Optimal Bounded Semi-Active Control of Hysteretic Systems with MR Damper

A bounded stochastic optimal semi-active control strategy for random excited hysteretic systems by using MR damper is proposed and illustrated by an example of a single degree-of-freedom hysteretic system. First, the dynamics of MR damper and the hysteretic force are expressed by using the Bouc-Wen model. Then, the system is converted into an equivalent nonlinear non-hysteretic stochastic system, from which the optimal bounded semi-active control law consisting of optimal unbounded control and bang-bang control is derived by using stochastic averaging method and stochastic dynamical programming principle. Finally, the response of optimally controlled system is predicted from solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.