TIME OPTIMAL CONTROL OF DISTRIBUTED PARAMETER SYSTEMS

In this paper, we consider the problem of finding the optimal control u（-） of the followingdistributed parameter system on a reflexive Banach space: ( dx（t）)/（dt）=Ax（t） + b(t, u（t）), u（t）∈U, x（0）=x, so that x（t） may hit the target Q（t） of the same space in the shortest possible time. When U is a setin another Banach space, is bounded and closed but not necessarity convex, the closure of the reach-able region R（t） for the above system is proved to be a convex set.Furthermore the necessaryand sufficient conditions for the maximum principle and a computing formula for the optimal timeto hold are derived. The boundary control problem for parabolic systems is discussed for applica-tion.