Covector mapping principle

The covector mapping principle is a special case of Riesz' representation theorem, which is a fundamental theorem in functional analysis.

The name was coined by Ross and coauthors,[1][2][3][4][5][6] It provides conditions under which dualization can be commuted with discretization in the case of computational optimal control.

An application of Pontryagin's minimum principle to Problem

represents the number of discrete points.

For convergence, it is necessary to prove that as In the 1960s Kalman and others[8] showed that solving Problem

In a series of papers starting in the late 1990s, Ross and Fahroo showed that one could arrive at a solution to Problem

The sequence of operations must be done carefully to ensure consistency and convergence.

The covector mapping principle asserts that a covector mapping theorem can be discovered to map the solutions of Problem