OPTIMAL BOUNDARY CONTROL OF THE WAVE EQUATION:

THE FINITE-TIME TURNPIKE PHENOMENON

MARTIN GUGAT

Communicated by Nicolae Cˆındea

It is well-known that vibrating strings can be steered to a position of rest in

finite time by suitably defined boundary control functions, if the time horizon is

sufficiently long. In optimal control problems, the desired terminal state is often

enforced by terminal conditions, that add an additional difficulty to the optimal

control problem. In this paper we present an optimal control problem for the

wave equation with a time-dependent weight in the objective function such that

for a sufficiently long time horizon, the optimal state reaches a position of rest in

finite time without prescribing a terminal constraint. This situation can be seen

as a realization of the finite-time turnpike phenomenon that has been studied

recently.