Instantaneous optimal control for linear, nonlinear and hysteretic structures: Stable controllers

Recently, instantaneous optimal control algorithms have been proposed and developed for applications to control of seismic-excited linear, nonlinear and hysteretic structural systems. In particular, these control algorithms are suitable for aseismic hybrid control systems for which the linear quadratic optimal control theory is not applicable. Within the framework of instantaneous optimal control, the weighting matrix Q should be assigned to guarantee the stability of the controlled structure. A systematic way of assigning the weighting matrix by use of the Lyapunov direct method is investigated. Based on the Lyapunov method, several possible choices for the weighting matrix are presented, and their control performances are examined and compared for active and hybrid control systems under seismic loads. For the particular structures considered, the simplest choice for the Q matrix seems to result in a good performance.