A Property of an Autonomous Minimax Optimal Control Problem

摘要

A control system, scalar product of X = f(x,u), with cost functional ess sup T sub zero or = t or = T sub 1, G (x(-t), u(t)) is considered. For an optimal pair (X bar (scalar product), u bar (scalar product)) there is a maximum principle of the form eta (t) f(x bar (t), u bar (t)) = Max, where u is an element of Omega (t), eta (t)f(x bar (t), u). By means of this fact it is shown that eta (t)f(x bar (t), u bar (t)) is equal to a constant almost everywhere.