Asymptotically nonexpansive mapping; Nonexpansive mapping; Implicit iterative sequence with errors for a finite family; Common fixed point; Opial condition; Demi-closed principle; Semi-compactness

Terminal-state tracking optimal control problems for linear parabolic equations are studied in this paper. The control objectives are to track a desired terminal state and the control is of the distributed type. Explicit solution formulae for the optimal control problems are derived in the form of eigen series. Pointwise-in-time L2 norm estimates for the optimal solutions are obtained and approximate controllability results are established. Exact controllability is shown when the target state vanishes on the boundary of the spatial domain. One-dimensional computational results are presented which illustrate the terminal-state tracking properties for the solutions expressed by the series formulae.  2005 Elsevier Inc. All rights reserved.