How Set-Valued Maps Pop Up in Control Theory

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

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