Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)
Marcus Wagner (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands (, , ) in presence of a convex control restriction. The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image...