Simultaneous optimization of structural and control systems of a SDOF building with a linear quadratic regulator controller aiming at performance-based design

A simultaneous optimization procedure is formulated in order to match desired performances of a building. Design variables of structural and control parts of a building with a linear quadratic regulator (LQR) controller are optimized simultaneously. Thenatural period and the damping factor of the LQR-controlled system are calculated based on eigenvalue analysis. Design responsespectra are used to consider input ground motion and to calculate the maximum control force as well as maximum responses. As anexample, this optimization procedure is applied to the seismic strengthening of a traditional wooden building by considering reduction of its displacement and acceleration responses.