Multipoint instantaneous optimal control of structures

Exact optimal classical closed-open loop control is not achievable for the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. In this study, a multipoint instantaneous performance index is proposed for active control of earthquake excited structures. Minimizing the proposed index with the aid of the Lagrange multipliers method results in a simple closed-loop control law which takes into account the near-future states of the structure not explicitly, but through their weighting matrices. The resulting control algorithm does not need the future knowledge of earthquake and also does not require the solution of the nonlinear matrix Riccati equation which increase the computer solution time. Effectiveness of the proposed algorithm is demonstrated numerically in the case of real-time control of a three-storey structure subject to earthquake excitation. Numerical results show that the proposed control results in significant decrease in the real time response and the base shear forces of the structure when compared to the uncontrolled case.