Stable Controllers for Instantaneous Optimal Control

Recently, instantaneous optimal control algorithms were proposed and developed for applications to control of seismically 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. It is shown that the performance of the stable controllers presented herein are remarkable.