QUADRATIC ORDER CONDITIONS FOR AN EXTENDED WEAK MINIMUM IN OPTIMAL CONTROL PROBLEMS WITH INTERMEDIATE AND MIXED CONSTRAINTS

摘要

We consider a general optimal control problem with intermediate and mixed constraints.Using a natural transformation (replication of the state and control variables), this problem is reduced to a standard optimal control problem with mixed constraints, which makes it possible to obtain quadratic order conditions for an "extended" weak minimum. The conditions obtained are applied to the problem of light refraction.