The use of seismic control systems in building structures requires simultaneous attention to uncertainties in model parameters, measurement noises, faults on sensors and dampers, and earthquake input. The present study suggests a procedure to resolve the complications of these issues in semi-active control of building structures. To this end, the effects of faults on sensors and dampers are decoupled by using transfer matrices. The sensor fault and the structure's state are estimated by a dynamic neural network (DNN)-based observer. Later, parametric uncertainty in the structure's model and fault on dampers are atoned by an adaptive controller that guarantees the stability of the system during an earthquake. In this controller, DNN is used to concurrently identify and compensate dampers' faults. The effectiveness of the proposed method was confirmed by numerical simulation of a three-story structure with magneto-rheological dampers.