A bounded stochastic optimal semi-active control

A bounded stochastic optimal semi-active control strategy for magneto-rheological/electro-rheological (MR/ER) dampers is developed from the previously proposed strategy by considering the constraint of semi-active control forces. The control force is separated into a semi-active part and passive part incorporated in the uncontrolled system. The control system is converted into an averaged control system for energy processes by using the stochastic averaging method. The bounded and dynamic constraint of semi-active control forces and a performance index are formulated to constitute a bounded stochastic optimal semi-active control problem. Then the dynamical programming equation is established by applying the stochastic dynamical programming principle to the control problem. The bounded optimal semi-active control forces are obtained from solving this equation based on the variation method. A bounded optimal active control law given is implementable by MR/ER dampers. Finally, an example of controlled and stochastically excited nonlinear system is studied to illustrate the efficiency and chattering attenuation of the developed bounded control.