Discretization of elliptic control problems with time dependent parameters (Q1007364)

The authors consider linear-quadratic problems of optimal control with an elliptic state equation and control constraints of the form \[ \min J(z,u)={1\over 2}\int^T_0 |z(t)- z_d(t)|^2+ u(t)^TR(t)u(t) \] \[ \text{s.t.}\quad -(P(t)z(t)')'+ A(t)z(t)= B(t)u(t)+ e(t)\quad\text{for a.a. }t\in [0,T], \] \[ z(0)= z(T)= 0, \] \[ a\leq u(t)\leq b\quad\text{for a.a. }t\in [0,T]. \] For a discretization of the state equation by the method of finite differences and a piecewise approximation of the control an error estimation for the solution of the discrete problem are developed. Some numerical examples are given.