In this study, a real-time adaptive control framework with a two-layer architecture is proposed for mitigating the seismic responses of tall buildings exhibiting nonlinear behavior. The proposed structure consists of a baseline adaptive controller and a supervisory hyper-adaptive layer that adjusts the adaptation parameters online using a filtered extremum-seeking algorithm. The baseline controller generates the control signal based on output-feedback adaptive laws, while the hyper-adaptive layer determines the direction and rate of updating the controller gains by estimating the instantaneous approximate gradient of the performance function. This mechanism, without relying on an accurate structural model or requiring prior identification, enables dynamic adaptation to sudden or gradual changes in system dynamics, nonlinear behaviors such as hysteresis, and structural uncertainties. The iRT-SAC framework is designed to guarantee boundedness of the adaptive parameters and closed-loop stability under challenging operating conditions, while minimizing the need for manual retuning or remodeling. To evaluate its performance, the proposed method is implemented on the 20-story benchmark structure of Ohtori et al. and compared with reference controllers including LQG, H_∞, fuzzy control, and Clipped-LQG. The results demonstrate approximately a 60% reduction in interstory drift and preservation of closed-loop stability in the presence of severe uncertainties and nonlinear behavior. Overall, iRT-SAC represents a model-light, robust, and practically deployable adaptive approach for tall and complex structures.