Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory.
The operations can be made commutative by an application of the covector mapping principle.
A number of interesting properties of a given problem can be derived by applying the Pontryagin's minimum principle or the Hamilton–Jacobi–Bellman equations.
[6] When an optimal control problem is discretized, the Ross–Fahroo lemma asserts that there is a fundamental loss of information.
[1][2][3] When the covector mapping principle is applied, it reveals the proper transformation for the adjoints.