In　this　letter,　an　adaptive　dynamic　programming　(ADP)　method　is　proposed　for　optimized　formation　control　of　second-order　linear　systems.　The　method　exploits　an　actor-critic　architecture,　where　an　actor　component　is　used　to　learn　the　optimal　formation　controller,　and　a　critic　component　is　used　to　learn　the　optimal　value　function.　Generally,　ADP　requires　a　priori　knowledge　of　persistence　of　excitation　(PE)　to　guarantee　the　stability　of　the　control　system.　However,　the　PE　condition　is　hard　to　verify　during　the　learning　process　and　in　practical　applications.　To　this　end,　this　letter　redesigns　the　updating　laws　of　the　actor　and　critic　components　to　ensure　that　the　Bellman　residual　error　can　eventually　approach　to　zero,　and　the　stability　of　the　control　system　can　be　guaranteed　without　introducing　the　PE　and　additional　constraints.　By　using　Lyapunov　stability　analysis,　we　prove　that　the　proposed　optimized　formation　scheme　can　achieve　the　desired　optimizing　performance.　Finally,　a　simulation　example　is　given　to　demonstrate　the　effectiveness　of　the　proposed　method.　©　2017　IEEE.