Adaptive control of earthquake-excited nonlinear structures with real-time tracking on prescribed performance criteria

A model reference adaptive control method is proposed to suppress the nonlinear responses of earthquake-excited structures with the proposed implementation of performance tracking criteria. The model reference concept is adopted to propose a comprehensive framework for real-time tracking on prescribed performances, and a deterministic reference model is presented to explicitly represent the prior-designed structural performances. The tracking error and the time-varying adaptive control law are systematically presented and designed by using the backstepping theory and the Lyapunov stability analysis. Little prior or explicit knowledge of structural nonlinear behavior is considered for the proposed adaptive backstepping law. Two performance schemes, inspired by the classical linear quadratic regulator control theory and the unknown disturbance cancelation, are developed. Illustrative examples of a bilinear single-degree-of-freedom system and a seismically base-isolated benchmark building structure are employed with a detail illustration and discussion about the control performance of the proposed methodology. Finally, an additional parametric study on the issues of the actuator saturation, the optimum parameter selection, and the switching delay is presented and discussed.