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Necessary optimality conditions for switching control problems. (English) Zbl 1183.49020

Summary: We consider smooth and nonsmooth switching control problems. By applying Taylor incremental formula for the cost functional, we obtain a necessary optimality condition for the smooth case. Then by applying the Fréchet superdifferential and uniform upper subdifferentiability, we extend necessary condition to the nonsmooth switching control problems.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49J52 Nonsmooth analysis
49J15 Existence theories for optimal control problems involving ordinary differential equations
78M50 Optimization problems in optics and electromagnetic theory
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