The　flexible　vibration　is　generated　after　all-flexible　space　manipulator　capturing　a　satellite,　and　the　collision　leads　to　unsteadiness　of　system.　For　the　unstable　composite　system,　the　self-turning　control　algorithm　based　on　hybrid　trajectory　is　designed　in　this　paper.　The　theory　of　gradient　descent　is　used　for　parameter　adaptive　rate　design　to　realize　the　real　time　adjustment　of　the　PID　control　parameters.　A　supervised　controller　is　designed　through　Lyapunov　function　to　generate　the　stability　and　H　∞　tracking　characteristic　of　the　system.　The　hybrid　trajectory　is　generated　based　on　the　concept　of　virtual　force,　which　is　used　to　accomplish　integrated　control　of　joint　movement　and　vibration　abatement.　At　last,　the　effectiveness　of　the　proposed　control　scheme　is　demonstrated　through　numerical　simulation.　©　2018,　The　Editorial　Board　of　Journal　of　System　Simulation.　All　right　reserved.