In　this　paper,　an　optimized　leader-follower　formation　control　for　second-order　linear　multi-agent　systems　using　the　actor-critic　reinforcement　learning　is　proposed.　An　optimal　control　problem　is　formulated　and　solved　using　a　combined　actor-　critic　reinforcement　learning　and　fuzzy　logic　systems(FLSs)　approximator.　Actor　FLSs　are　constructed　for　performing　control　behavior　and　critic　FLSs　are　responsible　for　evaluating　the　control　effectiveness,　respectively.　Through　theoretical　analysis,　we　show　that　the　desired　optimal　performance　can　be　achieved.　Finally,　simulation　examples　are　given　to　demonstrate　the　effectiveness　of　the　proposed　method.　©　2020　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.