This　paper　discusses　the　problem　of　time-varying　formation　control　for　multiple　spacecraft　while　achieving　H　∞　performance.　Firstly,　an　elaborate　formation　task　function　is　designed　by　using　estimator-based　null-space　based　behavioral　control　method,　and　a　predesigned　desired　velocity　is　calculated　for　each　spacecraft.　Then　by　employing　backstepping　technique　associated　with　the　universal　approximation　property　of　radial　basis　function　neural　networks　(RBFNN),　an　adaptive　H　∞　coordination　control　scheme　is　presented　to　drive　all　the　spacecraft　to　implement　the　time-varying　formation　task　in　switching　communication　graph.　Finally,　rigorous　theoretical　analysis　shows　that　the　proposed　algorithm　implements　the　time-varying　formation　task　successfully　with　H　∞　performance.　©　2018　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.