In recent years, considerable attention has been paid to the development of theories and applications associated with structural vibration control. Integrating the nonlinear mapping ability with the dynamic evolution capability, diagonal recurrent neural network (DRNN) meets the needs of the demanding control requirements in increasingly complex dynamic systems because of its simple and recurrent architecture. This paper presents numerical studies of multiple degree-of-freedom (MDOF) structural vibration control based on the approach of the backpropagation algorithm to the DRNN control method. The controller’s stability and convergence and comparisons of the DRNN method with conventional control strategies are also examined. The numerical simulations show that the structural vibration responses of linear and nonlinear MDOF structures are reduced by between 78% and 86%, and between 52% and 80%, respectively, when they are subjected to El Centro, Kobe, Hachinohe, and Northridge earthquake processes. The numerical simulation shows that the DRNN method outperforms conventional control strategies, which include linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) (based on the acceleration feedback), and pole placement by between 20% and 30% in the case of linear MDOF structures. For nonlinear MDOF structures, in which the conventional controllers are ineffective, the DRNN controller is still effective. However, the level of reduction of the structural vibration response of nonlinear MDOF structures achievable is reduced by about 20% in comparison to the reductions achievable with linear MDOF structures.

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