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We present a numerical construction of an optimal control based feedback law for the stabilization of discrete time nonlinear control systems. The feedback is based on a recently developed numerical solution method for optimal control problems using set oriented and graph theoretic algorithms. We show how this method can be used to construct approximately optimal and stabilizing feedback laws and present an a posteriori error estimation technique for the adaptive generation of the underlying set oriented space discretization.doi:10.15495/epub_ubt_00005518 fatcat:vkahxxshebe3jnl6c4th6jvhni