Admissible variations for optimal control problems with mixed constraints
Por:
Rosenblueth J.F.
Publicada:
1 ene 2005
Resumen:
The purpose of this paper is twofold. First, to establish second order necessary conditions for a fixed-endpoint control problem of Lagrange posed over piecewise continuous controls and involving mixed equality constraints. This yields the introduction of a set of admissible variations where the second variation is nonnegative together with a corresponding notion of a normal extremal. Second, to show how these conditions can be derived by means of a uniform implicit function theorem applied to the classical necessary conditions for a control problem without constraints. An example of an optimal control problem involving mixed constraints illustrates the usefulness of these results.