On the solution of some minimax problems

Abstract

In dynamic minimax and stochastic optimization problems frequently one is forced to use a suboptimal controller since the computation and implementation of the optimal controller based on dynamic programming is impractical in many cases. In this paper we study the performance of some suboptimal controllers in relation to the performance of the optimal feedback controller and the optimal open-loop controller. Attention is focused on some classes of, so called, open-loop-feed-back controllers. It is shown under quite general assumptions that these open-loop-feedback controllers perform at least as well as the optimal open-loop controller. The results are developed for general minimax problems with perfect and imperfect state information. In the latter case the open-loop-feedback controller mkes use of an estimator which is required to perform at least as well as a pure predictor in order for the results to hold. Some of the results presented have stochastic counterparts.

Keywords

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