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

In this paper, feedback laws for a class of infinite horizon control problems under state constraints are investigated. We provide a two-player game representation for such control problems assuming time-dependent dynamics and Lagrangian and the set constraints merely compact. Using viability results recently investigated for state constrained problems in an infinite horizon setting, we extend some known results for the linear-quadratic regulator problem to a class of control problems with nonlinear dynamics in the state and affine in the control. Feedback laws are obtained under suitable controllability assumptions.