Feedback approximation of the minimum energy control for linear infinite-dimensional systems with zero terminal state

The paper studies the minimum energy control problem for linear infinite-dimensional systems with an unbounded input operator and zero terminal state. This problem is approximated by the minimum energy control problem with a small terminal state for which the solution is derived in feedback form. The operators which comprise the feedback are described in terms of differential relations which, depending on circumstances, involve Liapunov or Riccati differential equations. A detailed example illustrates how the general results apply to the wave equation with control in Dirichlet boundary condition.This work was supported by the Polish Ministry of National Education under Grant DNS-T/02/097/90-2.