An effective computational design strategy for H ∞ vibration control of large structures with information constraints

In this paper, we present an effective computational strategy to design high-performance decentralized controllers with partial local-state information for vibration control of large building structures. Specifically, the building dynamical model is first decomposed into a set of approximate low-dimensional decoupled subsystems subject to the action of generalized disturbances, which include the effect of external physical disturbances, modeling approximation errors and mechanical subsystem interactions. Next, using the approximate decoupled subsystems, an overall structured state-feedback controller is obtained by designing a proper set of independent local controllers. The proposed computational strategy is applied to obtain two structured control systems for the seismic protection of a 35-story building: (i) a fully decentralized velocity-feedback controller with 35 interstory actuators that can be passively implemented by a set of viscous dampers, and (ii) a decentralized velocity-feedback controller with 15 interstory actuators, which can be implemented with a reduced set of collocated sensors and a system of five independent short-range communication networks. To assess the performance of the obtained structured controllers, the corresponding frequency and time responses are investigated and compared with the responses produced by optimal full-state H ∞ controllers. Moreover, to evaluate the effectiveness of the computational procedure, both structured and full-state controllers are designed for a proper set of buildings with different number of stories and the corresponding computation times are recorded and compared. The obtained results show that the computational cost of the proposed design methodology is remarkably low and also indicate that, despite the severe information constraints, the synthesized structured controllers are practically optimal.