The　adaptive　optimal　feedback　stabilization　is　investigated　in　this　article　for　discounted　guaranteed　cost　control　of　uncertain　nonlinear　dynamical　systems.　Via　theoretical　analysis,　the　guaranteed　cost　control　problem　involving　a　discounted　utility　is　transformed　to　the　design　of　a　discounted　optimal　control　policy　for　the　nominal　plant.　The　size　of　the　neighborhood　with　respect　to　uniformly　ultimately　bounded　stability　is　discussed.　Then,　for　deriving　the　approximate　optimal　solution　of　the　modified　Hamilton-Jacobi-Bellman　equation,　an　improved　self-learning　algorithm　under　the　framework　of　adaptive　critic　designs　is　established.　It　facilitates　the　neuro-optimal　control　implementation　without　an　additional　requirement　of　the　initial　admissible　condition.　The　simulation　verification　toward　several　dynamics　is　provided,　involving　the　F16　aircraft　plant,　in　order　to　illustrate　the　effectiveness　of　the　discounted　guaranteed　cost　control　method.