In　order　to　enhance　the　control　performance　of　a　self-sensing　magnetorheological　damper　(SMRD),　an　inverse　dynamics-based　collocated　linear-quadratic-Gaussian　(LQG)　control　strategy　(i-LQG)　was　proposed.　Control-oriented　forward　and　inverse　dynamic　models　of　the　SMRD　were　developed　by　employing　a　Bayesian　NARX　(nonlinear　autoregressive　with　exogenous　inputs)　network　technique　to　represent　its　nonlinear　dynamics.　The　dynamic　models　were　further　incorporated　into　the　LQG　control　loop　to　compensate　for　the　hysteretic　nonlinearity　of　the　SMRD　and　to　implement　semi-active　damping-force　tracking　control.　Experiments　were　conducted　to　compare　the　real-time　force　tracking　performance　when　the　SMRD　was　controlled　by　the　i-LQG　control　and　the　Heaviside　step　function-based　LQG　(H-LQG)　control,　respectively.　Results　show　that　the　i-LQG　control　commands　continuously　varying　voltage　to　enhance　the　real-time　SMRD　damping-force　tracking　with　a　50%　reduction　of　the　force　tracking　error　beyond　the　H-LQG　control.　The　structural　damping　with　the　i-LQG　control　is　increased　by　11%　compared　with　that　with　the　H-LQG　control,　which　verifies　that　the　proposed　i-LQG　control　is　able　to　realize　more　efficient　semi-active　structural　control　performance.　©　2017,　Zhejiang　University　Press.　All　right　reserved.