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The sufficient conditions for continuous epsilon-optimal feedbacks in control problems with a terminal cost

2011    Dzhafarov, V. Ya.; Subbotina, N. N.

The existence of continuous positional strategies of epsilon-optimal feedback is proved for linear optimal control problems with a convex terminal cost. These continuous feedbacks are determined from Bellman's equation in epsilon-perturbed control problems with an integral-terminal cost and a smooth value function. An example is given in which an epsilon-optimal continuous feedback does not exist. It is shown that the point limit of the epsilon-optimal feedbacks when epsilon -> 0 determines the optimal feedback, that is, a positional strategy and, possibly, a discontinuous strategy. (C) 2011 Elsevier Ltd. All rights reserved.