RT Monograph SR 00 A1 Frankowska, H. T1 How Set-Valued Maps Pop Up in Control Theory YR 1996 FD 1996-12 SP 17 AB We describe four instances where set-valued maps intervene either as a tool to state the results or as a technical tool of the proof. The paper is composed of four rather independent sections: (1) Set-Valued Optimal Synthesis and Differential Inclusions; (2) Viability Kernel; (3) Nonsmooth Solutions to Hamilton-Jacobi-Bellman Equations; (4) Interior and Boundary of Reachable Sets. PB WP-96-116 PP IIASA, Laxenburg, Austria AV Published LK https://pure.iiasa.ac.at/id/eprint/4911/