On Constructive Extractability of Measurable Selectors of Set-Valued Maps

This article investigates the possibility of constructive extraction of measurable selector from set-valued maps, which may commonly arise in viability theory, optimal control, discontinuous systems, etc. For instance, existence of solutions to certain differential inclusions often requires iterative extraction of measurable selectors. Next, optimal controls are in general nonunique which naturally leads to an optimal set-valued function. Finally, a viable control law can be seen, in general, as a selector. It is known that selector theorems are nonconstructive, and so selectors cannot always be extracted. In this article, we analyze under which particular conditions selectors are constructively extractable. An algorithm is derived from the theorem, and applied in a computational study with a three-wheel robot model.