A predictor-corrector method for dynamic programming

A bounded perturbation of the discrete dynamic programming functional equation arising from the Bolza problem yields a bounded change in its solution. This stability property encourages the development of approximation techniques for solving such equations. One such technique, involving the backward solution of an approximate functional equation as a prediction step followed by a forward reconstruction using true equations as a correction step, is then discussed. The errors arising out of such an approximation procedure are bounded. Numerical results are given, illustrating applicability to the optimal control of time-lag control processes.