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Currently, in discrete-time part, Hamiltonian is defined as H = L + lambda f, which is quite common in control theory texts. But in the continuous-time part, it is defined as H = lambda f - L, which is perhaps a bit less common, but the motivation for its introduction was that it mimics the development of the concept in physics (recall H = p y' - L). It is perhaps disputable if this desire to show how the control theoretic concepts are related to the classical concepts in physics outweighs the notational confusion caused by using two definitions of Hamiltoninan in a single course. Perhaps it would be better to unify it so that students do not have to bother and can live with just H = L + lambda f.
The text was updated successfully, but these errors were encountered:
Currently, in discrete-time part, Hamiltonian is defined as H = L + lambda f, which is quite common in control theory texts. But in the continuous-time part, it is defined as H = lambda f - L, which is perhaps a bit less common, but the motivation for its introduction was that it mimics the development of the concept in physics (recall H = p y' - L). It is perhaps disputable if this desire to show how the control theoretic concepts are related to the classical concepts in physics outweighs the notational confusion caused by using two definitions of Hamiltoninan in a single course. Perhaps it would be better to unify it so that students do not have to bother and can live with just H = L + lambda f.
The text was updated successfully, but these errors were encountered: