As　the　controller　parameter　adjustment　process　is　simplified　significantly　by　using　learning　algorithms,　the　studies　about　learning-based　control　attract　a　lot　of　interest　in　recent　years.　This　article　focuses　on　the　intelligent　servo　control　problem　using　learning　from　desired　demonstrations.　Compared　with　the　previous　studies　about　the　learning-based　servo　control,　a　control　policy　using　the　broad　learning　system　(BLS)　is　developed　and　first　applied　to　a　microrobotic　system,　since　the　advantages　of　the　BLS,　such　as　simple　structure　and　no-requirement　for　retraining　when　new　demos＇　data　is　provided.　Then,　the　Lyapunov　theory　is　skillfully　combined　with　the　complex　learning　algorithm　to　derive　the　controller　parameters＇　constraints.　Thus,　the　final　control　policy　not　only　can　obtain　the　movement　skills　of　the　desired　demonstrations　but　also　have　the　strong　ability　of　generalization　and　error　convergence.　Finally,　simulation　and　experimental　examples　verify　the　effectiveness　of　the　proposed　strategy　using　MATLAB　and　a　microswimmer　trajectory　tracking　system.