On the maximum principle for time-optimal controls for a class of distributed-boundary control problems

In this note, we present the necessary conditions of optimality for time-optimal controls for a class of distributed-boundary control problems in general Banach spaces using the semigroup theory. Theorem 3.1 is based on a recent general maximum principle due to Barbu (Ref. 1), which was proved for strictly convex reflexive Banach spaces. Theorem 3.2 generalizes this result (for time-optimal control problems) by lifting the assumption.This work was supported by the National Science and Engineering Council of Canada under Grant No. 7109.