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The vibration control system of a building structure under a strong earthquake can be regarded as a large complex system composed of a series of overlapping subsystems. In this paper, the overlapping decentralized control of building structure vibration under seismic excitation is studied. Combining the overlapping decentralized control method, H∞ control algorithm, and passive fault-tolerant control method, a passive fault-tolerant overlapping decentralized control method based on the H∞ control algorithm is proposed. In this paper, the design of robust H∞ finite frequency passive fault-tolerant static output feedback controller for each subsystem is studied. The fault matrix of the subcontroller is expressed by a polyhedron with finite vertices. In order to reduce the influence of external disturbance on the controlled output, the finite frequency H∞ control is adopted and the Hamiltonian matrix is avoided. In this paper, the passive fault-tolerant overlapping decentralized control method based on H∞ control algorithm is applied to the vibration control system of the four-story building structure excited by the Hachinohe seismic wave. One drive is set on each layer of the structure, and a total of four drives are set. Select the driver fault factor of 0.5 or 1 and the frequency band [0.3, 8] Hz. The overlapping decentralized control scheme and 16 fault-tolerant fault matrices are designed, and the numerical comparison results are given. The results show that both overlapping decentralized control strategy and multioverlapping decentralized control strategy have achieved good control results. Due to the different number of subsystems and overlapping information, the overlapping decentralized control scheme increases the flexibility of controller setting and reduces the computational cost.

Overlapping Decentralized Control Strategies of Building Structure Vibration Based on Fault-Tolerant Control under Seismic Excitation