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In this paper we give feedback laws for a class of parametrized infinitehorizon control problems under state constraints. We provide a two-playerrepresentation assuming time dependent dynamics and Lagrangian and the setconstraints merely compact. Using viability results recently investigated forinfinite horizon settings in presence of state constraints, we extend someknown results for the linear-quadratic regulator problem to control problemswith nonlinear dynamics in the state and affine in the control. Feedback lawsare obtained under suitable controllability assumptions.

A two-player game representation for a class of infinite horizon control problems under state constraints