women. Women in the anti-choice movement want to share in male power over women, and do so by denying their own womanhood, their own rights and responsibilities.”
—Ursula K. Le Guin (b. 1929)
“No method nor discipline can supersede the necessity of being forever on the alert. What is a course of history or philosophy, or poetry, no matter how well selected, or the best society, or the most admirable routine of life, compared with the discipline of looking always at what is to be seen? Will you be a reader, a student merely, or a seer? Read your fate, see what is before you, and walk on into futurity.”
—Henry David Thoreau (1817–1862)
“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)