An extended functional equation as a necessary and sufficient optimality condition for a discrete, control problem with incomplete information

Abstract

For optimal control problems with parameters depending on the time, the extended Bellmanean functional equations are in general only sufficient optimality conditions. It is shown by examples that the optimal control problem may have a greater number of solutions than the functional equation of this problem. However, a sufficient condition of the equality of the solution sets of the optimal control problem and the functional equation is given on the basis of rigorous concavity, too.