Suboptimality Theorems in Optimal Control
Necessary optimality conditions are statements about nothing if an optimal solution does not exist. Therefore it makes sense to embed such conditions in a general framework which excludes the possibility of empty (even false) assertions all the more as the assumptions for existence results are much stronger than those for necessary optimality conditions. We call such a framework suboptimality theorem and exemplify it by a simple problem of optimal control. Furthermore, we investigate the set of suboptimal solutions by means of a new theorem about the approximation of measurable by simple functions.
KeywordsOptimal Control Problem Existence Result Simple Function Optimal Control Theory Suboptimal Solution
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