A new stochastic optimal control strategy for hysteretic MR dampers

A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic behavior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then Itô stochastic differential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled diffusion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlinear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and effectiveness of the proposed control strategy.