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Optimal switching for ordinary differential equations. (English) Zbl 0641.49017
The authors consider some deterministic control problems where switching between various controls induces a given cost. Using the known relations between deterministic control problems, dynamic programming arguments, and viscosity solutions of Hamilton-Jacobi equations, the authors study this problem and, in particular, prove the uniqueness of the value functions as viscosity solutions of the associated system of first-order partial differential equations.

MSC:
49L99 Hamilton-Jacobi theories
35F30 Boundary value problems for nonlinear first-order PDEs
49L20 Dynamic programming in optimal control and differential games
35D05 Existence of generalized solutions of PDE (MSC2000)
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