Exact minimum-time control of a distributed system using a traveling wave formulation

In this paper, the minimum-time control problem for rest-to-rest translation of a one-dimensional second-order distributed parameter system by means of two bounded control inputs at the ends is solved. A traveling wave formulation allows the problem to be solved exactly, i.e., without modal truncation. It is found that the minimum-time control is not bang-bang, as it is for systems with a finite number of degrees of freedom. Rather, it is bang-off-bang, where a period of control inactivity in the middle of the control time interval is required for synchronization with waves propagated through the system.This research was supported in part by AFOSR Grant No. AFOSR-90-0297. The helpful suggestions of the referees are gratefully acknowledged.