INSTANTANEOUS OPTIMAL CONTROL FOR SEISMIC ANALYSIS OF NON-LINEAR STRUCTURES

In this paper, an effective active control algorithm is developed for the vibration control of non-linear structural systems subjected to earthquake excitation. It is an attempt to include the non-linear characteristics of the structural behaviour throughout the entire analysis (design and validation), accounting for the eventual cumulative structural damage and energy dissipation. This is a very important factor since, in current design practice, structures are assumed to behave nonlinearly when subjected to strong ground motion. The proposed algorithm focusses on the instantaneous optimal control approach for the development of the control algorithm where the nonlinearities are brought into the analysis through a non-linear state vector and a non-linear open loop term. A performance index that is quadratic in the control force and in the non-linear states and is subjected to a non-linear constraint equation, is minimised at every time step. The effectiveness of the proposed non-linear instantaneous optimal control (NIOC) strategy is critically evaluated in comparison with currently available active control techniques. Numerical simulation results indicate that the proposed approach provides a significant reduction of the peak response quantities, such as maximum response deformation, maximum response acceleration, ductility of the system, associated with a reduced maximum control force.