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- W2334872262 abstract "We consider state constrained optimal control problems in which the cost to minimize comprises an $L^infty$ functional, i.e. the maximum of a running cost along the trajectories. In absence of state constraints, a new approach has been suggested by a recent paper [9]. The main purpose of the present paper is to extend this approach and the related results to state constrained $L^infty$ optimal control problems. More precisely, using the $(L^infty, L^1)$-duality, the reference optimal control problem can be seen as a <em> static differential game</em>, in which an extra variable is introduced and plays the role of an opponent player who wants to <em> maximize</em> the cost. Under appropriate assumptions and employing suitable Filippov's type results, this static game turns out to be equivalent to the corresponding <em> dynamic differential game</em>, whose (upper) value function is the unique viscosity solution to a <em> constrained boundary value problem</em>, which involves a Hamilton-Jacobi equation with a <em> continuous</em> Hamiltonian." @default.
- W2334872262 created "2016-06-24" @default.
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- W2334872262 date "2015-01-01" @default.
- W2334872262 modified "2023-09-25" @default.
- W2334872262 title "State constrained $L^infty$ optimal control problems interpreted as differential games" @default.
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- W2334872262 doi "https://doi.org/10.3934/dcds.2015.35.3989" @default.
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