Real-time model predictive control of structures under earthquakes

This paper presents a general formulation of the model predictive control (MPC) scheme for controlling in real time the response of structures under earthquakes. The MPC scheme is based on an explicit use of a prediction model of the system response to obtain the control actions by minimizing an objective function. Optimization objectives in MPC include minimization of the difference between the predicted and desired response trajectories, and the control effort subjected to certain constraints. In this study, the prediction model is formulated using both feedforward (FF) and feedback (FB) components to increase the effectiveness of the MPC scheme. The FF loop in the prediction model is formulated using two types of input. First, it is designed using the established Kanai–Tajimi‐type model to represent the earthquake input. Second, a real‐time FF loop is introduced using an auto‐regressive (AR) model for earthquake ground motion which is constantly updated using real‐time on‐line observations. The real‐time FF loop certainly promises to add predictive and adaptive features to the control actions to account for any unusual features in the ground motion. The structural response with and without the FF and FB loops are compared. Examples are used to demonstrate the efficacy of the proposed methodology. These examples show that the MPC‐based controller is effective in reducing the structural response under different earthquakes which contain distinct features in their spectral and non‐stationary descriptions. The performance of the MPC scheme is then compared to H2 control strategies for different time horizons. The effectiveness of MPC is shown to be equivalent to the optimal control. This paper lays a foundation for capturing the main strengths of MPC, i.e. computational expediency, real‐time application, intrinsic compensation for time delays, treatment of constraints and potential for future extensions in structural control. Copyright © 2001 John Wiley & Sons, Ltd.