Response attenuation of seismically excited adjacent buildings connected by a MR damper is studied using semi-active LQR controller design. The modified Bouc–Wen model relating damper force to input voltage/states is considered. Thus, obtaining the input voltage to realize a desired control force is a non-trivial task. The desired control force is obtained using LQR control, and desired voltage predicted based on either a RNN model or a CVL. Results for the 5-storey and 3-storey interconnected buildings (B5–B3) are obtained in terms of peak and RMS responses. These are compared with passive-on control for which a constant saturation voltage is applied to the damper. Percentage reduction in maximum peak[RMS] response, when using LQR–CVL instead of passive on control, is 24[20] for interstorey drift, 18[23] for displacement, and 17[26] for accelerations. Corresponding further percentage reductions of 6[5], 5[5], and −5[4], and reductions in base shear, occur when considering LQR–RNN vis-á-vis LQR–CVL control. Peak accelerations for B5[B3] attenuate[increase] significantly, resulting in a re-distribution and reduction of base shear, when comparing semi-active versus passive-on control. Results show that connection of adjacent buildings using MR damper driven by a LQR–RNN controller provides a promising means of response attenuation.