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In this paper, an instantaneous optimal control performance index for active control of structures under seismic excitation is analytically proposed. Absolute velocity and absolute displacement terms are implemented to the conventional state vector terms and eventually to the resulting performance index expression. The seismic response reduction effectiveness of the proposed performance index is compared with the linear quadratic regulator control (LQR). For numerical verification of the performance index, an eight-story shear building with a fully active tendon controller system under unidirectional earthquake is considered as the first example. For a more complex model, a three-dimensional tier building under the effect of bidirectional earthquakes is selected as second numerical example. Unidirectional near fault and bidirectional near fault earthquakes are used in the simulations. The control energy demand of each control method is also considered in the comparison. It is obtained from numerical simulations that the proposed performance index is as effective as LQR in attenuating structural vibrations. However, the resulting performance index does not require a priori knowledge of the seismic excitation like the LQR. The nonlinear Riccati matrix equation solution of the LQR is not required in the proposed performance index as well.

Absolute Instantaneous Optimal Control Performance Index for Active Vibration Control of Structures under Seismic Excitation